Numerical simulation of Thermoelectric System

LATEST TRENDS on SYSTEMS (Volume II) Numerical simulation of Thermoelectric System ELENA-OTILIA VIRJOGHE*, DIANA ENESCU**, MARCEL IONEL**, MIHAIL-FLO...
Author: Norman Riley
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LATEST TRENDS on SYSTEMS (Volume II)

Numerical simulation of Thermoelectric System ELENA-OTILIA VIRJOGHE*, DIANA ENESCU**, MARCEL IONEL**, MIHAIL-FLORIN STAN* *Automatics, Informatics and Electrical Engineering Department **Electronic, Telecommunications and Energetically Engineering Department Valahia University Targoviste, Electrical Engineering Faculty 18-24 Unirii Blvd., 130082 Targoviste ROMANIA [email protected], [email protected], [email protected] , [email protected], www.valahia.ro Abstract: - The thermoelectric systems have attracted renewed interest as concerns with the efficient use of energy resources, and the minimization of environmental damage, have become important current issues. There has been he recognition that thermoelectric devices could play a role in generating electricity from waste heat, enabling cooling via refrigerators with no moving parts, and many other more specialized applications. This paper presents of numerical simulation for several the thermoelectric materials. Numerical simulation is carried out by using a finite element package ANSYS. Key-Words: - numerical simulation, Peltier cooling, materials properties, temperature, voltage, figure of merit.

1 Introduction

ZT =

The thermoelectric systems have been the subject of major advances in recent years, due to the development of semiconductors and the incorporation of the thermoelectric devices into domestic appliances. Generally, if a thermal gradient is applied to a solid, it will always be accompanied by an electric field in the opposite direction. This process is called as the thermoelectric effect. Thermoelectric material applications include refrigeration or electric power generation. The efficiency of a thermoelectric material is given by the figure of merit, Z, which is defined as [1]: Z=

α 2 ⋅σ  1  k

,  K 

(2)

k

An important point it is represented by achieving a high value of ZT, this being carried out by increasing the power factor (α2σ) and decreasing the thermal conductivity (k). One of the main applications of thermoelectric is for refrigeration purposes. An electrical current applied across a material will cause a temperature differential which can be used for cooling [1].

2 Problem's definition 

(1)

Consider the one dimensional  ∇ = 

d   steady-state, dx 

thermoelectric power generation problem, where only a single (n-or p-type) leg is considered. The thermoelectric material properties all vary with absolute temperature T. Positive electric current density and heat flux flows from Th to Tc. Positive electric field E and temperature gradient are in the opposite direction of J and Q (Fig.1). The electric current density is for a simple generator, given by [2]:

where: α - material's Seebeck coefficient, V/K, σ - electrical conductivity of material, S/m, k – thermal conductivity of material, W/(m.K). The numerator in equation (1) is called the power factor. Therefore, the most useful method in order to describe and compare the quality and thermoelectric efficiency of different material systems is the dimensionless figure of merit (ZT), where T is the temperature of interest. Therefore, equation (1) can be rewritten as:

ISSN: 1792-4235

α 2 ⋅σ ⋅T

J=

I A

(3)

630

ISBN: 978-960-474-214-1

LATEST TRENDS on SYSTEMS (Volume II)

where I is the electric current and A is the crosssectional area of the thermoelectric element.

∇(k∇T ) = −T

where T

dα J∇T − ρJ 2 dT

(6)

dα is the Thomson coefficient. dT

The electric power density P (power produced per volume) is the product of the electric field E and current density J: P = EJ

(7)

Using sign convention in Fig. 1, a purely resistive element (α=0) would require a negative electric field E = − ρ J to make a positive current (+J) so that the power density P = − ρJ 2 is negative (electric energy consumed).

Fig.1 Diagram of a single-element thermoelectric generator (Source:[2]) The direction of positive variables is shown relative to the hot-and cold side. For positive Seebeck coefficient (α>0), all of the variables are positive for a generator operating efficiently. For negative Seebeck coefficient (α

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