OPTIMIZATION OF THE GEOMETRY AND MATERIAL OF SOLAR WATER HEATERS

A THESIS SUBMITTED TO THE GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES OF THE MIDDLE EAST TECHNICAL UNIVERSITY BY

RUKEN Z LAN

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN THE DEPARTMENT OF PHYSICS

SEPTEMBER 2001 (The latest pre-submission version)

Approval of the Graduate School of Natural and Applied Sciences.

Prof. Dr. Tayfur ÖZTÜRK Director I certify that this thesis satisfies all the requirements as a thesis for the degree of Master of Science. Prof. Dr. Sinan B L KMEN Head of Department This is to certify that we have read this thesis and that in our opinion it’s fully, in scope and quality, as a thesis for the degree of Master of Science.

Prof. Dr. Ahmet ECEV T Supervisor

Prof. Dr. Ahmet ECEV T Prof. Dr. Demir NAN Prof. Dr. Faruk ARINÇ Prof. Dr. nci GÖKMEN Prof. Dr. Bülent G. AKINO LU

ii

ABSTRACT

OPTIMIZATION OF THE GEOMETRY AND MATERIAL OF SOLAR WATER HEATERS

Z LAN, Ruken M.Sc. Department of Physics Supervisor: Prof. Dr. Ahmet ECEV T

September 2001, 168 pages

This study includes three parts; optimization of the geometry of absorber plate for flat plate collectors, construction of new absorber plate and efficiency tests of collectors. The new absorber plate, which is economic and resembling the commercially available absorber plate has been built by hot deep galvanization and by utilization of point welding. Before building the components of the system, some of the geometrical parameters, which influence the performance, have been optimized. Time constant and thermal efficiency of the constructed absorber plate has been measured. A new type of efficient and cheap absorber plate, which is made up of galvanized iron was constructed and its efficiency and price were determined together with that of three commercially available collectors constructed in iii

Turkey, absorber plates of which are made up of aluminum and copper ( STEK Aluminum and Copper, DA SAN -Copper). Time constants of the tested collectors are determined to be 137 seconds for STEK Al, 75 seconds for STEK Cu, 95 seconds for DA SAN and 198 seconds for galvanized iron collector. For STEK’s aluminum collector the y-axis intercept of the efficiency curve is 0.90, for STEK’s copper collector it is 0.66; for DA SAN’s copper it is 0.81 and for the collector that has galvanized iron absorber plate it is 0.82, which is increased up to 0.83 after new optimization. The price of the constructed absorber plate was DM 43, after new optimization it is increased to DM 53. For STEK’s aluminum collector it is DM 100, for STEK’s copper collector it is DM 60 and for DA SAN’s copper collector it is DM 100. Keywords: Optimization, Flat Plate Collectors, Solar Water Heaters, Galvanized Iron Absorber Plate, Point Welding and Efficiency of Flat Plate Collectors, Efficiency Test Methods.

iv

ÖZ

GÜNE L SU ISITICILARININ GEOMETR S N N VE KULLANILAN MALZEMES N N OPT M ZASYONU

Z LAN, Ruken Yüksek Lisans, Fizik Bölümü Danı man: Prof. Dr. Ahmet ECEV T

Eylül 2001, 168 sayfa

Bu çalı ma üç bölümden olu maktadır; güne toplaçları için yutucu plakanın geometrik optimizasyonu, yeni bir yutucu plaka üretilmesi ve verim testleri.

Ekonomik ve piyasadaki toplaçlara yakın verimli, yeni yutucu plaka, demirin daldırma galvanizlenmesi ve punta kaynak kullanımı ile yapılmı tır. Plaka planlama a amasında verimi etkileyen önemli geometrik parametreler verimsel ve fiyatsal açıdan optimize edilmi tir. Üretilen toplacın verim ve zaman sabitleri ölçülmü tür. Bu toplacın verimi,

STEK firmasının bakır ve alüminyum ve

DA SAN firmasının bakır yutucu plakalı toplaçların verimleri test edilmi ve birbirleri ile fiyat ve verim açısından kıyaslanmı tır.

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Test edilen toplaçların tespit edilen zaman sabitleri STEK Al için 137 saniye, STEK bakır için 75 saniye, DA SAN bakır için 95 saniye, galvaniz kaplamalı demir yutucu plâkalı toplaç için 198 saniye olarak bulunmu tur. Toplaçlar için verim grafiklerindeki y-ekseninin kesim noktaları, STEK alüminyum için 0.90, STEK bakır için 0.66, DA SAN bakır için 0.81, ve yeni üretilen toplaç için 0.82 ve yapılan son optimizasyondan sonra 0.83’e çıkmı tır. Üretilen yutucu plâkanın mal olu

fiyatı 43 Alman Markı, son

optimizasyondan sonra 53 Alman Markı, DA SAN bakır için 100 Alman Markı, STEK alüminyum toplaç için 100 Alman Markı ve STEK bakır toplaç için 60 Alman Markı’dır. Anahtar Kelimeler : Optimizasyon, Düzlemsel Toplaçlar, Güne li Su Isıtıcıları, Galvanizli Demirden Yapılan Yutucu Yüzey, Punta Kaynak, Düzlemsel Toplaçların Verimleri, Verim Test Metotları.

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TO ALL THE PEOPLE WHO BELIEVES IN SOLIDARITY, WHO IS AGAINST ALL THE DISCRIMINATIONS AND IN PEACE WITH THE WORLD AND HIMSELF/HERSELF...

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ACKNOWLEDGEMENT

I would like to acknowledge Prof. Dr. Ahmet ECEV T for his many helpful suggestions during the course of this work, for his preserving efforts without which this work could not have been ended and I am also grateful to him for his unique friendship and endless supports throughout the year. I would also thank to Prof. Dr. Ramazan SEVER for his encouragement at the very beginning of this work. I am also grateful to Prof. Dr. Bülent G. AKINO LU for his help, encouragement and advice during this study. I am deeply indebted to Mehmet TA from FETA , Mehmet GÜRBÜZDAL from ALFA BOYA for their support and encouragement during construction part of this study. I am also thankful DA SAN and STEK; the companies who provided us with three solar water heaters. Particular thanks are due to Ataman ÖZDEM R, Mustafa U UZ and all the workers who, worked with me all along this study, for their invaluable help. I am also thankful to Necil ÖZTÜREL and Cenk ÖZBAY for their helps. Thanks are certainly due also to ule KARAMAN for her valuable effort and her patience, encouragement throughout this study and for typing this thesis. Finally, I would like to express my gratitude to my Uncle Celadet GAYDALI, my mother Fatma

NAN, my sisters Neslihan and Elif Z LAN for their

encouragement. viii

TABLE OF CONTENTS

ABSTRACT ............................................................................................ iii ÖZ...................................................................………………..............

v

ACKNOWLEDGEMENTS ..................................................................... viii TABLE OF CONTENTS LIST OF TABLES

..................................................................... ix

................................................................................ xiii

LIST OF FIGURES ................................................................................. xv LIST OF SYMBOLS .................................................................................. xvii CHAPTER 1. INTRODUCTION ................................................................................. 1 1.1. SHORTCOMINGS OF SOLAR ENERGY

................................. 5

1.2. SOLAR ENERGY POTENTIAL OF TURKEY

....................... 6

2. THE SUN AND THE SOLAR ENERGY ............................................. 8 2.1. THE SUN

................................................................................. 8

2.2. THE SOLAR ENERGY

......................................................... 10

2.3. THE SOLAR CONSTANT .......................................................... 10 2.4. ATTENUATION OF BEAM RADIATION .................................. 11 2.5. THE CELESTIAL SPHERE .......................................................... 14 2.6. BEAM RADIATION RECEIVED BY INCLINED SURFACES.. 14 2.7.1 Incidence Angles for Fixed Surfaces ……………………... 15 3. PRELIMINARY INTRODUCTION TO THE FLAT PLATE COLLECTOR

..……….................................................................... 17

3.1. FLAT PLATE COLLECTORS

.............................................. 17 ix

3.2. HISTORICAL BACKGROUND ON THERMAL PERFORMANCE, ECONOMIC ANALYSIS AND OPTIMIZATION ...................... 21 3.3. MAIN CHARACTERISTIC PARAMETERS OF A FLAT PLATE COLLECTOR

.......................................................... 37

3.3.1. The Absorber Plate

.......................................................... 39

3.3.2. The Covering Materials

.............................................. 43

3.4. BASIC FLAT PLATE COLLECTOR ENERGY BALANCE EQUATION …………………………………………….............. 46 3.5. EFFICIENCY OF A FLAT PLATE COLLECTOR ……….…… 52 4. MATERIALS AND METHODS: OPTIMIZATION, ECONOMY, CONSTRUCTION AND THERMAL PERFORMANCE TESTING…53 4.1. OPTIMIZATION OF FLAT PLATE COLLECTORS .................. 53 4.1.1. Choice of Fin Material .......................................................... 54 4.1.2. Choice of Thickness of Plate and Pipe Spacing .................. 55 4.2. THE COMPUTER PROGRAM .............................................. 56 4.3. ECONOMIC CONSIDERATION .............................................. 56 4.4.ECONOM C ANALYS S OF ABSORBER PLATE ........... 57 4.5. CONSTRUCTION OF A NEW ABSORBER PLATE

........... 59

4.6. PREPARATION OF EXPERIMENTAL SET-UP ...................... 65 4.7. TESTING OF FLAT PLATE COLLECTORS TO DETERMINE THEIR THERMAL PERFORMANCE

.................................. 66

4.7.1. Purpose ................................................................................. 66 4.7.2. Testing Preconditions .......................................................... 66 4.7.3. Apparatus And Instrumentation .................................. 68 4.8. USEFUL THERMAL PERFORMANCE EQUATIONS FOR CALCULATION ...................................................................... 69 4.8.1. Collector Thermal Efficiency .............................................. 69 4.8.2. Collector Time Constant ............................................... 71 4.9. TESTING PROCEDURE .......................................................... 71 4.9.1. Measurements ...................................................................... 72 4.9.2. Experimental Determination of the Collector Time Constant ...................................................................... 73 4.9.3. Experimental Determination of the Collector Thermal Efficiency ...................................................................... 74 x

4.9.4. Computation of Collector Thermal Efficiency

.......... 87

5. EXPERIMENTAL RESULTSAND DISCUSSION ....................... 78 5.1. RESULTS OF OPTIMIZATION ............................................. 78 5.2. FLAT PLATE COLLECTORS USED IN THE EXPERIMENTS. 79 5.2.1. ISTEK’ s Collectors (Standard) .................... 80 5.2.2. DA SAN’ s Copper Collector (DBC 90190) .................... 82 5.2.3. CONSTRUCTED COLLECTOR WHICH HAS GALVANIZED IRON ABSORBER PLATE ...................... 83 5.3. EXPERIMENTAL RESULTS-COMPARISON AND DISCUSSION ……………….............................................. 84 5.3.1. Collector Time Constant .............................................. 84 5.3.2. Thermal Efficiency ................……….............................. 84 5.3.2.1 Comparison of the Intercepts of the Efficiency Curves …………………………………………….. 85 5.3.2.2 Comparison of the Slopes of the Constructed FPC with the Other Collectors ……………... 88 5.3.2.3 Comparison of Theoretical and Experimental Efficiency ………………………...…………... 90 5.3.2.4 The Sources of Error ……………………………... 95 5.3.2.5 New Optimization Collector ……………………... 97 5.3.2.6 Comparison of the Newly Optimized with the Others …………………………………………….. 98 6. CONCLUSION

............................................……………………….. 103

REFERENCES ................................................................................. 107 APPENDICES A CALCULATION OF THERMAL CONDUCTIVITY OF GALVANIZED IRON PLATE .............................................. 115 B

A SAMPLE EFFICIENCY CALCULATION FOR THE COLLECTORS

C D E F G H

……………….............................................. 116

PRICES OF MATERIALS, WHICH ARE COMMERCIALLY AVAILABLE ………....................... 117 PARAMETERS USED IN OPTIMIZATION OF COLLECTOR EFFICIENCY ....………............................... 119 PRICE LISTS,EFFICIENCIES AND RELATED GRAPHS FOR FOUR DIFFERENT PARAMETERS ……………........... 120 EXPERIMENTAL RESULTS …………………………...… 154 THE SAMPLE CALCULATION FOR TIME CONSTANT.......158 GLOSSARY OF SOLAR HEATING TERMS............................ 159

xi

LIST OF TABLES

TABLE

2.1. Classification of solar radiation according to wavelength.

........... 13

2.2. Ultraviolet transmission of the atmosphere for a layer of Ozone 2.5 mm deep at NTP.

.......................................................... 13

3.1. Some α and ε for surfaces for solar energy applications.

........... 41

4.1. Physical properties of Al, Fe and Cu and their prices. ....................... 55 4.2. Collector properties and their prices.

....................…………........... 58

5.1. Optimum flat plate collector parameters.

…............................... 78

5.2. (a) Comparison of theoretical and experimental efficiency results for STEK’ s Al collector. .............................................. 91 5.2. (b) Comparison of theoretical and experimental efficiency results for STEK’ s Cu collector. …………………................... 92 5.2. (c) Comparison of theoretical and experimental efficiency results for DA SAN’ s Cu collector. …………………................... 93 5.2. (d) Comparison of theoretical and experimental efficiency results for galvanized iron collector. ............................................... 94 5.3. Experimental efficiency results and results of new optimization for galvanized iron collector. …………………………………… 101 B.1. A sample efficiency calculation for the collectors. ………….…. 116 C.1. Necessary values which are used in optimization.

…………….. 117

E.1. Value of parameters, price of absorber plate, efficiency of the collector, for each combination. …………………………………….. 120 E.2. Price of plate. paint. tube. header and welding for each combination.

.................................................................................. 128

xii

E.3. Price lists of absorber plate in terms of galvanization, cost of plate, and paint, tubes, welding and header, for each combination...... 136 E.4. Diameter of header, unit weight of tube and header, mass of plate, tube and absorber plate, for each combination. ................................... 144 F.1. The measured temperature and radiation data and efficiency values for STEK’ s Al collector. ....…….............................................. 154 F.2. The measured temperature and radiation data and efficiency values for STEK’ s Cu collector. .......................................................... 155 F.3. The measured temperature and radiation data and efficiency values for DA SAN’ s Cu collector. ......................................................… 156 F.4. The measured temperature and radiation data and efficiency values for galvanized iron collector. …………………………….............. 157

xiii

LIST OF FIGURES

FIGURE

2.1. The extraterrestrial solar spectrum. 2.2. The solar spectrum.

............................................... 11

...................................................................... 11

2.3. Diagram illustrating the angle of incidence,θ, the zenith angle, θz, the solar altitude angle, αa, the slope, β and the surface azimuth angle,γ.. 15 3.1. Small capacity natural circulation water heating system.

........... 19

3.2. (a) General view of the cross-section of a basic flat plate collector, (b) Detail of the tube and bonds.

………................................... 38

3.3. Qualitative temperature distribution in the absorber plate of a flat plate collector (a) region between two tubes (b) general temperature distribution (c) at any location y, the general temperature distribution in the x direction, (d) the temperature in the y direction.

.....................................………..................... 47

3.4. Plate and tube configuration of FPC (a) tube bonded below plate (b) tube bonded above plate (c) tubes in-line with absorber plate….. 50 4.1. Sample fin for the constructed FPC. …………............................... 61 4.2. 4.5 x 1.8 x 2.5 m fully automated galvanization pool at M TA ....... 61 4.3. Header and footer with tube spacing. ……...................................... 63 4.4. (a) Close view of produced collector, (b) Another close view of produced collector.

………………………………….................. 64

4.5. The flat plate collectors under test.

………………..……............ 65

4.6. A Kipp and Zonen type pyranometer used in measurement of solar radiation. …..………………………………………… 68 xiv

4.7. An Omni-Scribe-D5000 type chart recorder. ................................... 69 4.8. Chart recording of incident solar radiation, mV versus time. ........... 76 4.9. Chart recording of incident solar radiation for a cloudy day, mV versus time......................………..........………………………... 76 5.1. Cross-section of the FPC, which has aluminum absorber plate……...80 5.2. Cross-section of the FPC, which has copper absorber plate. ........... 81 5.3. Collector performance data a) for STEK’ s aluminum collector, b) for STEK’ s copper collector, c) for DA SAN’ s copper collector, d) for collector, which has galvanized iron absorber plate. …..…. 86 5.4. Comparison of efficiency curve of galvanized iron absorber plate and (a) STEK’ s aluminum collector, (b) STEK’ s copper collector, (c) DA SAN’ s copper collector. .........………...…...… 89 5.5. Collector efficiency (a) for constructed collector, with galvanized iron absorber plate (b) for newly optimized collector. ..……………. 98 5.6. Efficiency curve for newly optimized galvanized iron absorber plate and a) STEK’ s aluminum collector, b) STEK’ s copper collector, c) DA SAN’ s copper collector. …....................……... 99 E.1. Price of absorber plate and efficiency of collector for each combination. ……………………………………………………. 152 E.2. qu/ price, thickness of plate and tube spacing for each combination. .. 152 E.3. Price of absorber plate and efficiency of collector with best line. … 153

xv

LIST OF SYMBOLS

A

: Heat transfer area, m2

AH

: Cross-section area of the header, m2

Ap

: Area of plate, m2

AT

: Cross-section area of the tube, m2

a

: Width of plate, m

b

: Length of plate , m

bw

: Bond width , m

CA

: Effective heat capacity of the solar collector, J/C

Cb

: Bond conductance, W/m2-C

Cp

: Specific heat of the transfer fluid, J/kgC

DH

: Diameter of header, m

Di

: Inner diameter of tubes, m

Do

: Outer diameter of tubes, m

F

: Absorber plate efficiency factor, dimensionless

F′

: Collector efficiency factor, dimensionless

FR

: Solar heat removal factor, dimensionless

hf,i

Price of galvanization, DM : Heat transfer coefficient inside tube, W/m2-C

hw

: Heat transfer coefficient of wind, W/m2-C

Ib

: Beam component of solar radiation, W/m2

Ib,c

: Component of beam radiation intercepted by the collector surface , W/m2

xvi

Id

: Diffuse solar irradiation, W/m2

It

: Total solar irradiation, W/m2

k

: Thermal conductivity of air surrounding the cylinder, W/m-C

kb

: Bond thermal conductivity, W/m-C

kback

:Thermal conductivity of back insulation material, W/m-C

kp

: Thermal conductivity of plate, W/m-C

LH

: Length of header, m

Lloc

: Longitude the location, deg.

Lst

: Standard meridian for the local time zone, deg. : Length of tube, m

i

: Thickness of insulation, m

N

: Number of tubes, dimensionless

Nu

: Nusselt number, dimensionless

n

: Number of experiment for one collector, dimensionless

nd

: Day of year, dimensionless

m

: Mass flow rate of the transfer fluid, kg/s

P

: Price, DM

PG

: Price of galvanization per tones, DM/tones

PH

: Price of header per meter, DM/m

PPL

: Price of plate per m2

PPN

: Price of paint per m2

PPW

: Price of point welding per one tube, DM

PTB

: Price of each tube per meter, DM/m

Pw

: Price of 1 oxygen welding, DM

Qu

: Actual useful energy extraction from the collector, MJ

qtop,loss

: Heat loss, W/m2

qu

: Actual useful energy per unit area , MJ/ m2 17

R

: Thermal resistance of collector components, (W/m2-C)-1

Rb

: Ratio of beam radiation on a tilted plane to that on the plane of measurement, dimensionless

Ri

: Inner Radius of tube, m

Ro

: Outer Radius of tube, m

Ta

: Ambient air temperature, C

Tf

: Average fluid temperature, C

Ti

: Temperature of the transfer fluid entering the collector, C

To

: Temperature of the transfer fluid leaving the collector at a specified time, C

T o, initial

: Temperature of the transfer fluid leaving the collector at the beginning of a specified time period, C

Tp

: Average temperature of the absorbing surface for a flat plate collector, C

Tp,m

: Mean plate temperature, C

UL

: Solar collector heat transfer loss coefficient, W/m2-C

UT

: Solar collector total loss coefficient, W/m2-C

UWh

: Unit weight of headers, kg/m

UWtubes

: Unit weight of tubes, kg/m

Ub

: Collector back-loss conductance, W/m2-C

Ue

: Edge loss coefficient, W/m2-C

V

: Velocity of wind, m/s

VTL

: Value of DM 1 in terms of TL, TL

W Wp

: Tube spacing, m : Unit weight of plate, kg

18

Greek Letters :

α

: Absorbtance of the collector surface for solar radiation, dimensionless

αa

: Solar altitude angle, deg

β

: Collector tilt from horizontal, deg

γ

: Surface azimuth angle, deg

γb

: Bond thickness, m

δp

: Thickness of absorber plate, m

δs

: Solar declination angle, deg

εg

: Emittance of glass, dimensionless

εp

: Emittance of plate, dimensionless

η

: Collector efficiency, %, dimensionless

ηd

: Collector daily efficiency, dimensionless

ηe

: Experimental collector efficiency

ηt

: Theoretical collector efficiency

θ

: Angle of incidence between direct solar rays and normal to the collector surface, deg

θz

: Zenith angle, deg

λ

: Wavelength, µm

ρ

: Density of material, kg/m3

ρg

: Ground reflectance, dimensionless

σ

: Stefan-Boltzman Constant, 5.67x10-8 J/m2 s K4

τ

: Transmittance of the solar collector cover plate, dimensionless

φ

: Latitude of the experimental site, deg

ωs

: Solar hour angle, deg 19

CHAPTER 1

INTRODUCTION

The need for energy increases with elevated living standards each day. The main goal of the energy policy of any country should be obtaining clean, cheap and long-lasting energy since increasing living standards, growing world population and rapid developments in technology rises the need for energy each day, however, obtaining such energy will be harder due to the limited energy reservoirs present around the world. The environmental pollution resulting from the usage of energy is another serious problem. Due to these difficulties related to the energy issue, the world is seeking for alternative energy sources. In 1980, the population of our country was 44 million and it is 68 million in the year 2000. On the other hand our primary energy consumption was 32 MTEP in 1980, it was 74 MTEP in 1998. Beside this, primary energy sources production was 28.9 MTEP in 1998 [1]. The growth of economy and industry, the increase in population, urbanization, and the spread of technology led to remarkable increase in the Turkey’ s primary energy and electric consumption. Turkey is a country who has not completed its industrialization, and is still in the process of development and a rapid rise in energy consumption is expected all along this process of development. It is also estimated that energy demand in the year 2020 will be 65% higher than that of today and it will be 250% higher than that of today in the year 2050. In 1998, electric energy consumption per person was 1386 kWh, which constitutes about the 1/5th of the OECD average. For the year 2010, it is expected that existing electrical power capacity will increase 20

about three folds and in 2020 it will be about 5 folds of today’ s values [2]. The energy consumption by the houses and utilities were 15 MTEP in 1990 and it reached to 18.8 MTEP in 1998. These values indicate that, industrialization is continuing in our country, in particular; energy intensive industry is in progress. Although petroleum is the main fuel in industry, percentage of oil consumption dropped. During 1990-98 the share of the natural gas used in this sector increased rapidly from 5% to 10.6%. The percentage of energy consumption in transportation sector, given by the statistics, seems to decrease 19%, this is because of the illegal energy consumption [1]. Obviously the exhaustible forms of energy such as wood, coal, natural gas, and other fossil fuels will not meet this growing demand since these are mostly utilized for the advancement of technology in the industrialized countries and the rapid catching-up of the developing countries. So, it is hoped that the effective usage of solar energy, directly or indirectly, may extend the period of time in which the fossils are all used-up. Solar energy is of great importance in various engineering fields although it has some shortcomings as is presented in section 1.1. In recent years, the subject of solar energy utilization has been taken up by various major industries in the hope that it can eventually lessen the dependence of such industries to conventional energy sources that are decreasing with a very rapid rate. However, there is still much work to be done in this field. Solar energy is used in: ♦ Domestic water heating ♦ Space heating ♦ Solar cooling ♦ Distillation of salt water ♦ Heat engines ♦ Photovoltaic cells 21

♦ Solar cookers ♦ Solar furnaces It can be stated that environmental problems and problems related to shortage of energy have been and will be two of the main important issues of this century. Utilization of solar energy can greatly contribute to solving this problem, if and only if its economical and technical difficulties can be solved in the near future. Solar water heating represents the most widespread engineering use of solar energy recently [3]. Units built for commercial usage in many countries are competing with more or less successfully with the fossil fuel operated systems. Today, different designs of solar water heating systems are developed in different countries due to the variation in solar radiation, ambient temperature, material used, labor and fuel costs and interest rates, financial availability and hot water demand of these countries. A solar water-heating unit is composed of several components such as solar collectors, a storage tank, heat exchangers, circulation pumps, connection pipes, etc. The solar collector is the most essential equipment that transforms solar radiant energy to thermal energy. Non-concentrating flat plate collectors (FPC) and concentrating parabolic and cylindrical collectors are the two major types. The FPC is the simplest and one of the most effective means of collection of solar energy for use in systems that require thermal energy at comparatively low temperatures. In comparison with the concentrating types, which are mainly used in high temperature solar furnace applications, the FPC offers the following advantages [4].

