Solving Problems in Food Engineering

Stavros Yanniotis, Ph.D. Author

Solving Problems in Food Engineering

Stavros Yanniotis, Ph.D. Department of Food Science and Technology Agricultural University of Athens Athens, Greece

ISBN: 978-0-387-73513-9

eISBN: 978-0-387-73514-6

Library of Congress Control Number: 2007939831 # 2008 Springer Science+Business Media, LLC All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC., 233 Spring Street, New York, NY10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper 9 8 7 6 5 4 3 2 1 springer.com

‘‘Tell me and I will listen, Show me and I will understand Involve me and I will learn’’ Ancient Chinese Proverb

Preface

Food engineering is usually a difficult discipline for food science students because they are more used to qualitative rather than to quantitative descriptions of food processing operations. Food engineering requires understanding of the basic principles of fluid flow, heat transfer, and mass transfer phenomena and application of these principles to unit operations which are frequently used in food processing, e.g., evaporation, drying, thermal processing, cooling and freezing, etc. The most difficult part of a course in food engineering is often considered the solution of problems. This book is intended to be a step-by-step workbook that will help the students to practice solving food engineering problems. It presumes that the students have already studied the theory of each subject from their textbook. The book deals with problems in fluid flow, heat transfer, mass transfer, and the most common unit operations that find applications in food processing, i.e., thermal processing, cooling and freezing, evaporation, psychometrics, and drying. The book includes 1) theoretical questions in the form ‘‘true’’ or ‘‘false’’ which will help the students quickly review the subject that follows (the answers to these questions are given in the Appendix); 2) solved problems; 3) semisolved problems; and 4) problems solved using a computer. With the semisolved problems the students are guided through the solution. The main steps are given, but the students will have to fill in the blank points. With this technique, food science students can practice on and solve relatively difficult food engineering problems. Some of the problems are elementary, but problems of increasing difficulty follow, so that the book will be useful to food science students and even to food engineering students. A CD is supplied with the book which contains solutions of problems that require the use of a computer, e.g., transient heat and mass transfer problems, simulation of a multiple effect evaporator, freezing of a 2-D solid, drying, and others. The objectives for including solved computer problems are 1) to give the students the opportunity to run such programs and see the effect of operating and design variables on the process; and 2) to encourage the students to use computers to solve food engineering problems. Since all the programs in this CD are open code programs, the students can see all the equations and the logic behind the calculations. They are encouraged to see how the programs work vii

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Preface

and try to write their own programs for similar problems. Since food science students feel more comfortable with spreadsheet programs than with programming languages, which engineering students are more familiar with, all the problems that need a computer have EXCEL1 spreadsheet solutions. I introduce the idea of a digital SWITCH to start and stop the programs when the problem is solved by iteration. With the digital SWITCH, we can stop and restart each program at will. When the SWITCH is turned off the program is not running, so that we can change the values of the input variables. Every time we restart the program by turning the SWITCH on, all calculations start from the beginning. Thus it is easy to change the initial values of the input variables and study the effect of processing and design parameters. In the effort to make things as simple as possible, some of the spreadsheet programs may not operate on some sets of parameters. In such cases, it may be necessary to restart the program with a different set of parameters. I am grateful to Dr H. Schwartzberg, who read the manuscripts and made helpful suggestions. I will also be grateful to readers who may have useful suggestions, or who point out errors or omissions which obviously have slipped from my attention at this point. Athens May 2007

Stavros Yanniotis

Contents

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

vii

1.

Conversion of Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Examples Exercises

1

2.

Use of Steam Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Review Questions Examples Exercises

5

3.

Mass Balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Review Questions Examples Exercises

4.

Energy Balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Theory Review Questions Examples Exercises

5.

Fluid Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Review Questions Examples Exercises

6.

Pumps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Theory Review Questions Examples Exercises

ix

x

Contents

7.

Heat Transfer By Conduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Theory Review Questions Examples Exercises

55

8.

Heat Transfer By Convection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Theory Review Questions Examples Exercises

67

Heat Transfer By Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Review Questions Examples Exercises

95

9.

10.

Unsteady State Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 Theory Review Questions Examples Exercises

11.

Mass Transfer By Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 Theory Review Questions Examples Exercises

12.

Mass Transfer By Convection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 Theory Review Questions Examples Exercises

13.

Unsteady State Mass Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 Theory Review Questions Examples Exercises

14.

Pasteurization and Sterilization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 Review Questions Examples Exercises

Contents

xi

15.

Cooling and Freezing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 Review Questions Examples Exercises

16.

Evaporation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 Review Questions Examples Exercises

17.

Psychrometrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 Review Questions Examples Exercises

18.

Drying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 Review Questions Examples Exercises

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 Appendix: Answers to Review Questions . . . . . . . . . . . . . . . . . . . . . . . . . Moody diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gurney-Lurie charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Heisler charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pressure-Enthalpy chart for HFC 134a . . . . . . . . . . . . . . . . . . . . . . . Pressure-Enthalpy chart for HFC 404a . . . . . . . . . . . . . . . . . . . . . . . Psychrometric chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bessel functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Roots of d tand=Bi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Roots of dJ1(d)-Bi Jo(d)=0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Roots of d cotd=1-Bi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Error function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

275 280 281 284 285 286 287 288 290 291 292 293

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295