22

1) For their operation, no complicated mechanisms for following the apparent diurnal motion of the sun are needed, 2) Construction is simple and cost is relatively low, 3) Diffuse as well as direct solar radiation is utilized. This last advantage is especially important in view of the fact that, of the total solar radiation received on the surface of the earth (46% of the extraterrestrial radiation), approximately 40% (18% of the extraterrestrial radiation) is diffuse radiation [4]. Therefore the majority of applications incorporate flat plate configurations, since they have proven to be acceptable for heating from both performance and economical standpoints. Since the performance of a solar heating unit is directly related to the performance of the solar collector system, the determination of the thermal performance of the heating unit gains more importance. An FPC should have high thermal performance, long lifetime and at the same time should be inexpensive. This statement is valid for the whole system and also individual parts of the collector. In this study we have concentrated on the absorber plate. The purpose of this study is to determine the optimum parameters for an efficient absorber plate, made up of galvanized iron, construct the new absorber plate, and determine its thermal performance together with three commercially available FPC built in Turkey. The necessary optimization, production and material precautions are taken to have high thermal performance, long lifetime and low cost. We have built a new absorber plate for FPC by using galvanized iron, after calculation of optimum parameters, which have been chosen to obtain the best value of qu/price. Having constructed the plate, we tested thermal 23

performance of newly designed absorber plate against three commercially available collectors. The thermal tests are done under internationally accepted ASHRAE Standard (93/77) [5]. According to this standard, the thermal performances of the solar collectors are determined, in part, by obtaining values of instantaneous efficiency for a combination of values of incident isolation, ambient temperature and inlet fluid temperature. This requires experimentally measurement of the rate of incident solar radiation onto the solar collectors, as well as the rate of energy addition to the transfer fluid, as it passes through the collectors, all under steady state or quasi-steady state conditions. In the following chapters, after short information about the sun and solar energy, the general knowledge about the theory of FPC is given with short discussions of the previous studies made on these subjects found in the literature. Then, the optimization, construction of a new absorber plate and the method of testing to determine the thermal performance of solar collectors are introduced. The testing procedures, experimental set-up, and instrumentation are presented the next. The data obtained from the experiments performed on different solar collectors are evaluated to be able to make comparisons between them in terms of thermal performance, and the predictions and some comments are given for the future FPC with high thermal efficiencies in the conclusion and discussion chapters. Also, to compare the experimental results with the theoretical results, efficiencies are calculated for the same ∆T and I by using the excel program. Finally, supplementary information and a glossary of solar energy are presented in the appendices.

24

1.1. SHORTCOMINGS OF SOLAR ENERGY The first problem encountered in the engineering design of equipment for solar energy utilization is the low flux density, which makes large surfaces necessary to collect the solar energy for large-scale utilization. However, larger the surfaces, the more expensive the delivered energy becomes. The second practical limitation that is not apparent from the macroscopic energy view is that most of the solar energy falls on remote areas and would therefore require some means of transportation to be useful to the industrialized regions. The third limitation of solar energy as a large-scale source of power and heat is its intermittence. Solar energy has a regular daily cycle due to the turning of the earth around its axis, a regular annual cycle due to the inclination of earth’ s axis with the plane of the ecliptic and due to the motion of the earth around the sun and is also unavailable during periods of bad weather. In assessing the prospects for using solar energy, it therefore becomes particularly important to ascertain for which application the diffuse and cyclic nature of the source will not introduce insurmountable technical and economic problems. It is also necessary to recognize that because of its particular characteristics solar energy cannot be relied on as the solar energy source and will need supplementation from other sources for the time being [6]. 1.2. SOLAR ENERGY POTENTIAL OF TURKEY The Sun Belt where solar energy can be harnessed most efficiently passes partially through Turkey. The country has a roughly rectangular shape 25

and it lies within parallel lines, which increases its advantageous position for adopting solar energy more extensively. Annual solar energy falling on Turkey is 475.5 W/m2 per day, which is 2.7x1014 kcal/year. This is equivalent to 1010 tones of industrial coal. Turkey seems to have a huge solar energy potential. However, because of technical and economical problems of the systems it is not possible to collect and use this environmentally clean and sound energy at its full capacity [7]. It is shown by energy engineers that in the regions where the annual sunshine time is 2000 hours or more, solar energy can economically be utilized. This figure for Turkey is 2640 hours, indicating that it is one of the lucky countries, which can harness solar energy effectively. In spite of the wide variety of solar energy applications in the world, solar heating is primarily used for water heating in Turkey. For this reason, the majority of the firms manufacture FPC [7].

26

CHAPTER 2

THE SUN AND THE SOLAR ENERGY

2.1. THE SUN

The source of the sun’ s energy is a hydrogen-to-helium thermonuclear reaction. The outer layer of the sun, from which the solar radiation emanates, has an equivalent black-body temperature of about 5760 K. Approximately 30% of the solar energy impinging on the outer fringes of the earth’ s atmosphere is reflected back into space. The remaining 70%, approximately 120.000 terawatts, are absorbed by the earth and its atmosphere [3]. The sun has a very massive structure (about one third million times as massive as the earth). Under its own gravitational attraction, solar material is compressed to such a high control density and temperature that nuclear reactions take place. These nuclear reactions are the source of the energy which is continuously radiated to the space and which derives solar activity [4]. The sun is composed of five different layers [8, 9]. The core at the very center, contains most of the mass is almost entirely responsible for the sun’ s energy generation which is the result of fusion of hydrogen nuclei to form helium nuclei. The temperature, pressure and density are very high in this layer. The energy that is generated in the core is transferred toward the surface by radiation with a sharp decrease in the temperature, pressure and density up to a point at which the gas properties have changed to such an extent that the 27

gas above is convectively unstable and turbulent convection occurs at the convection zone. In moving outward through the convection zone, the gas density, temperature and the pressure continue to decrease. A layer is reached where a photon emitted outward has only a small probability of being reabsorbed or scattered. The photon then is more likely to escape into space through the transparent atmosphere above. It is this layer, called the atmosphere (light sphere) which we actually see and which defines the very sharp visible edge of the sun. Above the atmosphere there is a transparent layer of rarified gas, which is known as the chromo-sphere because of its red color. The light emitted by the chromo-sphere is of short wavelength because of the high temperature and is very weak because of the rarification of its gases. The high temperature above the photosphere i.e. in the chromo-sphere causes the radiation emission to be concentrated in the UV and XUV regions. The layer above the chromo-sphere is called the corona, which is made of highly ionized gases. Even though the effective temperature of this layer is high (about 6x106 K) the total amount of energy in the corona is small. The average energy per particle is large but the energy density is low because of the extremely low particle density. In summary, it is seen that the sun’ s energy is generated in the core and almost all of it is released in to space by the relatively thin photosphere. The convection zone also converts a small amount of the energy from the core into mechanical form, which together with the sharp drop in density is responsible for the very high temperature of the sun’ s outer atmosphere. Each layer has been seen to have its own distinctive character even though the layers overlap and merge into one another.

17

2.2. THE SOLAR ENERGY Solar radiation reaching the earth consists of direct and diffuse radiation. Direct radiation is neither scattered nor absorbed by the atmosphere and reaches the earth’ s surface as the beam component. On the other hand diffuse radiation is the scattered radiation along its path from sun to earth due to the clouds and air moisture. The solar radiation reaching the earth is fairly uniformly distributed over the globe and it is widely available from geographic point of view. Although the energy density falling on the earth is low, the direct path of solar energy is of high quality and can be used to generate high temperatures. Before solar energy can be used the sun’ s radiation must be converted into heat, mechanical power, or electricity. The conversion methods can be divided into natural and technological conversion systems [3]. In natural conversion, earth, wind or water serves as a solar energy collector and storage. Since no man-made collectors are needed, the cost of energy from natural systems is largely determined by conversion equipment. In technological conversion system, one may generate electricity directly by photovoltaic or photochemical conversion systems or one may use solar radiation to heat a working fluid by thermal conversion in solar collector. 2.3. THE SOLAR CONSTANT Most of the solar systems are below the atmosphere and the energy that reaches the ground is quite different from that available outside the atmosphere. However, the radiation reaching the earth is a fraction of the extraterrestrial radiation and of solar constant. The solar constant is the total energy that falls on a unit area exposed normally to the rays of the sun at the 18

average sun-earth distance which is the semi-major axis of the earth’ s orbit or one astronomical unit, equal to 1.49x1011 m, the NASA/ ASTM standard value of the solar constant is 1353 W/m2 with an estimated error of ±1.5% [5]. The extraterrestrial solar spectrum in the wavelength range 0.2-2.6 micrometers is shown in Figure 2.1.

Figure 2.1 The extraterrestrial solar spectrum [4]. 2.4. ATTENUATION OF BEAM RADIATION The electromagnetic spectrum emitted by the sun extends from fractions of an Ångström to hundreds of meters. The solar spectrum is usually divided into the wavelength regions indicated in Figure 2.2(1 cm=104 µm) [10].

19

Figure 2.2 The solar spectrum [4]. The X-rays and other short wave radiation of the solar spectrum are absorbed high in the ionosphere by nitrogen, oxygen and other atmospheric components; most of the ultraviolet radiation is absorbed by ozone. At wavelengths longer than 2.5 micrometers, a combination of low extraterrestrial radiation, and strong absorption by CO2 and H2O means that very little energy reaches the ground [4]. Thus from the viewpoint of terrestrial applications of solar energy, only radiation of wavelengths between 0.29 and 2.5 micrometers needs to be considered. This solar radiation is transmitted through the atmosphere undergoing variations due to scattering and absorption. Scattering, which results in attenuation of the beam radiation by air molecules, water vapor and dust particles, has been the subject of a number of studies [4,6,10,11,12], and approximate methods have been developed to estimate the magnitude of the effect. Absorption of radiation in the atmosphere in the solar energy spectrum is due largely to ozone in the ultraviolet and water vapor in the infrared bands. There is almost complete absorption of short-wave radiation below 0.29µm and for typical transmission given values in Table 2.1. Water vapor absorbs strongly in the infrared region. Beyond 2.3µm, the transmission of the atmosphere is very low due to absorption by H2O and CO2; 20

the energy in the extraterrestrial solar energy spectrum is less than 5% of the total solar spectrum and the energy received at the ground is small.

Table 2.1 Ultraviolet transmission of the atmosphere for a layer of Ozone, 2.5 mm deep at NTP [4]. λ(µµm)

τoλλ

0.29

0.00

0.30

0.10

0.31

0.50

0.33

0.90

0.35

1.00

The factors causing attenuation of the radiation are summarized below: Astronomical Factors (The solar spectrum between 0.30 and 5.0 microns and the magnitude of the solar constant, variation with the sun-earth distance, variation with the solar declination and variation with the time angle.) Geographic Factors (Variation with the latitude of the station, variation with the longitude of the station and dependence on the height above sea level.) Geometrical Factors (Dependence on the altitude of the sun, dependence on the azimuth of the sun, the effect of the tilt of the receiving plane relative to the horizon, and variation with the azimuth of the tilted plane.)

21

Physical Factors (Extinction by pure atmosphere, water content of the atmosphere and ozone content of the atmosphere.) Meteorological Factors (The effect of the cloudiness of the sky, the effect of the albedo of the ground)

2.5. THE CELESTIAL SPHERE In order to determine the position of the celestial bodies in the sky, they are assumed to lie on a single sphere, the celestial sphere. The radius of the sphere must be large enough to identify the celestial bodies as points on the sphere, and the center, depending on the different conventions, coincides with the position of the observer (horizontal system), or the center of the earth (equatorial system), or the center of the sun (ecliptic system), or the center of the galaxy (galactic system) [8]. The horizontal system is preferred when calculating the position of the sun with respect to the geographical coordinates on the earth. In this system, the reference plane is the horizon of the observer, i.e., and the plane passing through the observer and normal to the vertical. 2.6. BEAM RADIATION RECEIVED BY INCLINED SURFACES The amount of beam or direct radiation intercepted by a surface depends on the angle, θ, which is defined as the angle between the normal to the surface and a line collinear with the sun’ s rays. Figure 2.3 shows the incidence angle for a surface tilted at an angle β from the horizontal. 22

Figure 2.3 Diagram illustrating the angle of incidence,θ, the zenith angle, θz, the solar altitude angle, αa, the slope, β and the surface azimuth angle, γ [12]. By examining the figure, it is easy to see that the component of beam radiation Ib, c intercepted by the surface of a collector is given by

I b,c = I b cos θ

(2.1)

Where Ib is the beam radiation at the surface in the direction of the direct normal radiations.

2.6.1. Incidence Angles for Fixed Surfaces The incidence angle depends on the three basic solar angles, namely declination angle δs, hour angle ws and latitude φ of the location. Collector tilt angles are defined as positive for surfaces facing south. Various equations have been developed for the incidence angle for several geometries of interest. The 23

most useful equations are summarized below omitting the derivation [8], [6],

[13]. a) Generalized Equation for Fixed Planar Surfaces It is possible to generalize the equation to cover all of the different cases. In general the incidence angle on a planar, fixed surface is,

Cos θ = Sin δ s ( Sin φ Cos β − Cos φ Sin β Cos γ ) + Cosδ s Cos ω s (Cos φ Cosβ + Sin φ Sin β Cosγ ) + Cos δ s Sin β Sin γ Sinω s (2.2)

b) South-facing Tilted Surface The incidence angle for a south facing, γ = 0° and tilted surface is, Cos θ = Sin ( φ − β ) Sin δ s + Cos (φ − β ) Cos δ s Cos ω s

24

(2.3)

CHAPTER 3

PRELIMINARY INTRODUCTION TO THE FLAT PLATE COLLECTOR

3.1. FLAT PLATE COLLECTORS

Many of the systems, which utilize solar energy, first collected the energy as heat. A solar heat collector intercepts solar radiation, converting the radiation to thermal energy and transfers this heat to a working fluid. Solar energy is transmitted from the sun through space to earth by electromagnetic radiation. It must be converted to heat before it can be used in practical heating and cooling systems. Since solar energy is relatively dilute when it reaches the earth, the size of a system used to convert it to heat on a practical scale must be relatively large. Solar energy collectors, the devices used to convert the sun’ s radiation to heat, usually consist of a surface that efficiently absorbs radiation and converts this incident flux to heat which raises the temperature of the absorbing material. Part of this energy is then removed from the absorbing surface by means of a heat transfer fluid that may be either liquid or gaseous.

25

There are three types of thermal collectors: 1. Non-concentrating and stationary collectors (Passively heated space, FPC and solar ponds). 2. Slightly concentrating collectors, with or without periodic adjustments (cpc’ s V-troughs). 3. Concentrating tracking collectors. Among these, the FPC is the most common design for active low temperature solar thermal conversion. For non-concentrating or FPC, solar radiation intercepts on a metal or glass absorber plate which heat is transferred and used in the required thermal application. Since the absorber plate has a temperature greater than its environment, unrecoverable heat losses occur from the entire absorbing surface of the collector to the environment. Consequently, 100% collector efficiency cannot be realized in practice. A diagram of a simple, small capacity, natural circulation system, suitable for domestic purposes is shown, in Figure 3.1. The two main components of the system are the liquid FPC and the storage tank, which is located above the level of the collector.

53

Figure 3.1. Small capacity natural circulation water heating system [3].

As water in the collector is heated by solar energy, it flows automatically to the top of the water tank and it is replaced by cold water from the bottom of the tank. Hot water for use is withdrawn from the top of the tank. Whenever this is done, cold water automatically enters at the bottom and auxiliary-heating system is sometimes provided for use on cloudy or rainy days

[3]. FPC operation principles of which is briefly described above can supply hot water or hot air temperatures up to approximately 70°C with good efficiency. They require no moving parts have good durability and can collect both direct and diffuse radiation. The key elements for an FPC are a frame, one or two transparent covers, an absorber plate with flow channels connected to inlet and outlet 54

headers through which a working fluid passes and same black side insulation. The cover is usually made of glass or plastic that is transparent to radiation in the solar spectral range but opaque to infrared radiation from collector plate. One of the most cost-effective applications of FPC is domestic hot water heating. Concentrating collectors attempt to reduce heat loss by using an absorber area smaller than the area that intercepts the sun’ s rays, called the aperture area. This performance improvement is accomplished by reflecting the sun’ s rays from the large aperture area to the small absorbing area by shaped mirrors or other reflecting surfaces. Since only the direct or collimated portion of solar radiation is useable to effective concentration, most concentrators must move to track the sun and cannot collect as much diffuse radiation as FPC. Although the technology in this area is still developing, the majority of work, however, still incorporates flat plate configurations since they are more economic and perform at higher efficiencies at relatively low temperatures. In all solar thermal conversion processes, solar radiation is absorbed at the surface of a receiver, which contains or is in contact with flow passage through which a working fluid passes. As the receiver heats up, heat is transferred to the working fluid, which may be air, water, oil or a molten salt. The upper temperature that can be achieved in solar thermal conversion depends on the isolation, the degree to which sunlight is concentrated, and heat losses. Since the velocity of flow of the fluid can control its temperature, it is possible to match solar energy to load requirements not only according to the amount but also according to the temperature level, i.e., the quality of the energy required.

55

3.2. HISTORICAL BACKGROUND ON THERMAL PERFORMANCE, ECONOMIC ANALYSIS AND OPTIMIZATION FPC analysis and thermal performance evaluation have already been carried out and reported by various investigators. Hottel and Woertz [14], in 1942, constructed a special solar energy building at the M.I.T. and determined the performance of FPC that are placed on the roof of this building. Pleated to the collector performances, they analyzed the solar radiation on tilted surfaces, transmission of radiation through glass plates, absorbtivity of blackened surfaces, heat losses from the absorbing surface, reduction in the performance due to the dirt on the outer collector glass surface and the effect of shading on the efficiency of collectors. The experimental results seemed to be quite satisfactory when compared with the theoretically calculated values. Hottel [15], in 1950, summarized the general considerations concerning the collector performance as such: a) If energy is to be withdrawn from the collector at a temperature only slightly above atmospheric, the outward heat losses are negligible and a doubling of the intensity of solar irradiation of the collector doubles its useful output. If, however, the temperature of energy collection is quite high, it is apparent that a certain minimum or threshold solar intensity is necessary just to keep the collector at operating temperature with no net useful energy output. In a collector operating close to this critical condition, it is obvious that a small percent increase in solar intensity would produce a large percent increase in useful output. 56

b) If a collector is operating with only one plate and at a collection temperature close to atmospheric, the outward loss is low. Putting on a second plate will approximately have the losses, but they were already small, and at the same time the insolation reaching the black plate will be cut by some 10% due to reflection from the additional glass. These will more than offset the reduced outward loss and the second glass plate is unwarranted. If, however, the collector is operating at a high temperature the saving in outward losses by adding on more glass plates will more than offset the added reflection losses. In general, then, the optimum number of glass plates is larger, the higher the desired temperature of energy collection. c) By similar reasoning, the optimum plate number is larger, the weaker the insolation and the colder the outdoor temperature. Hottel also studied the effect of spacing between the glass cover sheets and concluded that the insulation properties of air-spaced layers of glass depend largely on the high thermal resistance of the stagnant layers of air at the glass surface. Experiments have shown that increasing the air space beyond ½ inch had little effect in reducing the conductance. Hottel and Whillier [16], in 1995, introduced a method by organizing solar radiation data into a form suitable for the rapid calculation of the performance of any kind of non-focusing solar collection equipment and hence the rapid determination of the size of solar collector required for a given application. For localities where full pyrheliometric data are not available and only the daily total insolation 57

can be obtained, a method is presented for estimating the hourly distribution of the energy and for using a whole-day solar utilizability curve as a basis for prediction of collector performance. Tabor [17], in 1955, investigated the possibility of making solar energy collectors of high efficiency by use of selective black surfaces. By means of two parameters, the overall transmission efficiency and the cut-off intensity, it is possible to determine the performance of a collector under various conditions of use. He also studied the effect of degree of concentration on the performance of solar collectors and his computations show that it should be possible to produce low-pressure steam without optical concentration and highpressure steam with a small degree of concentration. Ward [18], in 1955, constructed an FPC, which is capable of being manufactured cheaply on a large scale, and established a simple relation between the efficiency of the collector, the plate temperature and the rate of insolation for constant rates of flow of circulating water. He also constructed performance charts that make possible an assessment to be made of the practicability of using solar energy in the tropics for the production of heat and power. Hottel and Unger [19], in 1958, examined the properties of a copper oxide-aluminum selective black surface absorber of solar energy. Calculations of solar collector performance leads to the conclusion that the efficiency of one glass-plate collector with a selectively black receiving surface lies between the values for non-selective black systems containing two and three glass plates, and is nearer to the latter. Selectively black surfaces are particularly useful whenever heat is desired above 70°C or for miscellaneous heating purposes in which it is not possible to cover the absorber plate by a glass sheet. 58

Morse and Czarnecki [20], in 1959, reviewed the elements of a flat plate absorber and the factors influencing its design and operation. The thermal characteristics of energy received, losses, efficiency and the heat transfer to the circulating fluid are dealt within the light of design considerations. While doing this, the effect of orientation and its influence on the elevation of energy incident on inclined surfaces, the optimum angle inclination and the effect of changes in azimuth are also considered. They discussed the installation and operating problems; the location of an absorber and its materials of construction and economic factors. Robinson and Stotter [21], in 1959, proposed a standard test code for the determination of the efficiency of solar water heaters of the flat collector type and pointed out the required properties to be tested to obtain an objective estimate of the quality of the tested heater. The formulas of the aerial efficiency, orientation efficiency, thermal efficiency and the heat storage coefficient of solar water heaters are given separately in their study. Kudret Selçuk [22], in 1964, studied the performance of FPC at high temperatures. Depending upon the previous researches, he claims that the efficiencies of conventional glass-covered FPC are about 25-30 % at most at high temperatures. He investigated the possibility of using styrocel as a transparent cover for FPC so as to increase the efficiency at higher temperatures and he concluded that cell-like covers such as styrocel do indeed have some advantages over conventional covers. Hottel, Sarofim and Fahimian [23], in 1966, investigated the effect of scatter on the radiative properties of surfaces. Experimental values of the directional reflectance of well-defined particulate layers are presented. 59

Reflectances calculated using various theoretical models are compared with the experimental results. Rao and Suri [24], in 1969, dealed with a simplified approach for design calculations, involving estimation of collector area for solar water heaters and constructed curves that may be used for the required application. Garg [25], in 1971, reported the design details and performance of a large size solar water heater, which is tested under India conditions. He studied the various arrangements for connecting the collectors such as; cascade, series, series parallel and true parallel and revealed that for a solar water heating system having a large number of absorber banks, the true parallel arrangement yields maximum efficiency and economy. Ratzel and Bannerot [26], in 1977, introduced the result of a compilation of commercially available materials suitable for use in FPC with the estimated performance and durability data and other important mechanical and radiative properties of the selected material. Woodman [27], in 1977, gave the basic equations for calculating collector performance as a function of design and operating parameters and indicated the method of solution using a programmable desk calculator. The method is used to investigate the sensitivity of collector output to ambient air temperature, absorber plate temperature and emissivity, wind speed, atmospheric irradiation and the number of cover plates. He also analyzed the effect of cover plates and insulation on the collector heat losses. Janke and Boehm [28], in 1977, determined the energy density and flux available after passage of direct solar radiation through single and double glass 60

covers, for panels inclined at various angles and oriented with varying azimuths for several latitudes. They found that orientations other than south facing give greater availability of energy for a period of about 90 days centered about the summer solstice and give higher flux values early or late in the day for winter dates, but are inferior to south facing collectors in other respects. Marshal and Wedel [29], in 1977, investigated the use of Lexan (polycarbonate) and Kapton (polyamide) honeycombs to increase solar collector efficiency and concluded that the honeycomb placed between a flat black absorber and transparent cover provides considerable improvement in the performance of solar collectors over the operational temperature range of 70 to 120°C. Both instantaneous efficiencies and diurnal performances of properly designed honeycomb collectors are increased over those obtained with a single- or double- glazed non-honeycomb FPC. The honeycomb achieves the improved performances by reducing the convection and radiation losses. Smith, Cobble and Lukens [30], in 1977, investigated the thermal trap effect of the selective surface-like behavior of some transparent materials both theoretically and experimentally for an FPC. A comprehensive computer simulation of the thermal trap collector was also developed in order to study the effects upon performance of the various elements of the collectors. Four test collectors were built in which trap material and cover glazing that was removable and a series of experiments were run for trap materials of various thicknesses with and without cover glazing. The numerical model predicts that the thinner the trap material, the higher its efficiency should be. The experimental results revealed that, in general, the collector with a glazing performed at higher efficiencies than those without a glazing. Grossman, Shitzer and Zvirin [31], in 1977, developed a model for the heat transfer analysis of an FPC with a rectangular channel for water or 61

airflow. The thermal boundary layer development is investigated and overall efficiencies for uniform solar heat influx with variable heat losses from the plate are calculated for various cases, assuming a second-degree polynomial for temperature profiles with uniform and parabolic velocity profiles. Tabor [32], in 1978, suggested the necessary governing equation of the collector in order those tests on different solar collectors conducted at different times should be comparable. He described the theory and the experimental procedure, which involves connecting four similar collectors in series and measuring the temperature rise across each collector. Since at any instant time, the flow rates and the solar intensity are identical for all the collectors, a number of points on the efficiency-temperature curve are obtained, from which the characteristic equation of the collectors is readily established. He also established the rules to limit the permitted temperature rise and suggested a “standard day” to provide a quick comparison tests. Schröer, Stein and Talarek [33], in 1978, gave a sketch of collector thermal performance test methods being considered in Germany. A special emphasis is placed on mixed indoor/ outdoor testing according to the procedure

proposed

by

the

German

Solar

Industries

Association

Bundesverband Solarenergie (BSE). Comparison of two (BSE-type and NBStype) collector efficiency testing is given in the study. In 1981, Naidu and Agarwal [34] analyzed the thermal boundary layer problems associated with FPC by using fourth degree polynomials for temperature profiles and uniform and parabolic distributions for velocity profiles. Several particular cases of practical interest have been studied and in the case of no heat loss it is found that the Nusselt number for the heat transfer

62

in the fully developed region agrees completely with the exact value when assumed a fourth degree polynomial for temperature profiles. In his study, in 1994,Venkatesh [35] explained the operation of a continuous flow type domestic solar water heater with the help of a schematic diagram. Steady state thermal analysis of such a water heater is carried out. A water heater of this type with a collector area of 1m2 is subjected to tests. The experimental results are compared with predicted results. The experimental results have also been compared with those obtained from a water heater operating on thermosiphon flow. The performance of the continuous flow type water heater is shown to be comparable to that of the thermosiphon flow types. It is concluded that, in the Indian context, the continuous flow type water heater has more advantages than the thermosiphon flow type water heater in view of its low capital cost and the ease of operation and maintenance. Albizatti [36], in 1997, presented a theoretical model and a computer program to evaluate the thermal performance of FPC. The program predicts solar radiation received on tilted plane surfaces and the characteristic parameters and thermal efficiency of collectors are calculated. Studies are carried out to determine the effects of inlet fluid temperature and fluid velocity on the thermal performance. The calculation program may be applied to complement the experimental evaluation of solar collectors.

Khalifa [37], in 1999, conducted an investigation on a locally made natural circulation domestic hot water system to show the important variables, how they are related, and how they affect the performance of the solar system. For that purpose, several measurements were made, which included the temperature distribution along the fin between the absorber tubes and in the 63

flow direction and the thermosyphonic mass flow rate. Using these data, the main parameters of the solar collector were obtained. A comparison between the experimental and theoretical temperature distributions, in the flow direction of the absorber, is also included. The following conclusions are drawn from this investigation: 1. Instantaneous collector efficiencies of 0.21-0.35 were noticed. 2. The measured mass flow rate by the dye injection method was found to agree with the range given in the literature for natural circulation systems. 3. Collector overall heat loss coefficients of 6.9-7.5 (an average of 7.2 W/m2K) were estimated. 4. The study confirmed that the collector efficiency factor and the collector heat removal factor could be taken as constants for a given collector design.

Sumathy, [38], in 1999, studied the time constant for the given typical collector is determined which shows the transient behavior of the collector and the proper time interval to be selected for steady and quasi-steady state efficiency tests. The thermal performance of an FPC for the Hong Kong climate is presented. The fluid inlet-temperature strongly influences the performance of a collector and it is shown how the collector efficiency is strongly affected by the difference between the temperature of the absorber plate and the outer glass plate. Riffat, [39], in 2000, presented the results obtained from laboratory testing of four liquid FPC. The collectors tested include a wavy fin collector, two flat plate heat pipe collectors, and a clip fin solar collector. The clip fin solar collector was tested, so as to compare this simple and inexpensive type of collector against the more costly wavy fin collector and the flat plate heat pipe collector. Using a similar basis of comparison, efficiency values have been 64

formulated in order to compare the performance of the solar collectors. The experimental results show the clip fin solar collector to be promising, with experimental efficiencies approaching 86 per cent.

Nayak and Amer [40], in 2000, showed a critical evaluation of nine dynamic test methods for solar FPC. The theoretical basis, the technique of parameter estimation and the test procedure of each method have been reviewed and compared. Extensive experimental studies have been carried out under a wide range of weather and operating conditions. Two commercially available collectors (from two different manufacturers) have been used in the investigation. The tests were carried out at the same location using a common test-rig, measuring transducers and controlling and data-acquiring facilities. The characteristic parameters of the collectors have been obtained on the basis of each procedure and compared with those based on the steady-state ASHRAE 93-86 standard. Further, for the methods, which prescribe similar test sequences, the collector parameters have been extracted from the same data sets according to their procedures for providing a direct and very clear comparison between the methods. A sensitivity study has also been carried out in order to examine the effect of uncertainties in measurements on the values of the estimated parameters from different methods. Also investigated is the error propagation wherever applicable. Among the methods evaluated, the new dynamic method (NDM) seems to be quite reliable. The quick dynamic test (QDT) method is the simplest method and could be adopted by manufacturers as an effective tool for the purpose of quality control of their products. From the point of view of theoretical completeness, Perers’ method accounts for almost all effects.

65

Hussein, Ahmad and Mohamad [41], in 2000, performed a theoretical analysis of the instantaneous, daily, and yearly enhancement in solar energy collection of a tilted FPC augmented by a plane reflector is developed. The shadow effect due to the reflector on the collector is considered in the analysis. A FORTRAN computer program has been constructed based on the analysis in order to study the effect of different operational and design parameters of plane reflector-tilted FPC system on the collector solar energy collection. These parameters include collector-reflector system orientation and tilt angles, collector elongation ratio, and reflector overhang ratio. From the theoretical analysis of solar energy enhancement of tilted FPC augmented by plane reflectors, it is concluded that: 1. Tilting the reflector at its noon optimum tilt angle, i.e. the angle at which the collector illuminated area resulted from the reflector coincides on the collector area at noon, provides maximum daily boost factor. 2. The South-facing reflector provides higher yearly solar energy collection than the North facing one. 3. Changing the tilt angle of the South-facing reflector at its noon optimum angle up to twice a year provides more than 13% yearly enhancement in the collector solar energy collection. 4.

For maximum yearly solar energy collector, the optimum elongation

ratio of the collector is about 4, while that of the reflector overhang ratio is about 1.

66

5. The present analysis is an efficient tool to optimize the plane reflector tilted FPC systems. In addition to the above studies carried out to increase thermal performance, a number of trials have been performed to reduce the cost of solar water heaters and to find the optimum design. Whillier and Saluja, [42], in 1965, found that the fin efficiency, and the thermal conductance of the bond between the water carrying tubes and the flat absorbing plate, was of equal importance to the quality of the selective surface in determining the overall efficiency of the collector. The procedure followed in the tests involved the simultaneous testing of two identical commercially available solar water heaters, but with the selective surface of one painted over with flat black paint thus destroying the effectiveness of the coating. Straightforward calorimetric tests were carried out in which water was run through the collectors at a constant rate, and continuous measurements made of water temperature rise and of insolation rate. All tests were done with the collectors inclined at an angle of 15 degree from the horizontal. It was concluded that, bringing about reasonable improvements in the selective surface, the fin efficiency and the bond conductance could increase the efficiency factor remarkably. Kovarik, [43], in 1974, analyzed the problem of designing solar energy collectors for the delivery of heat at minimum cost in two different forms. In the first of these, a set of collectors was assumed to be available, each element having different properties uniformly distributed over its area; an optimal was achieved by a suitable combination of a subset of such collectors. In the second form the collector was designed with a non-uniform, continuously varying insulation thickness. The procedures introduced in this paper enable the designer 67

of solar collector systems to determine the most economical distribution of insulation and other design parameters determining the heat transfer coefficient. Test [44], in 1976 developed an analytical program suitable for the purpose of the hourly behavior of an FPC. The results indicate that cloudiness, collector coolant temperature; wind velocity and plate absorbtivity can have a drastic effect over (100°C) on the energy absorbed by a collector. The collector slope should be 15 degree plus the latitude and not vary much from this to obtain the maximum clear sky radiation in winter. A south-facing collector is best but it can vary ±20 degree from this position without a serious influence on performance. Coolant flow rates and tube spacing do not have a major effect on collector performance accept for extreme variations. MacGregor [45], in 1978, examined optimum choice of materials and optimum choice of plate geometry to reduce the cost of collector plates, which are often the single, the most expensive item in the system. By minimizing ratio of total cost per unit area to fin efficiency for various combinations of fin thickness and pipe spacing. The minimum value of 614.9 DM/m2 is for a combination of pipe spacing of 100 mm and fin thickness of 0.25 mm. For the example chosen, using a copper fin, the fin thickness could be anywhere in the range 0.25 mm to 0.5 mm and the pipe spacing could be anywhere between 100 mm and 150 mm without a significant drop in cost effectiveness. Blis [46], in 1959, Garg and Gupta [47], in 1967, have both described methods similar to the above for selecting the optimum combination of fin thickness and pipe spacing. Brandemuehl and Beckman, [48], in 1979, developed a procedure for assessing the economic viability of a solar heating system in terms of the life cycle savings of a solar heating system over a conventional heating system. 68

Using the generalized life cycle savings equation, a method is developed for calculating the solar heating system design, which maximizes the life cycle savings. A similar method was developed for determining the set of economic conditions at which the optimal solar heating system design is just competitive with the conventional heating system. Schröder and Reddemann [49], in 1982, assessed the size of solar water heater systems by three different economic criteria, life cycle savings, payback time and internal rate of return. The study is performed for three different climate conditions. It is also pointed out that the economics of a solar collector system can be substantially affected by the annual distribution of monthly water consumption and of monthly efficiency factors of converting fuel into useful energy. Results of this study show that unlike life cycle savings, the payback time and the internal rate of return cannot serve to optimize the collector design. Results also give an idea about how the economics are influenced by differences in geographical and climate conditions. Between the two extreme locations of Spain and Denmark the calculations, which are based on German economic conditions, reveal differences of around 4 year in pay back time, of 8 per cent in internal rate of return and of around a factor 3 for the life cycle savings. Differences, in the annual distributions of monthly heating load and conversion efficiency factor, between 25 and 150 per cent result, for payback time between 1 and 4 year for the internal rate of return between 2 and 5 per cent. Özsabuncuo lu [7], in 1995, presented the solar energy potential of Turkey. Cost comparison of solar collectors manufactured in Turkey has been made. The analysis has been carried out more realistically by considering time value of money, by assuming constant annual costs and inflated annual cost of the systems. Results obtained in this study revealed that under present market 69

conditions in Turkey with a 60% interest rate, solar systems are sixth of eight alternatives among others. Thus, with constant annual costs, solar energy systems are not preferable in the case of high inflation. Under inflationary economic conditions, when costs are inflated accordingly, in spite of its high initial cost, solar energy systems seem to be the least expensive alternative. He also concluded that investment in Research and Development activities is necessary to reduce total cost of the system through improved efficiency and better production technology. Tırıs, Tırıs and Türe, [50], in 1995, investigated the effects of various fin shapes on solar collector efficiency and material cost. The objective of this study was to optimize material savings by using different fin shapes while keeping the collector efficiency within allowable limits. The aluminum solar collector has been analyzed using four different fin designs. These were a) straight rectangular fin, b) a fin with a step change in local thickness, c) a straight triangular fin and d) a straight fin of inverse parabolic profile. For a reduction in collector efficiency of only 3.11%, a reduction in material cost of up to 16% can be achieved by using a straight fin with an inverse parabolic profile. The other designs investigated show similar but less marked improvements in material cost. When the ratio of material cost reduction to reduction in energy efficiency is calculated, design b has the highest value of the designs considered. It should be noted that some of the profiles examined in this work especially designs c and, may not be easily realized in mass production and the favorable results presented here may therefore be offset by increased production costs. Highgate and Probert [51], in 1996, has built and tested a lightweight flexible solar collector, with a wavelength-selective absorption surface and an insulation- transparent thermal-insulation protector for its aperture. Its 70

cheapness and high performance relative to a conventional FPC provide a prima-facie case for the more wide spread adoption of its design. As its objective the design of low cost lightweight solar thermal collectors based upon polymeric materials has been made. The intention was to devise a cheap low-weight system and thus the heat transfer medium chosen was air. The projected cost of the proposed collector system has been estimated to be between DM 9.1 - DM 13.7 per square meter of collector surface. Panteliou, Dentsoras and Daskalopoulos [52], in 1996, studied the application of expert systems to a mechanical engineering research domain with practical and commercial interest, such as design and manufacturing Solar Domestic Hot Water (SDHW) Systems. The issues studied were the selection and the design of SDHW Systems. The application of an expert system was explored. The appropriate computer program was developed to yield the selection of SDHW Systems using the software tool LEONARDO 3.0, an integrated environment for the development of expert systems. The program proved to be functional and user friendly to a high degree. Tiwari, Hong and Goyal [53], in 1998, studied on a thermal model for

optimization of the design parameters and estimation of the effect of various parameters on the thermal performance of this solar water heater is presented. The paper also presents the numerical computations with the climatic conditions of the Hanoi region, for three cases: (i) using a horizontal collector; (ii) using a sloped collector without reflector; and (iii) using a sloped collector with reflectors. On the basis of the numerical computations, conclusions for the application of this solar water heater in Vietnam have been made. It was concluded a built-in storage solar water heater with an absorber is more proper for domestic purposes. It is good only when the effective transmittanceabsorbtance product of the absorber is taken. 71

Mijovic [54], in 2000, carried out an economic analysis of solar water heating for Yugoslavia beginning with a description of the methodology and economic criteria status of energy in Yugoslavia covering the factors contributing to the cost effectiveness of solar water heating applications and ending with a case study. It was intended to determine whether the project was an attractive investment. Payback period of the project and the net present value of the project over its lifetime were calculated by a computer program. If the net present value of the system were greater than zero then the project would be an attractive investment. From the result of the study it was concluded that the system is an attractive investment under almost all assumptions. Hasan [55], in 2000, presented a systematic sizing approach for the solar system and applied this system to a certain case study. The solar system sizing is based on the life cycle cost, LCC, analysis. For the chosen case study of domestic water heating for a hotel, with hot water consumption of 2600 liters per day, the optimum collector area was found to be 37 m2, the solar fraction of heating 0.78, the LCC of system is DM 43951.8, with annual savings of 4268 DM/year and a pay back period of 3 years. With this optimized system, the cost of water heating is 5.7 DM/m3 compared to 8.3 DM/m3 for the conventional system.

72

3.3. MAIN CHARACTERISTIC PARAMETERS OF A FLAT PLATE COLLECTOR

An FPC is a non-concentrating solar collector in which the absorbing surface is essentially planar [5]. A typical FPC, such as shown in Figure 3.2(a) and Figure 3.2(b) consists of one or more transparent flat front plates, one or more insulating zones bounded by the covers, and an absorbing plate. Heat is removed from the absorbing plate by a gaseous or liquid heat transfer fluid, such as air or water. Thermal insulation is usually placed behind the absorber to prevent heat losses from the rear surface. The front covers are generally glass that is transparent to incoming solar radiation and opaque to the infrared reradiation from the absorber. The glass covers act as a convection shield to reduce losses from the absorber plate beneath.

73

(a)

(b) Figure 3.2 . (a) General view of the cross-section of a basic flat plate collector, (b) Detail of the tube and bonds [4]. The fraction of the solar radiation incident on a FPC, which is available for removal, is a strong function of the temperature at which it is desired to remove this energy. As the operating temperature of the collector is increased, convection and radiation losses from the collector to the surroundings increase correspondingly and the amount of energy remaining for utilization becomes quite small. At operating temperatures above 40°C, the losses from a conventional collector are predominantly those due to radiation. Since more than 99 % of the low-temperature energy reradiated by an 80°C absorber plate is of wavelengths above 4 microns, while more than 98 % of the solar radiation 74

reaching the collector is of wavelengths below 3 microns, so the use of selective black surface with a small emissivity for high wavelength radiation as the absorber plate in a solar energy collector, leads to a marked increase in the efficiency of collection [16], of course, with the aid of a properly selected covering material functioning as a convection shield and as a trap for the reradiating long-wave length solar insolation. So before going any further, it is better to investigate the properties of the most essential components of an FPC i.e., the absorber plate and the covering materials and their effects on the performance of the solar collectors.

3.3.1. The Absorber Plate

Traditionally, FPC utilizes absorber plates, which are painted black to reduce reflection losses. The absorptance for direct solar radiation is thus made nearly unity for normal incidence. Kirchoff’ s law states that the absorbtivity at any wavelength is equal to the emissivity at that wavelength [56]. A conventional blackened absorber has a high emittance and loss heat by radiation quite easily. To reduce this radiation loss, selective surfaces can be used. A selective surface is the one whose emittance is a function of wavelength. If a surface has a high absorbtance for solar radiation (wavelength shorter than 2.5µm) and has a low emittance at longer wavelengths where reradiation takes place, then it will operate at higher temperatures than a conventional blackened surface.

75

Basic studies of the reasons for spectral variation of absorbtance and thus emittance, as noted by Duffie [57] and Edwards et al. [58] have suggested several mechanisms of selectivity of energy-absorbing surfaces. These mechanisms, or reasons for selectivity, include: a) Variation of the optical constants ‘n’ (index of refraction) and ‘K’ (absorptive index) with wavelength for a single surface material, b) Surface roughness of dimensions large relative to solar energy wavelengths, but small relative to long-wave reradiation (leading to multiple reflection and increased absorbtance for short-wave radiation, but having little effect on long-wave emission), c) Layers of small particles of dimensions larger than solar wavelengths but smaller than long-wave reradiation (with the particles able to absorb radiation of wavelengths less than their size but transparent to longer wave radiation), d) Thin anti-reflection films that increase absorptance, e) Thick semiconductor films, opaque to short wave radiation, but transparent to long-wave radiation, over metal substrates that has low emittance. The material’ s properties needed for performance calculations are absorptance for solar radiation and emittance for long-wave radiation. The spectral distribution of solar energy varies to some extent with solar elevation and atmospheric conditions, but for most practical purposes a single value of α can be used irrespective of this small variation. Emissivities for long-wave 76

radiation are, to some degree, a function of surface temperature, with values of ε frequently given for temperatures near usual air temperatures and occasionally for higher temperatures. These data on α and ε are measured by heat balances under known or controlled conditions where the radiant fluxes can be determined or are calculated from measurements of reflectance at various wavelengths as determined with appropriately equipped spectrometers.

Table 3.1 shows α and ε for several surfaces of current or potential interest in various solar applications.

Table 3.1 Some α and ε for surfaces for solar energy applications [57]. Surface

α, solar

ε, at temperature

Approximate upper

radiation

less than 100°C

temperature range of application

CuO on Al

0.85

0.11

Tabor, Ni-black

0.89

0.12

0.91

0.16

0.75

0.10

with

0.80

0.35

black

0.93

0.93

0.95

0.91

200°C

treatment on galvanized iron

Stainless steel, 16%

204°C

Cr, heated for 3 hrs at 600°C All

treated

KMnO4 Commercial paints Platinum black

77

900°C

For the achievement of a selective surface, the study carried out by Hottel and Unger can be given as an example. Hottel and Unger [19] prepared a selective black surface absorber at M.I.T. in 1959. They first extensively studied the optical properties of aluminum surfaces and found that any anodyzing would increase the low temperature absorbtivity above the value for pure aluminum, because of the infrared absorption bands of the aluminum oxide. Then by spraying a dilute solution of cupric nitrate onto a heated aluminum sheet, a thin light green coating was performed on the aluminum surface, which upon heating above 170°C was converted to the black cupric oxide. Calculation of solar collector performance leads to the conclusion that the efficiency of a one-glass plate collector with a selectively black receiving surface lies between the values for non-selective black systems containing two and three glass plates and nearer the latter. This is based on a selective surface with low-temperature emissivity of 10 % and absorbtivity for sunlight of 92 %. For the collection of solar energy, if a particular surface does not have enough selectivity, one or more filters can be added which will let the energy coming from the source hit the absorbing surface, but then prevent the energy radiated from this surface from being absorbed. The filter does this by both reflecting part and absorbing part of the energy radiated from the surface. A great number of filter materials can be used both of the solid and liquid type, to form a highly selective system when combined with an otherwise not very selective surface. Some of the materials, which can be used as filters, due to their selective spectral transmission, are water, copper sulfate (CuSO4. 5H2O), solex heat absorbing glasses, heat transmitting glass and plastic [59]. Experiments showed that, for solar energy collection, water, copper sulfate, and the solex heat absorbing glass are the best of the filters whereas the heattransmitting glass proved to be the poorest. 78

Irvine et al. [60], studied the absorbtivity for solar radiation of a number of porous surfaces such as Poroloy surfaces and modified Tyler materials. The Poroloy materials used in their investigations were commercially fabricated stainless-steel wire wound on a mandrel one layer over another to yield the desired porosity. The material was then sintered and chemically treated to yield the appropriate proportions of chromium and nickel for the stainless steel Poroloy specimens tested. The modified Tyler materials were composed of screens, which had been fabricated by a special weaving process. The screens were then rolled to give the desired porosity. The experiments showed that the coated surfaces have collector efficiency higher than the porous surfaces. However, since the aging and mechanical strength characteristics of the coating have been a disadvantage in their use, porous surfaces can be thought as an alternative to the coated surfaces in solar energy applications. It can be concluded that the solar absorber plate must permit effective transfer of heat from the surface absorbing the radiation to the heat transfer fluid. It should be cheap, corrosion resistant and compatible with the heat transfer fluid and permit ready connection to external piping. Furthermore it should permit applications of the desired surface coating and the flow passages and manifolding for the absorber plates should be designed to have uniform flow distribution throughout the plate, a small overall pressure drop through the plate, and passage spacing and sizing must be selected for high fin efficiency. 3.3.2. The Covering Materials The collector cover is the material covering the aperture to provide thermal and environmental protection. Part of the solar energy impinging upon a stack of glass or plastic cover plates is reflected part of it is absorbed, and the 79

remainder is transmitted to the absorber plate. The solar energy transmittance is a function of the composition, surface treatment and thickness of the cover plates and the angle of incidence of the radiation. Not all of the energy absorbed by the cover plates is lost, since this energy raises the temperature of the glass plates and thus reduces the upward losses from the absorber plate. Similarly, part of the reflected energy from the absorber plate is absorbed by the glass plates and reduces upward losses. Significant developments in cover materials for solar energy collectors have been made in the field of plastic [57]. The new materials have properties unlike those of glass and have advantages and disadvantages relative to glass. The properties of glass can be modified and controlled to improve the performance of glass as a cover material. A. Plastics as a Cover Material Several newly available plastic films can be considered for covers for solar collectors. Some of these plastic films are fluorocarbon film, Teflon, polyvinyl fluoride film, Tedlar, and polyester film, Mylar type W. These materials differ in chemical composition, physical and radiation characteristics. They should not, in general, be considered as direct substitutes for glass, as collector designs should be modified to account for the different properties of the various plastic films. The more unusual properties of these films can be summarized as: a) They are used in thin sections (25µm to 125 µm), b) They are generally partially transparent to long-wave radiation,

80

c) Their physical properties are, in most cases, strong functions of temperature, which must be considered in design, d) Their lifetimes are limited by weathering. Weatherability the ability of a material to retain its properties when exposed to weather, radiation, moisture, flexing due to wind, etc. – is a critical property of plastics. It is a combination of optical, physical and chemical properties, and a structural factor that determines the potential lifetime of a material under given conditions is not available. However, the projected lifetimes of three unsupported films exposed to Florida weather is noted [57] as: Teflon, 20+ years; Tedlar, 9 years; Mylar type W, 4 years. The properties vary with temperature and exposure time. Of particular concern for solar collector is the solar-radiation transmittance of the film. Teflon and Tedlar have the advantage of relatively low refractive index, with resulting low reflection loss and good transmission. The films being thin, absorption is also low [57]. B. Glass as a Cover Material Glass, in its varying compositions, has properties that have long been used to advantage in solar collectors. Glass of low iron content, having a refractive index of 1.52, has a transmissivity of 0.90 for solar radiation at normal incidence [57] (The transmisivity of glass can be increased by adding films of refractive index intermediate between glass and air. Transmissivity can thereby be raised to 0.95). Glass has the advantages of very long-life if properly supported and protected from shock, and low transmissivity for longwave radiation.

81

Several investigators treat with the effects of several variables of glass specifications on the usefulness of glass covers. Composition can be altered to control the cut-off wavelength above which the glass becomes essentially opaque. For a cover material for high-temperature collectors, where the wavelengths of emitted radiation begin to overlap the solar spectrum, borosilicate glass (Pyrex) is suggested. Because its transmissivity cuts off sharply at wavelengths below 2.5µm, it is opaque for the short-wave end of the collector radiation. Thickness can also be varied within limits set by structural requirements and costs. The greater the thickness is, the greater the slope of the transmission curve that separates a region of high transparency from one of lower transparency. For high-temperature operation, an optimum thickness for the best performance may exist. It would be advantageous to reflect long-wave radiation rather than absorb it. It is pointed out that glasses have reflection bands up to 10 µm (the range of maximum emission for surfaces at 100°C) with the reflectance varying with the type of glass. It is also suggested that the reflectivity for longwave radiation of glass can be increased by depositing a very thin film of gold on their inner surface little additional reflection for short-wave radiation results from a change in the thickness of glass [57]. Mechanical, thermal and radiative properties of some cover materials can be found in the literature [26]. Thus as a summary, from a thermal/optical standpoint, the cover plates should be transparent to solar radiation and opaque to re-radiated infrared radiation. They should be low cost and easy to install, require little or no maintenance and be resistant to breakage and degradation. 82

3.4. BASIC FLAT PLATE COLLECTOR ENERGY BALANCE EQUATION In order to construct a model suitable for a thermal analysis of an FPC, the following simplifying assumptions will be made [4]: 1) The collector is thermally in steady state. 2) The temperature drop between the two surfaces of the absorber plate is negligible. 3) Heat flow is one-dimensional through the covers as well as through the back insulation. 4) The headers connecting the tubes cover only a small area of the collector and provide uniform flow to the tubes. 5) The sky can be treated as though it were a blackbody source for infrared radiation at an equivalent sky temperature. 6) The irradiation on the collector plate is uniform [4]. A qualitative variation of the temperature along the pipes (y-axis) and in the direction perpendicular to the pipes (x-axis) is shown in Figure 3.4. A thermal model for an FPC is built using the above assumptions, and considering quantitatively an infinitesimal length along the y-axis, at point x, y, and writing down the energy gains and losses of that point [4]. 83

Figure 3.3 Qualitative temperature distributions in the absorber plate of an FPC (a) region between two tubes (b) general temperature distribution (c) at any location y, the general temperature distribution in the x direction, (d) the temperature in the y direction [4].

The plate temperature at this point be Tp (x,y) and assume solar energy is absorbed at the rate Isαs., part of this energy is then transferred as heat to the working fluid and if the collector is in the steady state, Tp > Ta. Some of the heat loss occurs through the bottom of the collector. It passes first through the back insulation by conduction and then by convection to the environment. The back-loss coefficient is then calculated using,

Ub =

k back

(3.10)

i

the edge loss is calculated in a similar manner using,

84

Ue =

(UA)edge

(3.11)

Ap

If it is assumed that all losses occur to a common sink temperature Ta the collector overall loss coefficient UL is the sum of the top, bottom and edge loss coefficients [4]. U L = Ut +Ub +Ue

(3.12)

where the empirical equation, −1

Ut =

Nu C T p , m − Ta T p ,m (N u + f )

e

+

1 hw

+

σ (T p , m + Ta )(T p2, m + Ta2 )

(ε

+ 0.00591N u hw ) + −1

p

2 N u + f − 1 + 0.133ε p

εg

(3.13) is used for the top losses. The terms f, e, C, and hw will be calculated using,

f = (1 + 0.0089hw − 0.1166hwε p )(1 + 0.07866 N u )

(3.14)

e = 0.43(1 − 100 / T p , m )

(3.15)

(

)

C = 520 1 − 0.000051β 2 For 0< β < 700

(3.16)

hw = 2.8 + 3.0 × V

(3.17) 85

− Nu

In steady state, an energy balance that indicates the distribution of incident solar energy into useful energy gain, thermal losses, and optical losses describes the performance of a solar collector. Useful energy gain is given by

[

]

Qu = A p FR I t (τ α )e − A p FR U L (Ti − Ta )

(3.18)

where the first term is the energy gain and the second term is the energy losses from the collector per unit area. The solar radiation term It(τα)e incident to a unit collector area is a function of many parameters ; like beam and diffuse component of solar radiation on the horizontal surface, beam and diffuse transmittance and absorbtance products of the cover – absorber plate couple, slope of the collector, the zenith angle the incident angle, etc. Here the FPC heat removal factor FR, is

FR =

actual useful energy collected by a flat plate collector useful energy collected if the entire flat plate collector surface were at the inlet fluid temperature

(3.19)

and in equation it is

.

FR =

mCp A pU L

1 − exp

− A pU L F ′

(3.20)

.

mC p 86

(c)

Figure 3.4 Plate and tube configuration of FPC (a) tube bonded below plate (b) tube bonded above plate (c) tubes in-line with absorber plate [3].

Different absorber plate geometries require case consideration. Therefore it is necessary to derive the appropriate form of the collector efficiency factor F´, the following equations can be used to predict the thermal performance of an FPC [4]. In the case of tubes bonded below,

87

F′ =

1UL 1 1 1 W + + π Di h fi C b U L [Do + (W − Do )F ]

(3.21(a))

In the case of tubes bonded above,

F′ =

1 W UL 1 + D0 1 π Di h fi + WU W W L + Cb (W − Do )F

(3.21(b))

In the case of tubes in line with the absorber plate,

F′ =

1

(3.21(c))

UL 1 W + π Di h fi [Do + (W − Do )F ]

Here, for all the above- mentioned cases, the fin efficiency is,

F=

tanh [m (W − Do ) / 2] m (W − Do ) / 2

(3.22)

and the parameter m, Cb, and hfi are,

UL m= kp δ p

1/ 2

(3.23)

88

Cb =

h fi =

k b × bw

(3.24)

γb

Nu k Di

(3.25)

Thermal conductivity of galvanized iron absorber plate is calculated as shown in APPENDIX A.

3.5. EFFICIENCY OF A FLAT PLATE COLLECTOR 3.5.1. Thermal Efficiency of A Flat Plate Collector It has been shown and discussed by a number of investigators [4, 5, 14] that the efficiency ( ) of an FPC operating under steady-state conditions can be described by the following relationship:

η=

Q actual useful energy collected = u solar energy incident on the collector I t Ap

89

(3.26)

CHAPTER 4

MATERIALS AND METHODS

OPTIMIZATION, ECONOMY, PRODUCTION AND THERMAL PERFORMANCE TESTING

4.1. OPTIMIZATION OF FLAT PLATE COLLECTORS

The most serious drawback to the more wide spread adoption of solar water heating is the high initial cost of the equipment, particularly the collector absorber plates which are often the single most expensive item in this system. Thus a strong incentive is present for reducing the cost of this component. Possible methods of achieving this aim include, a) Improvement of manufacturing methods, b) Optimum choice of materials, c) Optimum choice of plate geometry, and particularly the best combination of fin thickness and spacing between pipes in collectors of the pipe and fin type [45]. 90

This study examines the latter two proposals by considering economy and efficiencyAssuming that materials have been chosen for the pipe and the fin, the material cost of the collector plate depends largely on the thickness of the fin and tube spacing. Material costs were obviously being reduced if fins were thinner and spacing between pipes was greater. However, this also leads to a reduction in the fin efficiency. Obviously a compromise is required to minimize the overall cost of the system for a given energy output.

4.1.1. Choice of Fin Material The function of the fin is to absorb the incident solar energy and to transfer it by conducting to the pipe at the center of the fin. In our study, galvanized iron was considered as the fin material because of the following reasons: a. Iron is cheaper than copper and aluminium. b. Galvanized iron is resistant to humidity and corrosion. c. Processing of iron is easier. In Table 4.1, some physical properties of possible fin materials and their prices are listed. Although thermal conductivity of iron is smaller than that of others as can be seen in the same table, because its price is much lower

(Table 4.1) galvanized iron was used as the fin material. Calculations also showed theoretically that we could reach approximately the same efficiency as commercially available collectors. Result is shown in APPENDIX B.

78

Table 4.1.Physical properties of Al, Fe and Cu and their prices. Material

Thermal Conductivity

Density

Price

(W/mC)

(kg/m3)

(TL/kg)

Fe

73

7870

200.000 TL

Al

204

2700

2.000.000 TL

Cu

386

8960

2.000.000 TL

All the price calculations are done when DM 1=365.000TL (February 2001). To start the optimization of geometry, first the proposed alternatives for the collector properties for aluminum, copper and iron collectors were examined [61].

PROPERTIES

ALTERNATIVES

Number of tubes

6-12

Tube spacing

90-170 mm

Inner diameter of tubes

10-13 mm

Outer diameter of tubes

10.5-13.5 mm

Then, prices of such materials, which are commercially available, were obtained from the companies, which are shown in APPENDIX C.

4.1.2. Choice of Thickness of Plate and Pipe Spacing 79

As it can be seen from the Eq.3.22 under “Basic Flat Plate Energy Balance Equation” in Section 3.4, efficiency of a collector mainly depends on three parameters; these are tube spacing, tube diameter and plate thickness.

4.2 THE COMPUTER PROGRAM A Microsoft EXCEL program is developed to calculate, the direct solar radiation energy incident on a plane at a given location, declination angle of the sun, hour angle, angle of incidence, azimuth angles and extraterrestrial solar insolation for each specified time of the day. Finally, collector heat removal factor, absorbed solar radiation, overall loss, the useful energy and efficiency of collector and price of an absorber plate are calculated. Numerical values of the parameters used in optimization of collector efficiency are presented in APPENDIX D. All the efficiency equations were written by using EXCEL, then price and efficiency results were calculated for different values of tube thickness, tube diameter and plate thickness by using the program to find the best combination in terms of collector efficiency and cost effectiveness, to achieve qu/price to have its maximum value. So that, the collector should be efficient. Collector areas were kept the same as the commercially available collectors. However, the number of tubes was changed.

80

4.3. ECONOMIC CONSIDERATION The use of solar energy for heating water or air to temperatures lower than 100 °C is an established process with adequately described technology. The economic aspects of various designs have received some attention, and research effort has been applied toward optimizing the design with respect to different parameters [62]. The costs of solar energy collecting systems differ depending upon the type of material for the case of collectors, absorber plate and water storage tank. Copper is more expensive material than regular steel; usage of copper thus increases the production cost of the systems. For the collecting case and the absorber plate various combinations of materials can be used: for instance, regular steel for the absorber plate or aluminum as the material for both the collecting case and absorber plate. A collector consisting of galvanized steel outside the case and regular steel absorber plate will be the least expensive system, if it has a water tank with internal and external layers made of galvanized steel. Costs of the systems at the stage production can vary by as much as 300%, depending upon type of the material [7].

4.4. ECONOMIC ANALYSIS OF ABSORBER PLATE The price of absorber plate is the sum of plate material price, galvanization, price of tubes and headers, in equation it reads like, P = AP [PPL + PPN + ] + G + N [ PTB + PPW + 2 PW ]+ 2aPH where 81

(4.1)

N=

a W

, A p = a.b

(4.2), (4.3)

and G = (PG × VTL / 1000 ) × ( × N × UWtubes + 2 × LH × UWH + WP )

(4.4)

where PG = DM 438, price of galvanization is DM 438 per tones of iron. and VTL = 525000 TL, although DM 1=365.000TL during the calculation for cost of galvanization and paint, DM 1 is taken equal to 525.000TL. UW = π (Ro2 − Ri2 )ρ

(4.5)

W p = ρ Ee × a × b × δ p

(4.6)

Price calculation includes labour cost which is calculation of 50% of the price of the work. The program is run for 250 possible combinations of numerical values of three parameter and their efficiency values. The relation among three different parameters and collector efficiency values and their graphical explanations with three different materials for different parameters, price lists, efficiencies and related graphics are given in APPENDIX E. Prices and properties of the collectors having copper and aluminum fins were obtained from DA SAN and STEK companies (Table 4.2).

82

Table 4.2 Collector properties and prices. Material

Do

W

δp

N

Dh

Price of absorber plate

mm

mm

mm

mm

DM

Galvanized Fe

13 x 1

90

1

10

32

43

Al ( stek)

16.6 x 2.8

74

1.5

12

30

100

Cu ( stek)

12.7 x 1

110

0.18

8

22

60

Cu (Da san)

12.7 x 0.7

100

0.4

9

28

100

4.5. CONSTRUCTION OF A NEW ABSORBER PLATE In this study after deciding on the material and optimal geometrical parameters, construction of an economical and efficient absorber plate was carried. The construction of the new absorber plate is based on two points: first one is the utilization of point welding to get a good conduction and second one is the galvanization of the iron absorber plate to increase fin efficiency and reduce corrosion. Point welding is a cheap process since during its operation the only requirement is the electricity. Before welding, material should be cleaned. The calculation of the price of point welding is given below: One point welding is done in one second; one fin includes 50 point welding point. One collector has 10 pipes, thus to construct one absorber plate 500 seconds is required.

83

Point welding specifications: 380 volt selective, 4 ampere The consumed electricity during point welding operation is: 380 Volt x 4 Ampere x 500/3600 =211.1 Wh = 0.211kWh According to Turkish Electricity Distribution Corporation price of 1 kWh electricity for industrial usage was 63.400TL in March 2001. It differs for cities having priority for development (58,600TL), for organized industry site 5% reduction [63]. Then, 0.211 kWh costs 13.377TL and with 5% reduction it is 12.708TL. For cities having priority for development 12.365 TL with 5% equals 11.747TL. During the price calculation and optimization the highest price (13.377TL) is considered.

Absorber plate and tubes joined together by using point welding. In order for point welding to be applied easily, the absorber plate was constructed by combining ten fins. Construction steps are shown below: 1. Ten absorber plate fins of length 178 cm and thickness 1 mm were cut (9 of which have a width of 90 mm and 1 having width of 80 mm), 2. Pipes diameter, thickness and length of which were 13 mm, 1mm and 180 cm, respectively, were constructed and connected to the cut absorber plate at the middle, 3. Header and footer were constructed by using 2 pipes with length of 96 cm, diameter of 32 mm and thickness of 1 mm, fourth fins were attached to each other, side by side together with the header and footer. 84

Following the welding, absorber fins, tubes, header and footer were galvanized together (Figure 4.1). In order to galvanize the iron, the absorber plate was dipped into the liquid zinc pool, a few minutes, and iron is covered with zinc, which was at 450 °C (Figure 4.2). The absorber plate was dipped into the pool in an inclined position so that inner surfaces of the pipes could be galvanized efficiently. Galvanization is the processes, which is required against corrosion.

Figure 4.1 Sample fin for the constructed FPC.

85

Figure 4.2 4.5 x 1.8 x 2.5 m fully automated galvanization pool at M TA .

To prevent the absorber plate from deformation, below suggestions should be considered. 1.

The part to be galvanized should be symmetrical. Asymmetrical

parts easily get deformed. 2.

Welding procedure leads to local temperature differences on the

material thus inner resistance. To avoid occurrence of this resistance, welding should be done continuously. 3.

The materials, which have different thicknesses, have different expansion and contraction properties. Thus the materials to be welded to each other should have the same or smilar thicknesses.

4.

The material should be produced smooth and homogeneous. 86

5.

Dimensions of the materials are also important. Dimensions should be appropriate for a one-time hot dip galvanization pool, if the galvanization is repeated deformation could occur.

The galvanized fins were examined; bond width and bond thickness are determined. Using Eqn. 3.24. Cb was calculated as, Cb = 793W/mC Bond conductance has different calculations for Fe, Cu and Al [4]. Header and footer cross-sectional areas were calculated by considering the smooth flow distribution, as below: AT = π (D0 / 2)2

(4.7)

AH = (N+1) AT

(4.8)

Header and footer were prepared having 10 holes with the radius of 12 mm, which should be parallel to each other (Figure 4.3). They were prepared before galvanization, then they were attached to the fins with oxygen welding, the absorber plate was tested for water leakage.

7.5cm 9cm

9cm

9cm

9cm

9cm

9cm

9cm

9cm 9cm 7cm

Figure 4.3 Header and footer with tube spacing.

In order for the collector paint to stick to the surface well, 35 gr of polyvinyl butyral was added to 1

of the paint in addition to 300 gr of thinner. The

paint, which is obtained from the DA SAN, was sprayed on the surface with a 87

paint-gun having an outlet pressure of 3.5 atmospheres. The thickness of paint was 5-10 microns. The price of paint is given as DM 2 per collector for DA SAN ’ s FPC that is painted 50 to 100 microns. Constructed absorber plate was placed into the collector cover (Figure

4.4) supplied by STEK.

(NA)

(a)

(b) Figure 4.4 (a) Close view of produced collector, (b) Another close view of produced collector. 88

4.6. PREPARATION OF THE EXPERIMENTAL SETUP In order to be able to make comparisons between three collectors produced in Turkey with the constructed collector design for this study, a standard testing procedure has to be followed. This study presents one such standard procedure. A test set-up is prepared at the roof of Physics Department at METU Campus for this purpose by considering the followings: The four collectors were directed to the south with the most appropriate angle (β), which maximize the incoming solar energy on the collector surface in summer in Ankara. The collector slope was calculated by subtracting 15 degrees from latitude of ANKARA, where the experiment was performed. Plumbing system was installed, the water storage tank and connecting pipes were insulated with insulation material so that they don’ t lose heat. As it can be seen in the Figure 4.5 thermometers were placed at the center of the pipes to measure inlet and outlet water temperatures.

89

Figure 4.5 The flat plate collectors under test. In Figure 4.5, the collector on the left is constructed galvanized iron collector, second is DA SAN’ s copper collector, third is STEK’ s copper collector, fourth is STEK’ s aluminum collector.

4.7.TESTING OF FLAT PLATE COLLECTORS TO DETERMINE THEIR THERMAL PERFORMANCE 4.7.1. Purpose In this part of the study, experiments were carried out according to the requirements and instructions approved by the ASHRAE Standard [5] which is applicable to both non-concentrating and concentrating solar collectors employing single inlet and outlet of transfer fluid. This standard contains 90

methods for conducting tests outdoors under natural solar irradiation and for conducting tests indoors under stimulated solar irradiation, and provides test methods and calculation procedures for determining steady state and quasisteady state thermal performance, time constants of solar collectors. In this study outdoor test is conducted.

4.7.2

Testing Preconditions Solar collectors are tested in accordance with the following

requirements [5]:

1)

The collector whose thermal performance is to be tested was pre-

conditioned prior to initiation of the test. Pre-conditioning consists of stagnation heat in a non-operational mode in a dry condition for three days in which the cumulative mean incident solar radiation measured in the plane of the collector is 17000 kj/m2-day. In this study collectors were exposed to that radiation.

2)

The size of collector to be tested is large enough so that the

performance characteristics determined are indicative of those that would occur when the collector is part of an installed system. The cover sizes of collectors used in this study are the same with standard ones (2x1m2).

3)

For tests conducted outdoors to determine thermal performance, the

collector is mounted in a location such that there will be no significant energy reflected or reradiated onto the collector from surrounding buildings or any other surfaces in the vicinity of the test stand for the duration of the tests. Experiment setup was installed according to these considerations.

91

4)

For tests conducted outdoors to determine thermal efficiency, the

tests are conducted at times having weather conditions such that the integrated average irradiation measured in the plane of the collector or aperture, reported and used for the computation of instantaneous efficiency values shall be not that less than 630 W/m2. During the study it was between 924 W/m2-1034 W/m2.

5)

For tests conducted to determine thermal efficiency at near-normal

incident conditions, the orientation of the collector is such that the incident angle (measured from the normal to the collector surface or aperture) is less than 30° during the period in which test data is being taken. Data were taken from one hour before solar noon to one-hour after the solar noon and the orientation of the collectors were 15 degrees.

6)

For tests conducted outdoors to determine collector thermal

efficiency, the range of ambient temperatures for all reported test points comprising the “efficiency curve” are less than 32 °C. In the study it was between 25°C – 34°C.

7)

The transfer fluid used in the solar collector has a known specific

heat, which varies by less than 0.5% of the temperature range of the fluid during a particular test period. The density of the transfer fluid is also known and it does not vary by more than 0.5% over a particular test period. Water is used as the heat transfer fluid and it obeys the above criterion.

4.7.3. Apparatus and Instrumentation A Kipp and Zonen Epply type pyranometer, shown in Figure 4.6 is used for measuring the total radiation incident upon the collector surface. It is 92

mounted such that its sensor is co-planer with the plane of the collector aperture so that it will detect incident radiation on the plane of the collector and it shall not cast a shadow onto the collector aperture at any time during test period. The calibration constant of the pyranometer is 9.19x10-6VW-1m2± %5.

Figure 4.6 A Kipp and Zonen type pyranometer used in measurement of solar radiation. Omni-Scribe-D5000 type chart recorder is shown in Figure 4.7, is connected to the pyranometer to record the total irradiation during the test periods.

93

Figure 4.7 An Omni-Scribe-D5000 type chart recorder. All temperature measurements (inlet, exit, and ambient temperatures), thermometers are used. In order to obtain different inlet fluid temperatures, needed for the construction of the efficiency curves, an electrical heater of 6 kW capacity is used. This heating capacity is able to raise the temperature of the inlet fluid with the prescribed flow rate of 0.02 kg/s.m2.

4.8. USEFUL THERMAL PERFORMANCE EQUATIONS FOR CALCULATION 4.8.1. Collector Time Constant It is necessary to determine the time constant of the solar collector in order to be able to evaluate the transient behavior of the collector, and to select the proper time intervals for the steady state efficiency tests. Whenever transient conditions exist, the qualities defined and do not govern the thermal performance of the collector since part of the solar energy absorbed is used for heating up the collector and also its components like glass cover, insulation material, back cover etc. 94

The governing equation for the transient behaviour of solar collector is: mCp C A dT f = FR I t (τα )e − FRU L (Ti − Ta ) − (To − Ti ) A p dt Ap

(4.9)

If (a) the solar radiation It, or inlet fluid temperature Ti or both It and Ti are suddenly changed and held constant and if (b) (τα)e, UL, Ta, m and Cp can be considered constant for the transient period and (c) the rate of change of the transfer fluid exit temperature with time is related to the rate of change of transfer fluid average temperature with time by

d Tf dt

=K

d To dt

(4.10)

where

K=

mCp F U L Ap

F′ −1 FR

(4.11)

Then, Eq.4.9 can be solved to give the exit temperature of the transfer as a function of time. FR I t (τ α )e − FRU L (Ti − Ta ) − (mC p A p )(To − Ti )

FR I t (τ α )e − FRU L (Ti − Ta ) − (mC p A p )(To ,initial − Ti )

=e

−

mCp K CA

t

(4.12)

The quantity KCA/ m Cp is known as the “time constant” and is the time required for the quantity of the left side Eq 4.12 to change from 1.0 to 0.368 where 0.368=1/e. 95

4.8.2 Collector Thermal Efficiency Considering Eq. 3.27 for the efficiency of an FPC and rewriting it in explicit form one obtains

η = FR (τ α )e − U L

(Ti − Ta )

(4.13)

It

which is at the same time in the form of

η=

m C P (To − Ti ) Ap I t

(4.14)

Eq.4.13 indicates that if the efficiency is plotted against (Ti-Ta)/It, a straight line will result where the slope is equal to FRUL and the y-intercept is equal to FR(τα)e. In reality, UL is not a constant but rather a function of the temperature of the collector and of the ambient weather conditions. In addition, the product (τα) varies with the incident angle between the solar radiation and the collector.

4.9. TESTING PROCEDURE All calculations and experiments are performed using solar time [4]. The calculation of the solar time is as follows: 96

Solar time = Standart time + 4 (Lst - Lloc) + E

(4.15)

where E = 229.2 (0.000075 + 0.001868 cosB – 0.032077 sin B –0.014615 cos2B –

(4.16)

0.04089 sin 2B)

where (4.17)

B = (nd – 1) 360/365

where; Lst : 30, Lloc : 32.88 for Ankara The first performance test to be conducted on the solar collector is the determination of its “time constant”. The method for conducting this test is explained in Section 4.8.2. After this is completed, a series of thermal efficiency tests are conducted as explained in Section 4.8.3.

4.9.1. Measurements a) Radiation Measurements The output of the pyranometer is recorded continuously from one hour before solar noon to one hour after solar noon every day on a calibrated automatic Omni-Scribe-D5000 model chart recorder.

b) Temperature Measurements

97

An ordinary mercury thermometer measures the ambient temperature periodically. An ordinary mercury thermometer measures inlet and outlet temperatures of water, which pass through the collector plate.

d) Flow Rate Measurements The flow rate of transfer fluid through the collector is standardized at one value for all data points. The recommended value of flow rate per unit area for tests is 0.02 kg/s.m2 when water is used as the transfer fluid. The flow rate is adjusted to this value by recording the amount of water in grams/second coming out from the collector. During the experiment it was kept constant. Thermal performance data are taken at five times the time constant [5]. The measured radiation and temperature values are listed in APPENDIX F.

4.9.2. Experimental Determination of the Collector Time Constant There are two methods for the determination of the collector time constant; one is cooling and the other is the heating method. In this study the former is used. Here is the summary of the cooling method: The inlet temperature of the transfer fluid, Ti, is adjusted to within ±1°C of the ambient temperature while circulating the transfer fluid, water, through the collector at the flow rate specified in Section 4.7.2 and maintaining steady state or quasi-steady state conditions with an incident solar flux of greater than 98

790 W/m2. The incident solar energy is then abruptly reduced to zero by shielding the collector from the sun. This may be accomplished shading with a white, opaque cover. The cover should be suspended off the surface of the collector so that ambient air is allowed to pass over the collector as prior to the beginning of the transient test. The temperature of the transfer fluid at the inlet, Ti, and outlet, To are continuously monitored as a function of time until the quantity To (t ) − Ti 1 < To,initial − Ti e

(4.18)

is reached. The time t at which the above equality is reached is called the time constant of the collector. The experiments carried out to find time constant were performed on July 18, between the time period preceeding solar noon and the period following solar noon, for each of the four collectors one by one. The study was performed under quasi-steady state conditions with an incident solar flux of greater than 790 W/m2. The incident solar energy was abruptly reduced to zero by shielding the collector from the sun by shading with a cover.

4.9.3. Experimental Determination of the Collector Thermal Efficiency The testing of the solar collector to determine its thermal efficiency is conducted in such a way that a governing “efficiency curve” for near normal 99

incidence is determined for the collector under test conditions described in the previous sections. At least four data points are taken for each value of Ti; two during the time period preceding solar noon and two in the period following solar noon, the specific periods being chosen so that the data points represents times symmetrical to solar noon. This latter requirement is made so that any transient effects that may be present will not bias the test results when they are used for design purposes. The efficiency curves will be established by data over a time period equal to the time constant over 5 minutes. In conducting the test outside, intensive care is taken to ensure that the incident solar energy is steady for each time interval during which an efficiency value is calculated. Thermal efficiency and time constants of all the collectors are compared at the same tilt angles (Figure 4.5). Figures 4.8 and

4.9 show a strip chart recording of incident solar radiation on a 25° inclined surface with a chart speed of 10 cm/s. The conditions of Figure 4.8 are perfectly acceptable for obtaining efficiency values, whereas those of Figure

4.9 are not. The experiments were performed from July 26 to August 07.

100

Figure 4.8 Chart recording of incident solar radiation, mV versus time.

101

Figure 4.9 Chart recording of incident solar radiation for a cloudy day, mV versus time.

4.9.4. Computation of Collector Thermal Efficiency

Eq.4.14 was used to calculate the thermal efficiency. At least twenty data points are obtained for the establishment of each efficiency curve and an equation for the curve is obtained using the standard technique of a leastsquares fit. 102

CHAPTER 5

EXPERIMENTAL RESULTS AND DISCUSSION

5.1 RESULTS OF OPTIMIZATION

According to optimization results, to find an economic and efficient absorber plate, five main FPC parameters are found to be applicable as stated in Table 5.1.

Table 5.1 Optimum FPC parameters. Thickness of plate

W

Do

Di

Number of pipes

0.001m

0.09m

0.013m

0.012m

10

Although 0.0005m, 0.0007m, 0.0008m thick absorber plates are more suitable according to our calculations because of the deformation occurring during galvanization and ruptures occurring during point welding their usage are impossible.

103

5.2 FLAT PLATE COLLECTORS USED IN THE EXPERIMENTS Four different types of flat plate solar collectors are tested during the experiments. Three of these collectors are commercially produced in Turkey and the fourth one is a new type, designed and constructed during this study. The descriptions and specifications of these collectors are given below:

105

5.2.1 ISTEK’s Collectors ( Standard ) a) Aluminum Collector

Figure 5.1 Cross-section of the FPC, which has aluminum absorber plate. PANEL

:The panel constructed from Etial-60

extrusion aluminum profile with 12 tubes whose diameter is 16 mm and thickness is 1.5 mm. The manifold tube is 30 mm. The panel surface is blacked painted.

CASING

: 1.2 mm thick extrusion aluminum profile.

INSULATION

: Glass wool

SEALING

: EPDM rubber that is resistant to the difference of temperature.

: ¾′′ Aluminum tips

OUTLET DIMENSIONS

: 1940 mm/940 mm/100 mm

GROSS AREA

: 1.82 m2

NET AREA

: 1.71 m2

TUBE SPACING WEIGHT of COLLECTOR

: 74 mm : 35 kg

103

b) Copper Collector

Figure 5.2 Cross-section of the FPC, which has copper absorber plate. PANEL

: 0.18 mm thick plates are stitched by ultrasonic

welding to the copper tubes whose diameter is 12.7 mm and thickness is 1 mm, it consists of 8 tubes, the manifold tube diameter is 26-28 mm and thickness is 0.8 mm the surface of the panel is coated with special collector paint.

INSULATION

: Glass wool

SEALING

: EPDM rubber that is resistant to the difference of temperature.

OUTLET

: ¾′′

DIMENSIONS

: 1940 mm/940 mm/100 mm

GROSS AREA

: 1.82 m2

NET AREA

: 1.71 m2

TUBE SPACING

: 110 mm

WELDING WIDTH

: 8 mm

BOND THICKNESS

: 0.8 mm

WEIGHT of COLLECTOR: 35 kg 104

5.2.2. DA SAN’s Copper Collector ( DBC 90190 ) As shown in the Figure 4.7, this collector has the following characteristics:

PANEL

: 0.4 mm thick plates of what are stitched by

ultrasonic welding to the copper tubes whose diameter is ½′′ and thickness is 0.7 mm it consists of 9 tubes, the manifold tube diameter is 22 mm and thickness is 0.8 mm the surface of the panel is coated with special collector paint. INSULATION

: Glass wool

SEALING

: EPDM rubber, which is resistant to the difference of temperature.

OUTLET

: ¾′′

DIMENSIONS

: 1945 mm/945 mm/105 mm

GROSS AREA

: 1.82 m2

NET AREA

: 1.64 m2

TUBE SPACING

: 100 mm

WELDING WIDTH

: 8 mm

BOND THICKNESS

: 0.8 mm

WEIGHT of COLLECTOR: 38 kg

105

5.2.3 CONSTRUCTED COLLECTOR WHICH HAS GALVANIZED IRON ABSORBER PLATE The collector as shown in Figure 4.6 has the following characteristics: PANEL

: 1 mm thick plates are stitched by point

welding to the iron tubes whose diameters is 13 mm and thickness is 1mm, it consists of 10 tubes, the manifold tube diameter is 32 mm and thickness is 1.2 mm the surface of the panel is coated with 10 micron special collector paint. INSULATION

: Glass wool

SEALING

: EPDM rubber that is resistant to the difference of temperature.

OUTLET

: 5/4′′

DIMENSIONS

: 1940 mm/940 mm/100 mm

GROSS AREA

: 1.82 m2

NET AREA

: 1.602 m2

TUBE SPACING

: 90 mm

WELDING WIDTH

: 13 mm

BOND THICKNESS

: 2 mm

WEIGHT of ABSORBER PLATE : 19.7 kg WEIGHT of COLLECTOR

: 50 kg

106

5.3. EXPERIMENTAL RESULTS – COMPARISON AND DISCUSSION 5.3.1 Collector Time Constant Following the experimental procedures given in Sections 4.8.2 and 4.8.3 time constants of the tested collectors are determined to be 137 seconds for STEK Al, 75 seconds for STEK Cu, 95 seconds for DA SAN, and 198 seconds for galvanized iron collector. The sample calculations are given in APPENDIX G. The transient behavior of the collectors can be discussed referring to these figures. The response of STEK’ s copper collector to sudden changes in incoming solar radiation is very rapid when compared with the other three. This means that it requires less time for the system to warm up and cool down with a sudden change in the solar flux. A solar collector having a short time constant may be advantageous if hot water is required shortly after the system starts operation. But if hot water demand is for a time after the system shut down or on partly cloudy days, a collector having a long time constant will be more advantageous since it would take a long time for the system to cool down when the sun is shaded with the clouds. It is up to the user to chose or designs a solar collector, having a short or long time constant, that fits best to his requirements.

5.3.2 Thermal Efficiency The selected data for efficiency calculations and the related efficiency curves are given in Figures 5.3(a)(b)(c)(d),(APPENDIX F).

5.3.2.1 Comparison of the Intercepts of The Efficiency Curves Figures 5.3 shows

efficiency values versus (Ti-Ta)/It. In all the figures it is

seen that STEK’ s aluminum collector performs more efficiently than the others at relatively low operating temperatures. When (Ti-Ta)/It gets higher, overall loss increases significantly as expected. 107

When (Ti-Ta)/It is small, efficiency values of all the tested collectors are satisfactory. The intercept points are shown in Figure 5.3(a)(b)(c)(d). For STEK’ s aluminum collector, it is 0.90, for STEK’ s copper collector it is 0.66, for DA SAN’ s copper it is 0.81, and for the collector that has galvanized iron absorber plate, it is 0.82 which is increased up to 0.83 after new optimization.

STEK's Al

y = 0.90+(-8.1)x

efficiency

1 0.8 0.6 0.4 0.2 0 0

0.005

0.01

0.015 (Ti-Ta)/It

(a)

108

0.02

0.025

0.03

STEK's Cu

y = 0.66+(-3.7)x

efficiency

1 0.8 0.6 0.4 0.2 0 0

0.005

0.01

0.015 0.02 (Ti-Ta)/It

0.025

0.03

(b) Figure 5.3. Collector performance data a) for STEK’ s aluminum collector, b) for STEK’ s copper collector, c) for DA SAN’ s copper collector, d) for collector, which has galvanized iron absorber plate.

DA SAN's Cu y =0.81+(-4.0)x 1 efficiency

0.8 0.6 0.4 0.2 0 0

0.005

0.01

0.015 (Ti-Ta)/It

(c) 109

0.02

0.025

0.03

Galvanized Fe

y = 0.82+(-10)x

1 efficiency

0.8 0.6 0.4 0.2 0 0

0.005

0.01

0.015 0.02 (Ti-Ta)/It

0.025

0.03

(d) Figure 5.3.(Continued). 5.3.2.2 Comparison of the Slopes of the Constructed FPC with the Other Collectors Efficiency curves of galvanized iron absorber plate and that of other collectors are shown together in the same graph one by one as indicated in Figure 5.4 (a)(b)(c). From the characteristic equations of the efficiency curves heat transfer loss coefficients of the collectors are determined. FRUL values for STEK’ s aluminum collector for 250 tilt angles are 8.1 W/m2-°C (Figure 5.4 (a)). For STEK’ s copper collector this value is 3.7 W/m2-°C (Figure 5.4 (b)). For DA SAN’ s copper collector it is 4.0 W/m2-°C (Figure 5.3 (c))

and for the produced

collector that has galvanized iron absorber plate, this value is 10 W/m2-°C. 110

As it can be seen from Figure 5.4 loss of galvanized iron absorber plate is higher. Therefore a new optimization was done to reduce the loss.

STEK' s Al and Galvanized Fe

efficiency

1 0.8 0.6

y =0.9+(-8.1)x

0.4 0.2 0

y =0.82+(-10)x

Al Fe

0

0.01

0.02

0.03

(Ti-Ta)/It

(a)

STEK's Cu and Galvanized Fe

efficiency

1

y = 0.82+(-10)x

0.8 0.6 0.4

y =0.66+(-3.7)x

0.2

Cu

0

Fe

0

0.005

0.01

0.015 (Ti-Ta)/It

(b) 111

0.02

0.025

0.03

Figure 5.4. Comparison of efficiency curve of galvanized iron absorber plate and (a) STEK’ s aluminum collector, (b) STEK’ s copper collector, (c) DA SAN’ s copper collector.

DA SAN's Cu and Galvanized Fe 1

y =0.81+(-4.0)x

efficiency

0.8 0.6

y = 0.82+(-10)x

0.4 0.2

Cu

0 0

0.005

0.01

0.015

0.02

0.025

0.03

Fe

(Ti-Ta)/It

(c) Figure 5.4.(Continued).

5.3.2.3. Comparison of Theoretical and Experimental Efficiency Table 5.2(a)(b)(c)(d) shows comparison of experimental and theoretical efficiency results for all the collectors. The values named as the theoretical result are the calculated values using the EXCEL program.

112

Table 5.2 (a) Comparison of theoretical and experimental efficiency results for STEK’ s Al collector. Ti

Ta °C

56.9 56.3 56.7 53.4 54.6 34.0 34.2 35.0 37.0 38.0 35.0 36.0 37.0 38.0 39.0 40.0 41.0 42.0 43.0 44.0 45.0 46.0 47.0

31.8 32.5 32.7 33.6 33.9 26.4 26.9 27.2 27.6 27.8 25.8 26.8 27.8 28.8 29.8 30.8 31.8 32.8 33.8 34.8 35.8 36.8 37.8

It W/m2

η Theoretical result

η Experimental result

946.68 973.88 979.33 968.44 935.80 979.33 1006.5 1028.3 1033.7 1033.7 924.92 941.24 968.44 973.88 963.00 903.16 924.92 957.56 924.92 924.92 919.48 957.56 979.33

0.64 0.70 0.70 0.75 0.71 0.87 0.85 0.88 0.84 0.83 0.83 0.84 0.84 0.84 0.86 0.71 0.84 0.83 0.71 0.76 0.71 0.86 0.85

0.65 0.68 0.69 0.71 0.71 0.86 0.84 0.85 0.83 0.81 0.82 0.79 0.82 0.79 0.83 0.74 0.83 0.79 0.79 0.77 0.83 0.84 0.83

113

Table 5.2 (b) Comparison of theoretical and experimental efficiency results for STEK’ s Cu collector. Ti

Ta

It

°C 58.2 38.5 55.2 54.2 50.0 49.0 56.0 56.8 55.1 42.0 35.0 37.0 38.0 35.7 42.0 33.5 37.8 38.0 39.6 39.2 40.0 49.2 46.1 45.0 45.0 35.5 34.0 32.8 33.0 45.0 43.9 37.8 34.5 34.2 35.0

°C 31.7 33.2 33.7 33.8 33.7 31.8 33.5 33.2 34.0 34.0 31.8 33.5 33.2 34.0 31.8 31.8 32.0 32.1 32.7 32.0 33.0 33.5 33.4 33.3 33.4 29.0 30.2 30.8 30.0 31.1 31.2 31.7 31.0 31.7 32.0

W/m2 941.24 941.24 935.80 1033.7 935.80 924.92 946.68 968.44 957.56 946.68 930.36 963.00 963.00 946.68 924.92 1088.1 957.56 941.24 935.80 924.92 919.48 919.48 930.36 935.80 946.68 957.56 946.68 946.68 957.56 946.68 946.68 941.24 946.68 935.80 924.92

η Theoretical result 0.55 0.64 0.62 0.53 0.59 0.78 0.56 0.56 0.57 0.63 0.64 0.63 0.64 0.61 0.62 0.76 0.75 0.75 0.70 0.84 0.64 0.67 0.60 0.65 0.60 0.65 0.66 0.72 0.72 0.75 0.61 0.58 0.65 0.66 0.56

114

η Experimental result 0.51 0.60 0.59 0.47 0.53 0.74 0.58 0.52 0.58 0.62 0.55 0.57 0.63 0.54 0.59 0.72 0.71 0.71 0.73 0.80 0.61 0.68 0.56 0.62 0.62 0.66 0.67 0.72 0.69 0.71 0.56 0.53 0.62 0.66 0.55

Tablo 5.2 (c) Comparison of theoretical and experimental efficiency results for DA SAN’ s Cu collector. Ti

Ta

It

°C 48.0 38.2 55.2 54.7 50.1 47.0 55.5 56.2 54.8 43.0 35.0 37.0 38.0 35.7 42.8 35.0 34.0 32.9 33.2 33.9 38.0 38.0 39.7 39.1 40.0 52.8 49.2 46.1 45.0 45.0 43.9 38.0 35.0 34.1 35.0

°C 31.7 33.2 33.7 33.8 33.7 31.8 33.5 33.2 34.0 34.0 31.8 33.5 33.2 34.0 31.8 31.8 32.0 32.1 32.7 32.0 33.0 33.5 33.4 33.3 33.4 29.0 30.2 30.8 30.0 31.1 31.2 31.7 31.0 31.7 32.0

W/m2 941.24 941.24 935.80 1033.7 935.80 924.92 946.68 968.44 957.56 946.68 930.36 963.00 963.00 946.68 924.92 957.56 946.68 946.68 957.56 1088.1 957.56 941.24 935.80 924.92 919.48 908.60 919.48 930.36 935.80 946.68 946.68 941.24 946.68 935.80 924.92

η Theoretical result 0.76 0.81 0.76 0.73 0.82 0.62 0.72 0.75 0.77 0.77 0.82 0.72 0.71 0.73 0.77 0.85 0.86 0.87 0.85 0.84 0.82 0.85 0.86 0.86 0.85 0.77 0.69 0.68 0.78 0.74 0.69 0.70 0.67 0.78 0.81

115

η Experimental result 0.76 0.8 0.74 0.68 0.80 0.66 0.69 0.74 0.74 0.77 0.77 0.71 0.76 0.69 0.77 0.85 0.86 0.88 0.83 0.82 0.83 0.89 0.89 0.94 0.89 0.76 0.67 0.68 0.76 0.74 0.67 0.68 0.66 0.75 0.80

Table 5.2 (d) Comparison of theoretical and experimental efficiency results for galvanized iron collector. Ti

Ta

It

°C 56.9 56.3 56.7 53.4 54.6 34.0 34.2 35.0 37.0 38.0 35.0 39.1 39.9 40.1 35.8 46.9 44.6 44.0 47.0 47.0 35.6 35.0 35.8

°C 31.8 32.5 32.7 33.6 33.9 26.4 26.9 27.2 27.6 27.8 25.8 26.8 27.8 28.8 29.8 30.8 31.8 32.8 33.8 34.8 35.8 36.8 37.8

W/m2 946.68 973.88 979.33 968.44 935.80 979.33 1006.5 1028.3 1033.7 1033.7 924.92 941.24 968.44 973.88 963.00 903.16 924.92 957.56 924.92 924.92 919.48 957.56 979.33

η Theoretical result 0.63 0.64 0.64 0.67 0.65 0.76 0.76 0.76 0.75 0.73 0.74 0.73 0.73 0.72 0.75 0.68 0.71 0.71 0.7 0.69 0.77 0.78 0.78

116

η Experimental result 0.52 0.52 0.58 0.58 0.58 0.72 0.72 0.73 0.74 0.71 0.71 0.74 0.71 0.73 0.75 0.65 0.70 0.70 0.69 0.68 0.76 0.77 0.76

5.3.2.4 The Sources of Error It should be kept in mind that the experiments were not performed on the same date. The experiment for 25° tilt angle was carried out between July 26 and August 07, 2001. Unfortunately,

due

to

experimental

limitations,

the

operating

temperature range was very low in this study. The 30°C - 60°C temperature range is considered as small range since the usual operating temperature of a solar collector system is between 60°C and 70°C under normal conditions. So in order to understand the thermal behavior of a collector as a whole it is necessary to work at relatively higher operating temperatures. This is especially important if the limiting points on the efficiency graphs are to be detected. The limiting point on the efficiency curves means the point at which the collector system reaches thermal saturation, i.e. by continuously increasing the inlet fluid temperature, the circulating fluid temperature will reach to a maximum point at which it does not accept anymore heat from the incoming solar radiation and even beyond that point it starts losing heat, causing a sharp drop in efficiency to zero value. The pyranometer used to measure the total solar radiation has not been calibrated for years since there was no proper calibration device readily available. For the measured radiation the accepted error is between 0.1-0.2mV. All the temperature

measurements,

including the

ambient air

temperature, are made with thermometers by the help of the magnifying glass with the 0.2°C errors. The mean absolute deviation of the theoretical and experimental values for STEK’ s aluminum and copper collectors is 0.03, for DA SAN’ s copper 117

collector it is 0.02 for galvanized iron absorber plate it is 0.03. The mean absolute deviation is found by using the given equation:

1 n

η t −η e

(5.1)

For the constructed collector, it is found that, when the ambient temperature is high, the difference between the experimental and theoretical efficiency is around ±0.09 when it is low the difference is around ±0.05, and for the others it is between ±0.01 and ±0.05. This difference can cause abovementioned errors. By using the given errors, error calculation has been carried out. The error result for the experimental efficiencies was between 0.06-0.09 and for the

(Ti-Ta)/It, it was between 0.005-0.009, obtained by the error calculations.

Although the flow is continuously controlled there might be some variations due to the changes in the rate of the city water, which feeds the water reservoir which is at about 6 m height. This variation will of course affect the result of the experiments to some extent. For flow rate measurements the calculated error is 0.004kg/m2s.

5.3.2.5 New Optimization The galvanized iron collector is inferior to the other three in terms of heat losses, as it is concluded from the comparison of the slopes. Hence an extra theoretical work is done to reduce the slope of the efficiency curve of the galvanized iron absorber plate. 118

According to the results of the new optimization, new parameters are found for tube spacing, thickness of plate, outer and inner diameters and number of tubes which are 70 mm, 1.2 mm, 13 mm, 12 mm, 12, respectively, and Figure 5.5 give the original efficiency curve of the constructed galvanized iron absorber plate and the curve of the newly optimized. During the new optimization it was found that the optimum value of tube spacing is 70 mm. Tube spacing cannot be smaller than 70 mm because of the difficulties in the welding process. For the produced collector FRUL value was reduced from 10 W/m2-°C to 6.9 W/m2-°C. The smaller UL values means a smaller slope on the efficiency versus (Ti-Ta)/It graph. Original efficiency curve and Curve of the newly optimized 1

(b)

efficiency

0.8 0.6

y = 0.83+(-6.9)x (a)

0.4

y = 0.82+(-10)x

0.2 0 0

0.005

0.01

0.015

0.02

0.025

0.03

(Ti-Ta)/It

Figure 5.5 Collector efficiency; (a) for constructed collector with

galvanized iron absorber plate, (b) for newly optimized collector.

119

5.3.2.6 Comparison of the Newly Optimized with the Others Figure 5.6 (a)(b)(c)

gives efficiencies of the newly optimized galvanized

iron absorber plate collector with STEK’ s aluminum, for STEK’ s copper and for DA SAN’ s copper collector in pair. Finally, in Table 5.3 result of the new optimization are listed. As it is given in Section 5.3.2.1, the intercept points of STEK’ s copper collector, produced and newly optimized collector can be assumed to be the same within the experimental errors. For DA SAN’ s copper collector the overall heat loss coefficient is smaller than that of produced and newly optimized collectors. For newly optimized collector this value is smaller than that of the produced collector. STEK's Al and Newly Optimized Fe

efficiency

1

y = 0.90+(-8.10)x

0.8 0.6

y = 0.83+(-6.9)x

0.4 0.2 0 0

0.005

0.01 0.015 (Ti-Ta)/It

(a)

120

0.02

0.025

0.03

STEK's Cu and Newly Optimized Fe 1

y = 0.83+(-6.9)x

efficiency

0.8 0.6

y = 0.66+(-3.7)x

0.4 0.2 0 0

0.005

0.01 0.015 (Ti-Ta)/It

0.02

0.025

0.03

(b) Figure 5.6. Efficiency curve for newly optimized galvanized iron absorber plate and a) STEK’ s aluminum collector, b) STEK’ s copper collector, c) DA SAN’ s copper collector.

DA SAN's Cu and Newly Optimized Fe

1

y = 0.81+(-4.0)x

0.8 efficiency

0.6

y = 0.83+(-6.9)x

0.4 0.2 0 0

0.005

0.01

0.015 0.02 (Ti-Ta)/It

(c) Figure 5.6.(Continued). 121

0.025

0.03

Table 5.3 Experimental efficiency results and results of new optimization for galvanized iron collector. Ti

Ta

It

°C

°C

W/m2

η Produced Collector

56.9 56.3 56.7 53.4 54.6 34.0 34.2 35.0 37.0 38.0 35.0 39.1 39.9 40.1 35.8 46.9 44.6 44.0 47.0 47.0 35.6 35.0 35.8

31.8 32.5 32.7 33.6 33.9 26.4 26.9 27.2 27.6 27.8 25.8 26.8 27.8 28.8 29.8 30.8 31.8 32.8 33.8 34.8 35.8 36.8 37.8

946.68 973.88 979.33 968.44 935.80 979.33 1006.5 1028.3 1033.7 1033.7 924.92 941.24 968.44 973.88 963.00 903.16 924.92 957.56 924.92 924.92 919.48 957.56 979.33

0.52 0.52 0.58 0.58 0.58 0.72 0.72 0.73 0.74 0.71 0.71 0.74 0.71 0.73 0.75 0.65 0.70 0.70 0.69 0.68 0.76 0.77 0.76

η Newly Optimized Collector 0.65 0.66 0.66 0.69 0.67 0.78 0.78 0.78 0.77 0.76 0.76 0.75 0.75 0.75 0.78 0.70 0.73 0.74 0.72 0.72 0.79 0.81 0.80

Price of DA SAN’ s collector is about twice that of newly optimized collector. However, weight of the newly optimized collector is higher than DA SAN’ s collector.

122

Comparing the newly optimized collector and STEK’ s copper collector,

FR(τα) value of newly optimized collector is higher, while FRUL value of STEK’ s copper collector is smaller, and their prices are nearly the same. While FR(τα) value of STEK’ s aluminum is higher than that of the newly optimized collector, FRUL value of newly optimized collector is smaller than STEK’ s aluminum, and price of STEK’ s aluminum is about twice that of newly optimized collector. After the new optimization, depending on the tube spacing, the number of pipes, were increased from 10 to 12. It’ s observed that number of pipes plays an important role on the thermal efficiency of collector. When the tube spacing is small efficiency increases. The number of pipes for STEK’ s aluminum collector is 12, for STEK’ s copper collector it is 8, for DA SAN’ s copper collector it is 9. The price of the produced absorber plate was DM 48, after above mentioned optimization it increased to DM 58, for DA SAN’ s copper collector it is DM 100, for STEK’ s aluminum collector it is DM 100, for STEK’ s copper collector it is DM 60. It should be noticed that considering the economic situation of Turkey, price of galvanization has been calculated by using 1.6 times price. If it would be calculated by using at recent values of DM, the price would be DM 43 instead of DM 48 and for newly optimized collector it would be DM 53 instead of 58.

123

CHAPTER 6

CONCLUSION

In this study, a new type of efficient and inexpensive absorber plate, which is made up of galvanized iron was prepared and its efficiency and price were investigated together with that of three commercially available collectors constructed in Turkey, with absorber plates made up of aluminum and copper ( STEK - Aluminum and Copper, DA SAN –Copper). It was observed that thickness of the absorber plate, spacing between pipes, diameters of pipes are the determining factors for the efficiency of the collectors. Concerning the low-cost criteria below mentioned parameters should be considered: 1. Tube spacing should be as small as possible. 2. Plate thickness should be as sbig as possible. As it is stated in Chapter 5, five main parameters of constructed flat plate collector are for tube spacing, thickness of plate, outer and inner diameters and number of tubes are 90 mm, 1 mm, 13 mm, 12 mm, 10, respectively.

124

In summary, the conclusions drawn from the given discussions in Chapter 5 are: a)

In order to produce an optimum collector in terms of economy and efficiency, parameters must be chosen depending on the efficiency and cost of absorber plate.

b)

To produce an economic, efficient and long life collector galvanized iron is suggested as an alternative absorber plate material.

c)

From the experimental results it is seen that DA SAN’ s copper collector attains higher efficiency values at higher operating temperatures when compared with the other types.

d)

At relatively low operating temperature STEK’ s aluminum collector performs with higher efficiency than others.

e)

The constructed and tested collector with galvanized iron absorber plate has higher FR(τα) value, than STEK’ s copper and DA SAN’ s copper collectors.

f)

The time constants of collectors are determined to be 137 seconds for

STEK’ s aluminum collector, 75 seconds for

STEK’ s copper collector, 95 seconds sec for DA SAN’ s copper collector, and 198 seconds for the constructed collector with galvanized iron absorber plate. g)

The price of the constructed galvanized iron absorber plate was 115

DM 43, and that of the newly optimized collector it is DM 53, for STEK’ s aluminum collector it is DM 100, for STEK’ s copper collector it is DM 60 and for DA SAN’ s copper collector it is DM 100. h)

For STEK’ s aluminum collector, the intercept point is 0.90, for STEK’ s copper collector it is 0.66, for DA SAN’ s copper it is 0.81, and for the collector that has galvanized iron absorber plate, it is 0.82 which is increased up to 0.83 after new optimization.

i)

FRUL value for 250 tilt angles for STEK’ s aluminum collector is 8.1 W/m2-°C, for STEK’ s copper collector it is 3.7 W/m2-°C. For DA SAN’ s copper collector this value is 4 W/m2-°C. For the constructed collector FRUL value was reduced from 10 W/m2-°C to 6.9 W/m2-°C after new optimization.

As a result of this study, new parameters for tube spacing, thickness of plate, outer and inner diameters and number of tubes are; 70 mm, 1.2 mm, 13 mm, 12 mm, 12, respectively. The test results indicate that it is possible to produce efficient and low cost absorber plates by changing the material of absorber plate. It was observed that the newly optimized efficiency values of galvanized iron are very near to currently used materials, copper and aluminum. Therefore, galvanized iron can be accepted as a good alternative for the flat plate collector for collecting solar energy when its price is considered.

116

It is believed collector industry in Turkey will develop if more functional designs are made with optimum material selection with consideration of cost, followed by proper performance tests, which will help to obtain collectors with higher thermal efficiencies. Also by using suitable selective surface, it is found by using the EXCEL program, that the efficiency can be increased by 5 % of the present efficiency value. This study believed to be the first step for this achievement and hope to be developed further in near future.

117

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125

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Kovarik, M., 1974. “ Optimal Solar Energy Collector System” , Solar

Energy, Vol.17, pp. 91-95. [63]

Turkish Electricity Distribution Corporation, “ Tariffs” , The Internet

World Wide Web, (http://www.tedas.gov.tr/).

126

APPENDIX A

CALCULATION OF THERMAL CONDUCTIVITY OF GALVANIZED IRON PLATE

R = b/kA 1/R =1/R1 + 1/R2 + 1/R3 kpA/b = k1 A1 /b + k2 A2 /b +............. knAn /b kp A = Σni=1 ki Ai kp = (Σni=1 ki Ai ) / Σni=1 Ai kp = ( 2 kgδg + kFe AFe) / ( 2δg + AFe ) Plate area is , AFe = 1x 10 -3 x 2 = 2x10-3 m2

δg= 70 10-6 m (thickness of galvanization.) Ag = 2 x δg kg = 112 W/mK kFe = 73 W/mK kp = ( 2 x 112 x 70 10-6 + 73 x 1x 10 -3 x 2) / ( 2 x 70 10-6 + 1x 10 -3 x 2 ) kp = 75.55 W/mK

127

APPENDIX B

A SAMPLE EFFICIENCY CALCULATION FOR THE COLLECTORS

Table B1. A sample efficiency calculation for the collectors. ( for Ti = 25°C Ta = 23°C. It = 916.7 W/m2)

STEK

Efficiency

STEK

DA SAN

Galvanized Iron

Aluminum

Copper

Copper

(This Study)

0.74

0.63

0.66

0.68

128

APPENDIX C

PRICES OF MATERIALS. WHICH ARE COMMERCIALLY AVAILABLE

Cu ÖZMAR Tube

Price (TL/kg)

12 mm x 1 mm

2.750.000 +%17

10 mm x 1 mm

2.750.000 +%17

Plate

Price (TL/kg)

2x1 m

2.200.000+%17

Fe

BA KENT METAL Plate

Price (TL/kg)

Black

DKP

2 x 1 x 0.5 mm

280.000

+

%17

265.000+%17 2 x 1 x 0.7 mm and thicker 180.000+%17 265.000+ % 17 (%10 reduction for over 5000 kg )

129

Fe BORUSAN Tube

Price (TL/m)

10 mm x 1 mm

199.000 +%17

13 mm x 1 mm

200.000 +%17

13 mm x 1.5 mm

257.000 +%17

(%30 reduction for over 5000 kg)

Al ALMAR Plate

Price (TL/kg)

2x1mx 0.4mm

1.929.000+%17

0.4-1mm and thicker

2.250.000+%17

Al KURDO LU Tube

Price (TL/kg)

10 mm x 1 mm

130

2.350.000 + %17

APPENDIX D

PARAMETERS USED IN OPTIMIZATION OF COLLECTOR EFFICIENCY

Table D1. Parameters used in optimization of collector efficiency.

Day of the year Hour

198 12:00-13:00

Latitude

40

Wind speed

2m/s

Ta

23°C

It

916.7W/m2

Ti

25°C

Flowrate: Cp

0.0278kg/s 4190J/kg°C

Absorbtance of plate

0.94

Ground reflectance Emittance of glass

0.4 0.88

Emittance of plate

0.9

Nusselt number

3.7 0°

Surface azimuth angle

30°

Angle of tilt 131

APPENDIX E PRICE LISTS AND RELATED GRAPHS FOR FOUR DIFFERENT PARAMETERS

Table E1 Value of parameters, price of absorber plate, efficiency of the collector, for each combination. Price

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

(DM) 45.1 35.0 30.6 27.3 24.9 43.9 37.4 33.0 29.7 27.3 45.4 39.0 34.6 31.3 28.9 47.0 40.6 36.2 32.9 30.5 49.4 43.0 38.5 35.3 32.9 53.4

Collector efficiency

0.66 0.62 0.59 0.56 0.52 0.68 0.65 0.62 0.59 0.56 0.68 0.66 0.63 0.61 0.58 0.69 0.66 0.64 0.62 0.59 0.69 0.67 0.65 0.63 0.61 0.69

qu/Price

Thickness of plate (m) (MJ/m2DM) 0.05 0.0005 0.06 0.0005 0.06 0.0005 0.07 0.0005 0.07 0.0005 0.05 0.0008 0.06 0.0008 0.06 0.0008 0.07 0.0008 0.07 0.0008 0.05 0.001 0.06 0.001 0.06 0.001 0.06 0.001 0.07 0.001 0.05 0.0012 0.05 0.0012 0.06 0.0012 0.06 0.0012 0.06 0.0012 0.05 0.0015 0.05 0.0015 0.06 0.0015 0.06 0.0015 0.06 0.0015 0.04 0.002

132

W tube spacing (m) 0.09 0.11 0.13 0.15 0.17 0.09 0.11 0.13 0.15 0.17 0.09 0.11 0.13 0.15 0.17 0.09 0.11 0.13 0.15 0.17 0.09 0.11 0.13 0.15 0.17 0.09

Do (m) 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01

Di

N

(m) 0.0093 9 0.0093 8 0.0093 6 0.0093 5 0.0093 5 0.0093 9 0.0093 8 0.0093 6 0.0093 5 0.0093 5 0.0093 9 0.0093 8 0.0093 6 0.0093 5 0.0093 5 0.0093 9 0.0093 8 0.0093 6 0.0093 5 0.0093 5 0.0093 9 0.0093 8 0.0093 6 0.0093 5 0.0093 5 0.0093 9 (Continued)

Table E1(Continued) Price

27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58

(DM) 47.0 42.5 39.3 36.9 41.7 35.2 30.7 27.5 25.0 44.1 37.6 33.1 29.9 27.4 45.7 39.4 34.8 31.5 29.0 46.9 41.0 36.4 33.1 30.6 49.3 43.4 38.8 35.5 33.0 53.3 47.3 42.8

Collector efficiency 0.68 0.66 0.64 0.62 0.66 0.62 0.59 0.56 0.52 0.68 0.65 0.62 0.59 0.56 0.68 0.66 0.63 0.61 0.58 0.69 0.66 0.64 0.62 0.59 0.69 0.67 0.65 0.63 0.61 0.69 0.68 0.66

qu/Price

Thickness W of tube spacing plate (m) (MJ/m2DM) (m) 0.05 0.002 0.11 0.05 0.002 0.13 0.05 0.002 0.15 0.06 0.002 0.17 0.05 0.0005 0.09 0.06 0.0005 0.11 0.06 0.0005 0.13 0.07 0.0005 0.15 0.07 0.0005 0.17 0.05 0.0008 0.09 0.06 0.0008 0.11 0.06 0.0008 0.13 0.07 0.0008 0.15 0.07 0.0008 0.17 0.05 0.001 0.09 0.06 0.001 0.11 0.06 0.001 0.13 0.06 0.001 0.15 0.07 0.001 0.17 0.05 0.0012 0.09 0.05 0.0012 0.11 0.06 0.0012 0.13 0.06 0.0012 0.15 0.06 0.0012 0.17 0.05 0.0015 0.09 0.05 0.0015 0.11 0.06 0.0015 0.13 0.06 0.0015 0.15 0.06 0.0015 0.17 0.04 0.002 0.09 0.05 0.002 0.11 0.05 0.002 0.13 152

Do

Di

N

(m) 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01

(m) 0.0093 0.0093 0.0093 0.0093 0.0092 0.0092 0.0092 0.0092 0.0092 0.0092 0.0092 0.0092 0.0092 0.0092 0.0092 0.0092 0.0092 0.0092 0.0092 0.0092 0.0092 0.0092 0.0092 0.0092 0.0092 0.0092 0.0092 0.0092 0.0092 0.0092 0.0092 0.0092

8 6 5 5 9 8 6 5 5 9 8 6 5 5 9 8 6 5 5 9 8 6 5 5 9 8 6 5 5 9 8 6

59 39.5 60 37.0 61 41.8

0.64 0.62 0.66

0.05 0.06 0.05

0.002 0.002 0.0005

0.15 0.17 0.09

0.01 0.0092 5 0.01 0.0092 5 0.01 0.009 9

Table E1(Continued) Price

62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89

(DM) 35.7 31.2 27.8 25.2 44.2 38.1 33.5 30.2 27.6 45.8 39.7 35.1 31.8 29.2 47.4 41.3 36.7 33.4 30.8 49.8 43.7 39.1 35.7 33.2 53.7 47.7 43.1 39.7

Collector efficiency

0.62 0.59 0.56 0.52 0.68 0.65 0.62 0.59 0.56 0.68 0.66 0.63 0.61 0.58 0.69 0.66 0.64 0.62 0.59 0.69 0.67 0.65 0.63 0.61 0.69 0.68 0.66 0.64

qu/Price

(MJ/m2DM) 0.06 0.06 0.07 0.07 0.05 0.06 0.06 0.07 0.07 0.05 0.06 0.06 0.06 0.07 0.05 0.05 0.06 0.06 0.06 0.05 0.05 0.06 0.06 0.06 0.04 0.05 0.05 0.05

W Do Thickness of tube spacing plate (m) 0.0005 0.0005 0.0005 0.0005 0.0008 0.0008 0.0008 0.0008 0.0008 0.001 0.001 0.001 0.001 0.001 0.0012 0.0012 0.0012 0.0012 0.0012 0.0015 0.0015 0.0015 0.0015 0.0015 0.002 0.002 0.002 0.002 153

(m) 0.11 0.13 0.15 0.17 0.09 0.11 0.13 0.15 0.17 0.09 0.11 0.13 0.15 0.17 0.09 0.11 0.13 0.15 0.17 0.09 0.11 0.13 0.15 0.17 0.09 0.11 0.13 0.15

(m) 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01

Di

N

( m) 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009

8 6 5 5 9 8 6 5 5 9 8 6 5 5 9 8 6 5 5 9 8 6 5 5 9 8 6 5

90 91 92 93 94

37.2 42.8 36.1 31.6 28.3

0.62 0.66 0.63 0.60 0.56

0.06 0.05 0.06 0.06 0.07

0.002 0.0005 0.0005 0.0005 0.0005

0.17 0.09 0.11 0.13 0.15

0.01 0.013 0.013 0.013 0.013

0.009 0.0123 0.0123 0.0123 0.0123

5 9 8 6 5

Table E1(Continued) Price

95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120

(DM) 25.8 45.1 38.5 34.0 30.7 28.2 46.7 40.1 35.6 32.3 29.8 48.3 41.7 37.2 33.9 31.4 50.7 44.1 39.6 36.3 33.8 54.7 48.0 43.6 40.2 37.7

Collector efficiency 0.53 0.68 0.65 0.63 0.60 0.57 0.68 0.66 0.64 0.61 0.59 0.69 0.67 0.64 0.62 0.60 0.69 0.67 0.65 0.63 0.61 0.69 0.68 0.66 0.64 0.62

qu/Price

Thickness of plate (MJ/m2DM) (m) 0.07 0.0005 0.05 0.0008 0.06 0.0008 0.06 0.0008 0.06 0.0008 0.07 0.0008 0.05 0.001 0.05 0.001 0.06 0.001 0.06 0.001 0.07 0.001 0.05 0.0012 0.05 0.0012 0.06 0.0012 0.06 0.0012 0.06 0.0012 0.05 0.0015 0.05 0.0015 0.05 0.0015 0.06 0.0015 0.06 0.0015 0.04 0.002 0.05 0.002 0.05 0.002 0.05 0.002 0.05 0.002 154

W tube spacing (m) 0.17 0.09 0.11 0.13 0.15 0.17 0.09 0.11 0.13 0.15 0.17 0.09 0.11 0.13 0.15 0.17 0.09 0.11 0.13 0.15 0.17 0.09 0.11 0.13 0.15 0.17

Do

Di

N

(m) 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013

(m) 0.0123 0.0123 0.0123 0.0123 0.0123 0.0123 0.0123 0.0123 0.0123 0.0123 0.0123 0.0123 0.0123 0.0123 0.0123 0.0123 0.0123 0.0123 0.0123 0.0123 0.0123 0.0123 0.0123 0.0123 0.0123 0.0123

5 9 8 6 5 5 9 8 6 5 5 9 8 6 5 5 9 8 6 5 5 9 8 6 5 5

121 122 123 124 125 126 127 128 129 130

43.1 36.3 31.9 28.5 26.0 45.5 38.7 34.3 30.9 28.3

0.66 0.63 0.60 0.56 0.53 0.68 0.65 0.63 0.60 0.57

0.05 0.06 0.06 0.07 0.07 0.05 0.06 0.06 0.06 0.07

0.0005 0.0005 0.0005 0.0005 0.0005 0.0008 0.0008 0.0008 0.0008 0.0008

0.09 0.11 0.13 0.15 0.17 0.09 0.11 0.13 0.15 0.17

0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013

0.0122 0.0122 0.0122 0.0122 0.0122 0.0122 0.0122 0.0122 0.0122 0.0122

Table E1(Continued) Price

131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150

(DM) 47.0 40.3 35.8 32.5 29.9 48.6 41.9 37.4 34.0 31.5 51.0 44.3 39.8 36.4 33.9 55.0 48.3 43.8 40.4 37.9

Collector efficiency

0.68 0.66 0.64 0.61 0.59 0.69 0.67 0.64 0.62 0.60 0.69 0.67 0.65 0.63 0.61 0.69 0.68 0.66 0.64 0.62

qu/Price

(MJ/m2DM) 0.05 0.05 0.06 0.06 0.07 0.05 0.05 0.06 0.06 0.06 0.05 0.05 0.05 0.06 0.06 0.04 0.05 0.05 0.05 0.05

Thickness W Do of tube spacing plate (m) 0.001 0.001 0.001 0.001 0.001 0.0012 0.0012 0.0012 0.0012 0.0012 0.0015 0.0015 0.0015 0.0015 0.0015 0.002 0.002 0.002 0.002 0.002 155

(m) 0.09 0.11 0.13 0.15 0.17 0.09 0.11 0.13 0.15 0.17 0.09 0.11 0.13 0.15 0.17 0.09 0.11 0.13 0.15 0.17

(m) 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013

Di

N

(m) 0.0122 0.0122 0.0122 0.0122 0.0122 0.0122 0.0122 0.0122 0.0122 0.0122 0.0122 0.0122 0.0122 0.0122 0.0122 0.0122 0.0122 0.0122 0.0122 0.0122

9 8 6 5 5 9 8 6 5 5 9 8 6 5 5 9 8 6 5 5

9 8 6 5 5 9 8 6 5 5

151 152 153 154 155 156 157 158 159 160 161 162

43.7 36.8 32.3 28.8 26.3 45.3 46.1 39.2 34.7 31.2 28.7 47.4

0.66 0.63 0.60 0.56 0.53 0.68 0.68 0.65 0.63 0.60 0.57 0.68

0.05 0.06 0.06 0.07 0.07 0.05 0.05 0.06 0.06 0.06 0.07 0.05

0.0005 0.0005 0.0005 0.0005 0.0005 0.0007 0.0008 0.0008 0.0008 0.0008 0.0008 0.001

0.09 0.11 0.13 0.15 0.17 0.09 0.09 0.11 0.13 0.15 0.17 0.09

0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013

0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012

Table E1(Continued) Price Collector efficiency

166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182

(DM) 30.3 49.2 42.4 37.9 34.4 31.8 51.6 44.8 40.2 36.8 34.2 55.6 48.8 44.2 40.8 38.2 44.2

0.59 0.69 0.67 0.64 0.62 0.60 0.69 0.67 0.65 0.63 0.61 0.69 0.68 0.66 0.64 0.62 0.66

qu/Price

(MJ/m2DM) 0.06 0.05 0.05 0.06 0.06 0.06 0.04 0.05 0.05 0.06 0.06 0.04 0.05 0.05 0.05 0.05 0.05

Thickness W of tube plate spacing (m) 0.001 0.0012 0.0012 0.0012 0.0012 0.0012 0.0015 0.0015 0.0015 0.0015 0.0015 0.002 0.002 0.002 0.002 0.002 0.0005 156

(m) 0.17 0.09 0.11 0.13 0.15 0.17 0.09 0.11 0.13 0.15 0.17 0.09 0.11 0.13 0.15 0.17 0.09

Do

Di

N

(m) 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013

(m) 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.0118

5 10 8 7 6 5 10 8 7 6 5 10 8 7 6 5 10

10 8 7 6 5 10 10 8 7 6 5 10

183 184 185 186 187 188 189 190 191 192 193 194 195 196 197

37.3 32.7 29.2 26.6 46.6 39.7 35.1 31.6 29.0 48.2 41.3 36.7 33.2 30.6 49.8

0.63 0.60 0.56 0.53 0.68 0.65 0.63 0.60 0.57 0.68 0.66 0.64 0.61 0.59 0.69

0.06 0.06 0.06 0.07 0.05 0.05 0.06 0.06 0.07 0.05 0.05 0.06 0.06 0.06 0.05

0.0005 0.0005 0.0005 0.0005 0.0008 0.0008 0.0008 0.0008 0.0008 0.001 0.001 0.001 0.001 0.001 0.0012

0.11 0.13 0.15 0.17 0.09 0.11 0.13 0.15 0.17 0.09 0.11 0.13 0.15 0.17 0.09

0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013

0.0118 0.0118 0.0118 0.0118 0.0118 0.0118 0.0118 0.0118 0.0118 0.0118 0.0118 0.0118 0.0118 0.0118 0.0118

8 7 6 5 10 8 7 6 5 10 8 7 6 5 10

Di

N

(m) 0.0118 0.0118 0.0118 0.0118 0.0118 0.0118 0.0118 0.0118 0.0118 0.0118 0.0118 0.0118 0.0118 0.0115 0.0115

7 6 5 10 8 7 6 5 10 8 7 6 5 10 8

Table E1(Continued) Price Collector efficiency

199 200 201 202 203 204 205 206 207 208 209 210 211 212 213

(DM) 38.3 34.8 32.1 52.2 45.3 40.6 37.1 34.5 56.2 49.3 44.6 41.1 38.5 45.1 38.0

qu/Price (MJ/m2DM)

0.64 0.62 0.60 0.69 0.67 0.65 0.63 0.61 0.69 0.68 0.66 0.64 0.62 0.66 0.63

0.06 0.06 0.06 0.04 0.05 0.05 0.06 0.06 0.04 0.05 0.05 0.05 0.05 0.05 0.06

Thickness W Do of tube plate spacing (m) 0.0012 0.0012 0.0012 0.0015 0.0015 0.0015 0.0015 0.0015 0.002 0.002 0.002 0.002 0.002 0.0005 0.0005 157

(m) 0.13 0.15 0.17 0.09 0.11 0.13 0.15 0.17 0.09 0.11 0.13 0.15 0.17 0.09 0.11

(m) 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013

214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231

33.2 29.5 26.8 47.5 40.4 35.6 31.9 29.2 49.1 42.0 37.2 33.5 30.8 50.7 43.6 38.8 35.1 32.4

0.60 0.56 0.53 0.68 0.65 0.63 0.60 0.57 0.68 0.66 0.64 0.61 0.59 0.69 0.67 0.64 0.62 0.60

0.06 0.06 0.07 0.05 0.05 0.06 0.06 0.07 0.05 0.05 0.06 0.06 0.06 0.05 0.05 0.06 0.06 0.06

0.0005 0.0005 0.0005 0.0008 0.0008 0.0008 0.0008 0.0008 0.001 0.001 0.001 0.001 0.001 0.0012 0.0012 0.0012 0.0012 0.0012

0.13 0.15 0.17 0.09 0.11 0.13 0.15 0.17 0.09 0.11 0.13 0.15 0.17 0.09 0.11 0.13 0.15 0.17

0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013

0.0115 0.0115 0.0115 0.0115 0.0115 0.0115 0.0115 0.0115 0.0115 0.0115 0.0115 0.0115 0.0115 0.0115 0.0115 0.0115 0.0115 0.0115

7 6 5 10 8 7 6 5 10 8 7 6 5 10 8 7 6 5

Di

N

(m) 0.0115 0.0115 0.0115 0.0115 0.0115 0.0115 0.0115 0.0115 0.0115

10 8 7 6 5 10 8 7 6

Table E1(Continued) Price

232 233 234 235 236 237 238 239 240

(DM) 53.0 46.0 41.2 37.5 34.8 57.0 49.9 45.2 41.5

Collector efficiency

0.69 0.67 0.65 0.63 0.61 0.69 0.68 0.66 0.64

qu/Price

(MJ/m2DM) 0.04 0.05 0.05 0.06 0.06 0.04 0.05 0.05 0.05

Thickness W Do of tube plate spacing (m) 0.0015 0.0015 0.0015 0.0015 0.0015 0.002 0.002 0.002 0.002 158

(m) 0.09 0.11 0.13 0.15 0.17 0.09 0.11 0.13 0.15

(m) 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013

241 38.8

0.62

0.05

0.002

0.17

0.013 0.0115 5

Tablo E2. Price of plate. paint. tube. header and welding for each combination. P. of Plate P. of Paint P.of Tube -%0.30 2

1 2 3 4 5 6 7 8 9

(DM/m )

(DM/m2) (DM/m) (DM/m)

P. of p.w.

P.of weld.

P.of Header (DM/each) (DM/each) (DM/m)

0.76

0.055

0.64

0.38

0.037

0.55

0.76

0.055

0.64

0.38

0.037

0.55

0.76

0.055

0.64

0.38

0.037

0.55

0.76

0.055

0.64

0.38

0.037

0.55

0.76

0.055

0.64

0.38

0.037

0.55

0.76

0.055

0.64

0.38

0.037

0.55

0.76

0.055

0.64

0.38

0.037

0.55

0.76

0.055

0.64

0.38

0.037

0.55

0.76

0.055

0.64

0.38

0.037

0.55

159

0.62 0.54 0.48 0.45 0.45 0.62 0.54 0.48 0.45

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

0.76

0.055

0.64

0.38

0.037

0.55

0.76

0.055

0.64

0.38

0.037

0.55

0.76

0.055

0.64

0.38

0.037

0.55

0.76

0.055

0.64

0.38

0.037

0.55

0.76

0.055

0.64

0.38

0.037

0.55

0.76

0.055

0.64

0.38

0.037

0.55

0.76

0.055

0.64

0.38

0.037

0.55

0.76

0.055

0.64

0.38

0.037

0.55

0.76

0.055

0.64

0.38

0.037

0.55

0.76

0.055

0.64

0.38

0.037

0.55

0.76

0.055

0.64

0.38

0.037

0.55

0.76

0.055

0.64

0.38

0.037

0.55

0.76

0.055

0.64

0.38

0.037

0.55

0.76

0.055

0.64

0.38

0.037

0.55

0.76

0.055

0.64

0.38

0.037

0.55

0.76

0.055

0.64

0.38

0.037

0.55

0.76

0.055

0.64

0.38

0.037

0.55

0.76

0.055

0.64

0.38

0.037

0.55

0.76

0.055

0.64

0.38

0.037

0.55

0.76

0.055

0.64

0.38

0.037

0.55

0.76

0.055

0.64

0.38

0.037

0.55

0.76

0.055

0.64

0.38

0.037

0.55

0.76

0.055

0.64

0.38

0.037

0.55

0.45 0.62 0.54 0.48 0.45 0.45 0.62 0.54 0.48 0.45 0.45 0.62 0.54 0.48 0.45 0.45 0.62 0.54 0.48 0.45 0.45 0.62 0.54

Tablo E2.(Continued) P.

of P. of Paint

-%0.30

P. of p.w.

P.of weld.

(DM/m2) (DM/m) (DM/m)

(DM/each)

(DM/each) (DM/m)

Plate

P.of Tube

P.of Header

2

33 34 35

(DM/m ) 0.76 0.76 0.76

0.055 0.055 0.055

0.64 0.64 0.64

0.38 0.38 0.38 160

0.037 0.037 0.037

0.55 0.55 0.55

0.48 0.45 0.45

36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64

0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76

0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055

0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64

0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38

0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037

0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55

0.62 0.54 0.48 0.45 0.45 0.62 0.62 0.54 0.48 0.45 0.45 0.62 0.54 0.48 0.45 0.45 0.62 0.54 0.48 0.45 0.45 0.62 0.54 0.48 0.45 0.45 0.62 0.54 0.48

P.of Tube

-%0.30

P. of p.w.

P.of weld.

(DM/m2) (DM/m) (DM/m)

(DM/each)

(DM/each) (DM/m)

Tablo E2.(Continued) P.

of P. of Paint

Plate 2

(DM/m ) 161

P.of Header

65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94

0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76

0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055

0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64

0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38

162

0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037

0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55

0.45 0.45 0.62 0.54 0.47 0.45 0.45 0.62 0.54 0.48 0.45 0.45 0.62 0.54 0.48 0.45 0.45 0.62 0.54 0.48 0.45 0.45 0.62 0.54 0.48 0.45 0.80 0.67 0.67 0.62

Tablo E2.(Continued) P.

of P. of Paint P.of Tube -%0.30

P. of p.w.

P.of weld.

(DM/m2) (DM/m) (DM/m)

(DM/each)

(DM/each) (DM/m)

Plate

P.of Header

2

95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123

(DM/m ) 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76

0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055

0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64

0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38

163

0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037

0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55

0.62 0.80 0.67 0.67 0.62 0.62 0.80 0.67 0.67 0.62 0.62 0.80 0.67 0.67 0.62 0.62 0.80 0.67 0.67 0.62 0.62 0.80 0.67 0.67 0.62 0.62 0.80 0.67 0.67

Tablo E2.(Continued) P.

of P. of Paint P.of

-%0.30

P. of p.w.

P.of weld.

(DM/m2) (DM/m) (DM/m)

(DM/each)

(DM/each) (DM/m)

Tube

Plate

P.of Header

2

124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154

(DM/m ) 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76

0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055

0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64

0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38

0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 164

0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55

0.62 0.62 0.80 0.67 0.67 0.62 0.62 0.80 0.67 0.67 0.62 0.62 0.80 0.67 0.67 0.62 0.62 0.80 0.67 0.67 0.62 0.62 0.80 0.67 0.67 0.62 0.62 0.80 0.67 0.67 0.62

155 156

0.76 0.76

0.055 0.055

0.64 0.64

0.38 0.38

0.037 0.037

0.55 0.55

0.62 0.80

Tablo E2.(Continued) P.

of

Plate

P. of Paint

P.of Tube

-%0.30

P. of p.w.

P.of weld.

P.of Header

(DM/m2)

(DM/m)

(DM/m)

(DM/each) (DM/each) (DM/m)

0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055

0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64

0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38

2

157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183

(DM/m ) 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76

165

0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037

0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55

0.80 0.67 0.67 0.62 0.62 0.80 0.67 0.67 0.62 0.62 0.80 0.67 0.67 0.62 0.62 0.80 0.67 0.67 0.62 0.62 0.80 0.67 0.67 0.62 0.62 0.80 0.67

184 185 186 187 188 189 190

0.76 0.76 0.76 0.76 0.76 0.76 0.76

0.055 0.055 0.055 0.055 0.055 0.055 0.055

0.64 0.64 0.64 0.64 0.64 0.64 0.64

0.38 0.38 0.38 0.38 0.38 0.38 0.38

0.037 0.037 0.037 0.037 0.037 0.037 0.037

0.55 0.55 0.55 0.55 0.55 0.55 0.55

0.67 0.62 0.62 0.80 0.67 0.67 0.62

P.of weld.

P.of Header

Tablo E2.(Continued) P.

of

Plate

P. of Paint

P.of Tube

-%0.30

P. of p.w.

(DM/m2)

(DM/m)

(DM/m)

(DM/each) (DM/each) (DM/m)

0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055

0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64

0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38

2

191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211

(DM/m ) 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76

166

0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037

0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55

0.62 0.80 0.67 0.67 0.62 0.62 0.80 0.67 0.67 0.62 0.62 0.80 0.67 0.67 0.62 0.62 0.80 0.67 0.67 0.62 0.62

212 213 214 215 216 217

0.76 0.76 0.76 0.76 0.76 0.76

0.055 0.055 0.055 0.055 0.055 0.055

0.64 0.64 0.64 0.64 0.64 0.64

0.38 0.38 0.38 0.38 0.38 0.38

0.037 0.037 0.037 0.037 0.037 0.037

0.55 0.55 0.55 0.55 0.55 0.55

0.80 0.67 0.67 0.54 0.54 0.80

Tablo E2.(Continued) P.

of P. of Paint P.of Tube -%0.30

P. of p.w.

P.of weld.

(DM/m2) (DM/m) (DM/m)

(DM/each)

(DM/each) (DM/m)

Plate

P.of Header

2

218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234

(DM/m ) 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76

0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055

0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64

0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 167

0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037

0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55

0.67 0.67 0.54 0.54 0.80 0.67 0.67 0.54 0.54 0.80 0.67 0.67 0.54 0.54 0.80 0.67 0.67

235 236 237 238 239 240 241

0.76 0.76 0.76 0.76 0.76 0.76 0.76

0.055 0.055 0.055 0.055 0.055 0.055 0.055

0.64 0.64 0.64 0.64 0.64 0.64 0.64

0.38 0.38 0.38 0.38 0.38 0.38 0.38

0.037 0.037 0.037 0.037 0.037 0.037 0.037

0.55 0.55 0.55 0.55 0.55 0.55 0.55

0.54 0.54 0.80 0.67 0.67 0.54 0.54

Tablo E3 Price lists of absorber plate in terms of galvanization, cost of plate, and paint, tubes, welding and header, for each combination. P.of Galvanization

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(DM) 4.21 3.95 3.76 3.62 3.52 5.7 5.44 5.26 5.11 5.01 6.7 6.44 6.25 6.11 6.01 7.7 7.43 7.25 7.11 7.01

P.of Plate, and Paint (DM) 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31

P.of P.of P.of Tubes Welding Header (DM)

(DM)

(DM)

6.86 5.61 4.75 4.11 3.63 6.86 5.61 4.75 4.11 3.63 6.86 5.61 4.75 4.11 3.63 6.86 5.61 4.75 4.11 3.63

28.96 23.69 20.05 17.37 15.33 28.96 23.69 20.05 17.37 15.33 28.96 23.69 20.05 17.37 15.33 28.96 23.69 20.05 17.37 15.33

1.24 1.08 0.96 0.91 0.91 1.24 1.08 0.96 0.91 0.91 1.24 1.08 0.96 0.91 0.91 1.24 1.08 0.96 0.91 0.91

168

21 22 23 24 25 26 27 28 29 30 31

9.19 8.93 8.75 8.6 8.5 11.68 11.42 11.24 11.09 10.99 4.33

1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31

6.86 5.61 4.75 4.11 3.63 6.86 5.61 4.75 4.11 3.63 6.86

28.96 23.69 20.05 17.37 15.33 28.96 23.69 20.05 17.37 15.33 28.96

1.24 1.08 0.96 0.91 0.91 1.24 1.08 0.96 0.91 0.91 1.24

Table E3 (Continued) P.of Galvanization

32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

(DM) 4.06 3.86 3.71 3.6 5.82 5.55 5.35 5.2 5.09 6.82 6.55 6.35 6.19 6.09 7.82 7.55 7.35 7.19 7.08

P.of Plate, and Paint (DM) 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31

P.of P.of P.of Tubes Welding Header (DM)

(DM)

(DM)

5.61 4.75 4.11 3.63 6.86 5.61 4.75 4.11 3.63 6.86 5.61 4.75 4.11 3.63 6.86 5.61 4.75 4.11 3.63

23.69 20.05 17.37 15.33 28.96 23.69 20.05 17.37 15.33 28.96 23.69 20.05 17.37 15.33 28.96 23.69 20.05 17.37 15.33

1.08 0.96 0.91 0.91 1.24 1.08 0.96 0.91 0.91 1.24 1.24 1.08 0.96 0.91 0.91 1.24 1.08 0.96 0.91

169

51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

9.31 9.04 8.84 8.69 8.58 11.8 11.53 11.33 11.18 11.07 4.62 4.28 4.04 3.88 3.73

1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31

6.86 5.61 4.75 4.11 3.63 6.86 5.61 4.75 4.11 3.63 6.86 5.61 4.75 4.11 3.63

28.96 23.69 20.05 17.37 15.33 28.96 23.69 20.05 17.37 15.33 28.96 23.69 20.05 17.37 15.33

0.91 1.24 1.08 0.96 0.91 0.91 1.24 1.08 0.96 0.91 0.91 1.24 1.08 0.96 0.91

Table E3(Continued) P.of Galvanization

66 67 68 69 70 71 72 73 74 75 76 77 78 79 80

(DM) 6.11 5.77 5.54 5.37 5.22 7.11 6.77 6.53 6.37 6.22 8.11 7.76 7.53 7.36 7.21

P.of Plate, and Paint (DM) 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31

P.of P.of P.of Tubes Welding Header (DM)

(DM)

(DM)

6.86 5.61 4.75 4.11 3.63 6.86 5.61 4.75 4.11 3.63 6.86 5.61 4.75 4.11 3.63

28.96 23.69 20.05 17.37 15.33 28.96 23.69 20.05 17.37 15.33 28.96 23.69 20.05 17.37 15.33

0.91 1.24 1.08 0.96 0.91 0.91 1.24 1.08 0.96 0.91 0.91 1.24 1.08 0.96 0.91

170

81 82 83 84 85 86 87 88 89 90 91 92

9.6 9.26 9.02 8.86 8.71 12.09 11.75 11.51 11.35 11.2 4.76 4.42

1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31

6.86 5.61 4.75 4.11 3.63 6.86 5.61 4.75 4.11 3.63 6.88 5.63

28.96 23.69 20.05 17.37 15.33 28.96 23.69 20.05 17.37 15.33 28.96 23.69

0.91 1.24 1.08 0.96 0.91 0.91 1.24 1.08 0.96 0.91 1.61 1.35

Table E3(Continued) P.of Galvanization

93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110

(DM) 4.17 3.99 3.87 6.26 5.91 5.66 5.48 5.36 7.25 6.90 6.66 6.48 6.36 8.25 7.90 7.65 7.48 7.35

P.of Plate, and Paint (DM) 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31

P.of P.of P.of Tubes Welding Header (DM)

(DM)

(DM)

4.77 4.13 3.64 6.88 5.63 4.77 4.13 3.64 6.88 5.63 4.77 4.13 3.64 6.88 5.63 4.77 4.13 3.64

20.05 17.37 15.33 28.96 23.69 20.05 17.37 15.33 28.96 23.69 20.05 17.37 15.33 28.96 23.69 20.05 17.37 15.33

1.35 1.24 1.24 1.61 1.35 1.35 1.24 1.24 1.61 1.35 1.35 1.24 1.24 1.61 1.35 1.35 1.24 1.24

171

111 112 113 114 115 116 117 118 119 120 121 122 123

9.75 9.40 9.15 8.97 8.85 12.2 11.9 11.6 11.5 11.34 4.95 4.58 4.31

1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31

6.88 5.63 4.77 4.13 3.64 6.88 5.63 4.77 4.13 3.64 6.88 5.63 4.77

28.96 23.69 20.05 17.37 15.33 28.96 23.69 20.05 17.37 15.33 28.96 23.69 20.05

1.61 1.35 1.35 1.24 1.24 1.61 1.35 1.35 1.24 1.24 1.61 1.35 1.35

124

4.11

1.31

4.13

17.37

1.24

Table E3(Continued) P.of Galvanization

125 126 127 128 129 130 131 132 133 134 135 136 137 138 139

(DM) 3.96 6.44 6.08 5.80 5.61 5.45 7.44 7.07 6.80 6.60 6.44 8.44 8.07 7.80 7.60

P.of Plate, and Paint (DM) 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31

P.of P.of P.of Tubes Welding Header (DM)

(DM)

(DM)

3.64 6.88 5.63 4.77 4.13 3.64 6.88 5.63 4.77 4.13 3.64 6.88 5.63 4.77 4.13

15.33 28.96 23.69 20.05 17.37 15.33 28.96 23.69 20.05 17.37 15.33 28.96 23.69 20.05 17.37

1.24 1.61 1.35 1.35 1.24 1.24 1.61 1.35 1.35 1.24 1.24 1.61 1.35 1.35 1.24

172

140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160

7.44 9.93 9.56 9.29 9.10 8.94 12.4 12.0 11.8 11.6 11.4 5.34 4.88 4.58 4.35 4.16 6.33 6.83 6.37 6.07 5.84

1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31

3.64 6.88 5.63 4.77 4.13 3.64 6.88 5.63 4.77 4.13 3.64 6.88 5.63 4.77 4.13 3.64 6.88 6.88 5.63 4.77 4.13

15.33 28.96 23.69 20.05 17.37 15.33 28.96 23.69 20.05 17.37 15.33 28.96 23.69 20.05 17.37 15.33 28.96 28.96 23.69 20.05 17.37

1.24 1.61 1.35 1.35 1.24 1.24 1.61 1.35 1.35 1.24 1.24 1.61 1.35 1.35 1.24 1.24 1.61 1.61 1.35 1.35 1.24

Table E3(Continued) P.of Galvanization

161 162 163 164 165 166 167 168 169 170

(DM) 5.65 7.83 7.37 7.07 6.84 6.65 8.82 8.37 8.06 7.83

P.of Plate, and Paint (DM) 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31

P.of P.of P.of Tubes Welding Header (DM)

(DM)

(DM)

3.64 6.88 5.63 4.77 4.13 3.64 6.88 5.63 4.77 4.13

15.33 28.96 23.69 20.05 17.37 15.33 28.96 23.69 20.05 17.37

1.24 1.61 1.35 1.35 1.24 1.24 1.61 1.35 1.35 1.24

173

171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195

7.65 10.3 9.86 9.56 9.33 9.14 12.8 12.4 12.0 11.8 11.6 5.69 5.19 4.82 4.55 4.34 7.18 6.68 6.31 6.04 5.83 8.18 7.67 7.31 7.04

1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31

3.64 6.88 5.63 4.77 4.13 3.64 6.88 5.63 4.77 4.13 3.64 6.88 5.63 4.77 4.13 3.64 6.88 5.63 4.77 4.13 3.64 6.88 5.63 4.77 4.13

15.33 28.96 23.69 20.05 17.37 15.33 28.96 23.69 20.05 17.37 15.33 28.96 23.69 20.05 17.37 15.33 28.96 23.69 20.05 17.37 15.33 28.96 23.69 20.05 17.37

1.24 1.61 1.35 1.35 1.24 1.24 1.61 1.35 1.35 1.24 1.24 1.61 1.35 1.35 1.24 1.24 1.61 1.35 1.35 1.24 1.24 1.61 1.35 1.35 1.24

Table E3(Continued) P.of Galvanization

196 197 198 199 200 201 202

(DM) 6.83 9.18 8.67 8.30 8.04 7.82 10.7

P.of Plate, and Paint (DM) 1.31 1.31 1.31 1.31 1.31 1.31 1.31

P.of P.of P.of Tubes Welding Header (DM)

(DM)

(DM)

3.64 6.88 5.63 4.77 4.13 3.64 6.88

15.33 28.96 23.69 20.05 17.37 15.33 28.96

1.24 1.61 1.35 1.35 1.24 1.24 1.61

174

203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230

10.2 9.80 9.53 9.32 13.2 12.7 12.3 12.0 11.8 6.21 5.60 5.17 4.85 4.62 7.70 7.10 6.66 6.35 6.12 8.70 8.09 7.66 7.34 7.11 9.69 9.09 8.65 8.34

1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31

5.63 4.77 4.13 3.64 6.88 5.63 4.77 4.13 3.64 6.88 5.63 4.77 4.13 3.64 6.88 5.63 4.77 4.13 3.64 6.88 5.63 4.77 4.13 3.64 6.88 5.63 4.77 4.13

23.69 20.05 17.37 15.33 28.96 23.69 20.05 17.37 15.33 28.96 23.69 20.05 17.37 15.33 28.96 23.69 20.05 17.37 15.33 28.96 23.69 20.05 17.37 15.33 28.96 23.69 20.05 17.37

1.35 1.35 1.24 1.24 1.61 1.35 1.35 1.24 1.24 1.61 1.35 1.35 1.08 1.08 1.61 1.35 1.35 1.08 1.08 1.61 1.35 1.35 1.08 1.08 1.61 1.35 1.35 1.08

Table E3(Continued) P.of Galvanization

231

(DM) 8.11

P.of Plate, and Paint (DM) 1.31

P.of P.of P.of Tubes Welding Header (DM)

(DM)

(DM)

3.64

15.33

1.08

175

232 233 234 235 236 237 238 239 240 241

11.2 10.6 10.2 9.84 9.60 13.7 13.1 12.6 12.3 12.1

1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31 1.31

6.88 5.63 4.77 4.13 3.64 6.88 5.63 4.77 4.13 3.64

28.96 23.69 20.05 17.37 15.33 28.96 23.69 20.05 17.37 15.33

176

1.61 1.35 1.35 1.08 1.08 1.61 1.35 1.35 1.08 1.08

Table E4. Diameter of header, unit weight of tube and header, mass of plate, tube and absorber plate, for each combination. Dh Uwtube Uwheader Mass of Plate Mass of 1tube

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

(m)

(kg)

(kg)

(kg)

(kg)

Mass of Absorber (kg)

0.031 0.028 0.026 0.024 0.023 0.031 0.028 0.026 0.024 0.023 0.031 0.028 0.026 0.024 0.023 0.031 0.028 0.026 0.024 0.023 0.031 0.028 0.026 0.024 0.023 0.031 0.028 0.026 0.024 0.023 0.03

0.161 0.161 0.161 0.161 0.161 0.161 0.161 0.161 0.161 0.161 0.161 0.161 0.161 0.161 0.161 0.161 0.161 0.161 0.161 0.161 0.161 0.161 0.161 0.161 0.161 0.161 0.161 0.161 0.161 0.161 0.181

0.740 0.666 0.617 0.567 0.543 0.740 0.666 0.617 0.567 0.543 0.740 0.666 0.617 0.567 0.543 0.740 0.666 0.617 0.567 0.543 0.740 0.666 0.617 0.567 0.543 0.740 0.666 0.617 0.567 0.543 0.715

6.33 6.33 6.33 6.33 6.33 10.1 10.1 10.1 10.1 10.1 12.7 12.7 12.7 12.7 12.7 15.2 15.2 15.2 15.2 15.2 18.9 18.9 18.9 18.9 18.9 25.3 25.3 25.3 25.3 25.3 6.33

0.29 0.29 0.29 0.29 0.29 0.29 0.29 0.29 0.29 0.29 0.29 0.29 0.29 0.29 0.29 0.29 0.29 0.29 0.29 0.29 0.29 0.29 0.29 0.29 0.29 0.29 0.29 0.29 0.29 0.29 0.33

10.7 10.0 9.60 9.20 8.90 14.5 13.8 13.3 13.0 12.7 17.0 16.3 15.9 15.5 15.3 19.5 18.9 18.4 18.0 17.8 23.3 22.7 22.2 21.8 21.6 29.7 29.0 28.5 28.2 27.9 11.0

177

Table E4 (Continued) Dh Uwtube Uwheader Mass of Plate Mass of 1tube

32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61

(m)

(kg)

(kg)

(kg)

(kg)

Mass of Absorber (kg)

0.028 0.026 0.024 0.023 0.03 0.028 0.026 0.024 0.023 0.03 0.028 0.026 0.024 0.023 0.03 0.028 0.026 0.024 0.023 0.03 0.028 0.026 0.024 0.023 0.03 0.028 0.026 0.024 0.023 0.03

0.181 0.181 0.181 0.181 0.181 0.181 0.181 0.181 0.181 0.181 0.181 0.181 0.181 0.181 0.181 0.181 0.181 0.181 0.181 0.181 0.181 0.181 0.181 0.181 0.181 0.181 0.181 0.181 0.181 0.222

0.666 0.617 0.567 0.543 0.715 0.666 0.617 0.567 0.543 0.715 0.666 0.617 0.567 0.543 0.715 0.666 0.617 0.567 0.543 0.715 0.666 0.617 0.567 0.543 0.715 0.666 0.617 0.567 0.543 0.715

6.33 6.33 6.33 6.33 10.1 10.1 10.1 10.1 10.1 12.7 12.7 12.7 12.7 12.7 15.2 15.2 15.2 15.2 15.2 18.9 18.9 18.9 18.9 18.9 25.3 25.3 25.3 25.3 25.3 6.33

0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.40

10.3 9.8 9.4 9.1 14.8 14.1 13.6 13.2 12.9 17.3 16.6 16.1 15.7 15.5 19.8 19.2 18.7 18.3 18.0 23.6 23.0 22.5 22.1 21.8 30.0 29.3 28.8 28.4 28.1 11.7

178

62 63 64 65

0.027 0.025 0.024 0.022

0.222 0.222 0.222 0.222

0.641 0.592 0.567 0.518

6.33 6.33 6.33 6.33

0.40 0.40 0.40 0.40

10.9 10.3 9.80 9.50

Table E4(Continued) Dh Uwtube Uwheader Mass of Plate Mass of 1tube

66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92

(m)

(kg)

(kg)

(kg)

(kg)

Mass of Absorber (kg)

0.030 0.027 0.025 0.024 0.022 0.030 0.027 0.025 0.024 0.022 0.03 0.027 0.025 0.024 0.022 0.030 0.027 0.025 0.024 0.022 0.030 0.027 0.025 0.024 0.022 0.041 0.037

0.222 0.222 0.222 0.222 0.222 0.222 0.222 0.222 0.222 0.222 0.222 0.222 0.222 0.222 0.222 0.222 0.222 0.222 0.222 0.222 0.222 0.222 0.222 0.222 0.222 0.212 0.212

0.715 0.641 0.592 0.567 0.518 0.715 0.641 0.592 0.567 0.518 0.715 0.641 0.592 0.567 0.518 0.715 0.641 0.592 0.567 0.518 0.715 0.641 0.592 0.567 0.518 0.986 0.888

10.1 10.1 10.1 10.1 10.1 12.7 12.7 12.7 12.7 12.7 15.2 15.2 15.2 15.2 15.2 18.9 18.9 18.9 18.9 18.9 25.3 25.3 25.3 25.3 25.3 6.33 6.33

0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.38 0.38

15.5 14.7 14.1 13.6 13.3 18.1 17.2 16.6 16.2 15.8 20.6 19.7 19.1 18.7 18.3 24.4 23.5 22.9 22.5 22.1 30.7 29.8 29.2 28.8 28.4 12.1 11.2

179

Table E4(Continued)

(m) 0.034 0.032 0.031 0.041 0.037 0.034 0.032 0.031 0.041 0.037 0.034 0.032 0.031 0.041 0.037 0.034 0.032 0.031 0.041 0.037 0.034 0.032 0.031 0.041 0.037 0.034 0.032 0.031 0.04 0.037 0.034

(kg) 0.212 0.212 0.212 0.212 0.212 0.212 0.212 0.212 0.212 0.212 0.212 0.212 0.212 0.212 0.212 0.212 0.212 0.212 0.212 0.212 0.212 0.212 0.212 0.212 0.212 0.212 0.212 0.212 0.241 0.241 0.241

(kg) 0.814 0.764 0.740 0.986 0.888 0.814 0.764 0.740 0.986 0.888 0.814 0.764 0.740 0.986 0.888 0.814 0.764 0.740 0.986 0.888 0.814 0.764 0.740 0.986 0.888 0.814 0.764 0.740 0.962 0.888 0.814

(kg) 6.33 6.33 6.33 10.1 10.1 10.1 10.1 10.1 12.7 12.7 12.7 12.7 12.7 15.2 15.2 15.2 15.2 15.2 18.9 18.9 18.9 18.9 18.9 25.3 25.3 25.3 25.3 25.3 6.33 6.33 6.33

(kg) 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.44 0.44 0.44

Mass of Absorber (kg) 10.6 10.1 9.80 15.9 15.0 14.4 13.9 13.6 18.4 17.5 16.9 16.5 16.1 20.9 20.1 19.4 19.0 18.7 24.7 23.9 23.2 22.8 22.5 31.1 30.2 29.6 29.1 28.8 12.6 11.6 10.9

124 0.032

0.241

0.764

6.33

0.44

10.4

Dh 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123

Uwtube Uwheader Mass of Plate Mass of 1tube

180

Table E4(Continued) Dh Uwtube Uwheader Mass of Plate Mass of 1tube 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156

(m) 0.030 0.040 0.037 0.034 0.032 0.030 0.040 0.037 0.034 0.032 0.030 0.040 0.037 0.034 0.032 0.030 0.040 0.037 0.034 0.032 0.030 0.040 0.037 0.034 0.032 0.030 0.040 0.036 0.034 0.032 0.030 0.040

(kg) 0.241 0.241 0.241 0.241 0.241 0.241 0.241 0.241 0.241 0.241 0.241 0.241 0.241 0.241 0.241 0.241 0.241 0.241 0.241 0.241 0.241 0.241 0.241 0.241 0.241 0.241 0.296 0.296 0.296 0.296 0.296 0.296

(kg) 0.715 0.962 0.888 0.814 0.764 0.715 0.962 0.888 0.814 0.764 0.715 0.962 0.888 0.814 0.764 0.715 0.962 0.888 0.814 0.764 0.715 0.962 0.888 0.814 0.764 0.715 0.962 0.863 0.814 0.764 0.715 0.962

(kg) 6.33 10.1 10.1 10.1 10.1 10.1 12.7 12.7 12.7 12.7 12.7 15.2 15.2 15.2 15.2 15.2 18.9 18.9 18.9 18.9 18.9 25.3 25.3 25.3 25.3 25.3 6.33 6.33 6.33 6.33 6.33 8.86

(kg) 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.54 0.54 0.54 0.54 0.54 0.54 181

Mass of Absorber (kg) 10.0 16.4 15.4 14.7 14.2 13.8 18.9 18.0 17.3 16.8 16.4 21.4 20.5 19.8 19.3 18.9 25.2 24.3 23.6 23.1 22.7 31.5 30.6 29.9 29.4 29.0 13.6 12.4 11.6 11.0 10.6 16.1

157 158 159 160

0.040 0.036 0.034 0.032

0.296 0.296 0.296 0.296

0.962 0.863 0.814 0.764

10.1 10.1 10.1 10.1

0.54 0.54 0.54 0.54

17.3 16.2 15.4 14.8

Table E4(Continued) Dh Uwtube Uwheader Mass of Plate Mass of 1tube 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188

(m) 0.030 0.040 0.036 0.034 0.032 0.030 0.040 0.036 0.034 0.032 0.030 0.040 0.036 0.034 0.032 0.030 0.040 0.036 0.034 0.032 0.030 0.039 0.036 0.033 0.031 0.029 0.039 0.036

(kg) 0.296 0.296 0.296 0.296 0.296 0.296 0.296 0.296 0.296 0.296 0.296 0.296 0.296 0.296 0.296 0.296 0.296 0.296 0.296 0.296 0.296 0.349 0.349 0.349 0.349 0.349 0.349 0.349

(kg) 0.715 0.962 0.863 0.814 0.764 0.715 0.962 0.863 0.814 0.764 0.715 0.962 0.863 0.814 0.764 0.715 0.962 0.863 0.814 0.764 0.715 0.937 0.863 0.789 0.740 0.690 0.937 0.863

(kg) 10.1 12.7 12.7 12.7 12.7 12.7 15.2 15.2 15.2 15.2 15.2 18.9 18.9 18.9 18.9 18.9 25.3 25.3 25.3 25.3 25.3 6.33 6.33 6.33 6.33 6.33 10.1 10.1

(kg) 0.54 0.54 0.54 0.54 0.54 0.54 0.54 0.54 0.54 0.54 0.54 0.54 0.54 0.54 0.54 0.54 0.54 0.54 0.54 0.54 0.54 0.63 0.63 0.63 0.63 0.63 0.63 0.63 182

Mass of Absorber (kg) 14.4 19.9 18.7 17.9 17.4 16.9 22.4 21.2 20.5 19.9 19.4 26.2 25.0 24.3 23.7 23.2 32.5 31.4 30.6 30.0 29.5 14.5 13.2 12.2 11.6 11.0 18.2 17.0

189 190 191 192 193 194 195

0.033 0.031 0.029 0.039 0.036 0.033 0.031

0.349 0.349 0.349 0.349 0.349 0.349 0.349

0.789 0.740 0.690 0.937 0.863 0.789 0.740

10.1 10.1 10.1 12.7 12.7 12.7 12.7

0.63 0.63 0.63 0.63 0.63 0.63 0.63

16.0 15.3 14.8 20.8 19.5 18.6 17.9

Table E4(Continued) Dh Uwtube Uwheader Mass of Plate Mass of 1tube (m) (kg) 196 0.029 0.349 197 0.039 0.349 198 0.036 0.349 199 0.033 0.349 200 0.031 0.349 201 0.029 0.349 202 0.039 0.349 203 0.036 0.349 204 0.033 0.349 205 0.031 0.349 206 0.029 0.349 207 0.039 0.349 208 0.036 0.349 209 0.033 0.349 210 0.031 0.349 211 0.029 0.349 212 0.038 0.425 213 0.035 0.425 214 0.032 0.425 215 0.03 0.425 216 0.029 0.425 217 0.038 0.425 218 0.035 0.425 219 0.032 0.425 220 0.03 0.425

(kg) 0.690 0.937 0.863 0.789 0.740 0.690 0.937 0.863 0.789 0.740 0.690 0.937 0.863 0.789 0.740 0.690 0.912 0.838 0.764 0.715 0.690 0.912 0.838 0.764 0.715

(kg) 12.7 15.2 15.2 15.2 15.2 15.2 18.9 18.9 18.9 18.9 18.9 25.3 25.3 25.3 25.3 25.3 6.33 6.33 6.33 6.33 6.33 10.1 10.1 10.1 10.1

(kg) 0.63 0.63 0.63 0.63 0.63 0.63 0.63 0.63 0.63 0.63 0.63 0.63 0.63 0.63 0.63 0.63 0.77 0.77 0.77 0.77 0.77 0.77 0.77 0.77 0.77 183

Mass of Absorber (kg) 17.3 23.3 22.0 21.1 20.4 19.9 27.1 25.8 24.9 24.2 23.7 33.4 32.1 31.2 30.5 30.0 15.8 14.2 13.1 12.3 11.7 19.6 18.0 16.9 16.1

221 222 223 224 225 226 227 228 229 230

0.029 0.038 0.035 0.032 0.030 0.029 0.038 0.035 0.032 0.030

0.425 0.425 0.425 0.425 0.425 0.425 0.425 0.425 0.425 0.425

0.690 0.912 0.838 0.764 0.715 0.690 0.912 0.838 0.764 0.715

10.1 12.7 12.7 12.7 12.7 12.7 15.2 15.2 15.2 15.2

0.77 0.77 0.77 0.77 0.77 0.77 0.77 0.77 0.77 0.77

15.5 22.1 20.5 19.4 18.6 18.1 24.6 23.1 22.0 21.2

Table E4(Continued) Dh Uwtube Uwheader Mass of Plate Mass of 1tube 231 232 233 234 235 236 237 238 239 240 241

(m) 0.029 0.038 0.035 0.032 0.030 0.029 0.038 0.035 0.032 0.030 0.029

(kg) 0.425 0.425 0.425 0.425 0.425 0.425 0.425 0.425 0.425 0.425 0.425

(kg) 0.690 0.912 0.838 0.764 0.715 0.690 0.912 0.838 0.764 0.715 0.690

(kg) 15.2 18.9 18.9 18.9 18.9 18.9 25.3 25.3 25.3 25.3 25.3

(kg) 0.77 0.77 0.77 0.77 0.77 0.77 0.77 0.77 0.77 0.77 0.77

184

Mass of Absorber (kg) 20.6 28.4 26.9 25.8 25.0 24.4 34.7 33.2 32.1 31.3 30.7

Figure E1. Price of absorber plate and efficiency of collector for each combination.

Figure E2. qu/ price, thickness of plate and tube spacing for each combination.

185

Figure E3. Price of absorber plate and efficiency of collector with best line.

186

APPENDIX F EXPERIMENTAL RESULTS

Table F1. The measured temperature and radiation data and efficiency values for STEK’ s Al collector.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

It W/m2 946.68 973.88 979.33 968.44 935.80 979.33 1006.5 1028.3 1033.7 1033.7 924.92 941.24 968.44 973.88 963.00 903.16 924.92 957.56 924.92 924.92 919.48 957.56 979.33

Ta °C 31.8 32.5 32.7 33.6 33.9 26.4 26.9 27.2 27.6 27.8 25.8 27.1 28.0 28.8 28.9 29.2 30.8 31.0 31.0 32.0 31.0 32.2 32.0

Ti °C 56.8 56.0 56.7 53.2 54.8 34.2 34.9 35.4 37.0 38.2 36.0 42.0 43.0 42.0 36.0 47.0 41.5 43.0 47.1 48.0 35.6 35.0 35.8

To °C 63.1 62.8 63.6 60.2 61.6 42.8 43.5 44.3 45.8 46.8 43.8 49.6 51.1 49.9 44.2 53.8 49.4 50.7 54.6 55.3 43.4 43.2 44.1 187

Ti-Ta/It Efficiency °Cm2/W 0.0264 0.65 0.0241 0.68 0.0245 0.69 0.0202 0.71 0.0223 0.71 0.0080 0.86 0.0079 0.84 0.0080 0.85 0.0091 0.83 0.0101 0.81 0.0110 0.82 0.0158 0.79 0.0155 0.82 0.0136 0.79 0.0074 0.83 0.0197 0.74 0.0116 0.83 0.0125 0.79 0.0174 0.79 0.0173 0.77 0.005 0.83 0.0029 0.84 0.0039 0.83

Table F2. The measured temperature and radiation data and efficiency values for STEK’ s copper collector. It

Ta °C 1 941.24 31.7 2 941.24 33.2

Ti °C 58.2 38.5

To °C 63.1 44.3

Ti-Ta/It Efficiency °Cm2/W 0.0282 0.51 0.0056 0.60

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

55.2 54.2 50.0 49.0 56.0 56.8 55.1 42.0 35.0 37.0 38.0 35.7 42.0 33.5 37.8 38.0 39.6 39.2 40.0 49.2 46.1 45.0 45.0 35.5 34.0 32.8 33.0 45.0 43.9 37.8 34.5 34.2 35.0

60.8 59.2 55.1 56.0 61.6 61.9 60.8 48.0 40.2 42.6 44.2 40.9 47.6 41.5 44.8 44.8 46.6 46.8 45.7 55.6 51.4 50.9 51.0 42.0 40.5 39.8 39.8 51.9 49.3 42.9 40.5 40.5 40.2

0.0230 0.0197 0.0174 0.0186 0.0238 0.0244 0.0220 0.0085 0.0034 0.0036 0.0050 0.0018 0.0110 0.0014 0.0050 0.0048 0.0066 0.0064 0.0072 0.0207 0.0164 0.0160 0.0147 0.0039 0.0021 0.0007 0.0003 0.0147 0.0134 0.0065 0.0037 0.0027 0.0032

W/m2

935.80 1033.7 935.80 924.92 946.68 968.44 957.56 946.68 930.36 963.00 963.00 946.68 924.92 1088.1 957.56 941.24 935.80 924.92 919.48 919.48 930.36 935.80 946.68 957.56 946.68 946.68 957.56 946.68 946.68 941.24 946.68 935.80 924.92

33.7 33.8 33.7 31.8 33.5 33.2 34.0 34.0 31.8 33.5 33.2 34.0 31.8 32.0 33.0 33.5 33.4 33.3 33.4 30.2 30.8 30.0 31.1 31.8 32.0 32.1 32.7 31.1 31.2 31.7 31.0 31.7 32.0

188

0.59 0.47 0.53 0.74 0.58 0.52 0.58 0.62 0.55 0.57 0.63 0.54 0.59 0.72 0.71 0.71 0.73 0.80 0.61 0.68 0.56 0.62 0.62 0.66 0.67 0.72 0.69 0.71 0.56 0.53 0.62 0.66 0.55

Table F3 The measured temperature and radiation data and efficiency values for DA SAN’ s Cu collector.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

It

Ta

Ti

To

Ti-Ta/It

Efficiency

W/m2 941.24 941.24 935.80 1033.7 935.80 924.92 946.68 968.44 957.56 946.68 930.36 963.00 963.00 946.68 924.92 957.56 946.68 946.68 957.56 1088.1 957.56 941.24 935.80 924.92 919.48 908.60 919.48 930.36 935.80 946.68 946.68 941.24 946.68 935.80 924.92

°C 31.7 33.2 33.7 33.8 33.7 31.8 33.5 33.2 34.0 34.0 31.8 33.5 33.2 34.0 31.8 31.8 32.0 32.1 32.7 32.0 33.0 33.5 33.4 33.3 33.4 29.0 30.2 30.8 30.0 31.1 31.2 31.7 31.0 31.7 32.0

°C 58.0 38.2 55.2 54.7 50.1 47.0 55.5 56.2 54.8 43.0 35.0 37.0 38.0 35.7 42.8 35.0 34.0 32.85 33.2 33.9 38.0 38.0 39.7 39.1 40.0 52.8 49.2 46.1 45.0 45.0 43.9 38.0 35.0 34.1 35.0

°C 65.0 45.6 62.0 61.6 57.4 53.0 61.9 63.2 61.7 50.1 42.0 43.7 45.2 42.1 49.8 43.0 42.0 41.0 41.0 42.6 45.8 46.2 47.9 47.6 48.0 59.6 55.2 52.3 52.0 51.9 50.1 44.3 41.1 41.0 42.3

°Cm2/W 0.0279 0.0053 0.0230 0.0202 0.0175 0.0164 0.0232 0.0237 0.0217 0.0095 0.0034 0.0036 0.0050 0.0018 0.0119 0.0033 0.0021 0.0008 0.0005 0.0017 0.0052 0.0048 0.0067 0.0063 0.0072 0.0262 0.0207 0.0164 0.0160 0.0147 0.0134 0.0067 0.0042 0.0026 0.0032

0.76 0.80 0.74 0.68 0.8 0.66 0.69 0.74 0.74 0.77 0.77 0.71 0.76 0.69 0.77 0.85 0.86 0.88 0.83 0.82 0.83 0.89 0.89 0.94 0.89 0.76 0.67 0.68 0.76 0.74 0.67 0.68 0.66 0.75 0.80

189

Table F.4 The measured temperature and radiation data and efficiency values for galvanized iron collector. It 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 21 23

W/m2 946.68 973.88 979.33 968.44 935.80 979.33 1006.5 1028.3 1033.7 1033.7 924.92 941.24 968.44 973.88 963.00 903.16 924.92 957.56 924.92 924.92 919.48 957.56 979.33

Ta

Ti

To Ti-Ta/It Efficiency

°C °C °C °Cm2/W 31.8 56.9 61,6 0,0265 32.5 56.3 61,2 0,0244

32.7 33.6 33.9 26.4 26.9 27.2 27.6 27.8 25.8 27.1 28.0 28.8 28.9 29.2 30.8 31.0 31.0 32.0 31.0 32.2 32.0

56.7 53.4 54.6 34.0 34.2 35.0 37.0 38.0 35.0 39.1 39.9 40.1 35.8 46.9 44.6 44.0 47.0 47.0 35.6 35.0 35.8

62,1 58,8 59,8 40,8 41,1 42,2 44,3 45.0 41,3 45,8 46,5 46,9 42,7 52,5 50,8 50,4 53,1 53.0 42,3 42,1 42,9

0,0245 0,0204 0,0221 0,0078 0,0073 0,0076 0,0091 0,0099 0,0099 0,0127 0,0123 0,0116 0,0072 0,0196 0,0149 0,0136 0,0173 0,0162 0,0050 0,0029 0,0039

190

0,52 0,52 0,58 0,58 0,58 0,72 0,72 0,73 0,74 0,71 0,71 0,74 0,71 0,73 0,75 0,65 0,70 0,70 0,69 0,68 0,76 0,77 0,76

APPENDIX G

THE SAMPLE CALCULAT ON FOR T ME CONSTANT

STEK’s Al Ti :18.1°C To,initial :25.8°C To,t=(To-Ti)x0.368+Ti=20.93°C 1.minute To,t = 23.5°C To,t = 21.5°C

2.

Time Constant is 137 seconds (2′17′′).

Galvanized Fe Ti :17.7°C To,initial :25.8°C To,t=(To-Ti)x.368+Ti=20.68°C 1.minute To,t = 24.1°C 2

To,t = 22.5°C

3

To,t = 21.4°C

Time Constant is 198 seconds (3′18′′)

191

APPENDIX H

GLOSSARY OF SOLAR HEAT NG TERMS

A


   
      
    


        
   
    
  
   
       
 
     
 
 
   
     

  
    
 
   
    
      
 

    
 
  
   

        
    
  

        
   
     
 
     
   
   
     
      
        
    
 
   
  
        
    

    
    
      
  
    
   
       
      
        
  
         
  
  
       
 
   
        

 
     
     

         
   
       
   
  
      
    
   
    
     
  
    
    
 
  
        
  
     
    

  
     
    
 
    



  
  

 
 
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