Energy and exergy analysis of an annular thermoelectric cooler

doi:10.1016/j.enconman.2015.10.029

Energy Conversion and Management

Volume 106, December 2015, Pages 804-814

https://doi.org/10.1016/j.enconman.2015.10.029 Get rights and content

Highlights

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Exergy analysis in the annular thermoelectric cooler (ATEC) system is proposed.
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Analytical expressions for the cooling power, exergy efficiency of an ATEC is derived.
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The effects of S_r and θ in Q_c and exergy efficiency of an ATEC is studied.

Abstract

In this paper the concept of annular thermoelectric cooler (ATEC) has been introduced. An exoreversible thermodynamic model of the annular thermoelectric cooler considering Thomson effect in conjunction with Peltier, Joule and Fourier heat conduction has been investigated using exergy analysis. New expressions for optimum current at the maximum energy/exergy efficiency, maximum cooling power conditions and dimensionless irreversibilities in the ATEC are derived. The modified expression for figure of merit of a thermoelectric cooler considering the Thomson effect has also been obtained. The results show that the cooling power, energy and exergy efficiency of the ATEC is lower than the flat plate thermoelectric cooler. The effects of annular shape parameter (S_r = r₂/r₁), dimensionless temperature ratio (θ = T_h/T_c) and the electrical contact resistances on cooling power, energy/exergy efficiency of an ATEC have been studied. It has also been proved that because of the influence of Thomson effect, the cooling power and energy/exergy efficiency of the ATEC is increased. This study will help in the designing of the actual annular thermoelectric cooling systems.

Introduction

Thermoelectric devices are solid state direct energy conversion devices for converting heat into electricity and vice versa [1], [2], [3], [4]. It operates on the combination of Seebeck, Peltier and Thomson effects. Thermoelectric devices have numerous advantages of being solid state device with no moving parts and require no maintenance. They provide noiseless operation, and offer light weight, compactness and hence, occupy small space [5]. The thermoelectric devices have better efficiency at lower power levels compared with conventional thermodynamic devices for power generation and space conditioning. Therefore, the thermoelectric devices are best suited for low power applications [6].

Thermoelectric cooler works as a reversed heat engine operating between the two heat reservoirs and its actual efficiency is lower than the ideal Carnot efficiency because of the irreversibilities induced by the electrical, thermal and the thermoelectric properties of the thermoelectric materials.

The single and multistage thermoelectric coolers have been analysed based on various thermodynamic techniques, such as non-equilibrium thermodynamics and entropy generation method by various researchers [7], [8], [9], [10], [11]. These studies provide the analytical framework for the design of thermoelectric cooling system. Wang et al. [12], [13] have modelled the thermoelectric system using three dimensional temperature and electric potential coupled model and analysed the system with different operating temperature, current and with convective and radiative heat transfer from the thermo-elements. The results show that the heat transfer from the thermo-elements have influence in the energy efficiency and cooling power of thermoelectric cooler. Huang et al. [14] optimised the geometry of the thermocouples using simplified conjugate-gradient method and found that the optimum geometry evaluated by this method had improved the cooling power of the thermoelectric cooler.

Fraisse et al. [15] studied the electrical analogy model to analyse the performance of the thermo-elements and found that the electrical analogy model is accurate in predicting the performance of the thermo-elements in steady state and transient operating conditions. Fraisse et al. [16] have compared different modelling approaches for the design and analysis of thermoelectric systems and found that the electrical analogy model and the finite element analysis (FEA) model predict the performance of the thermoelectric system accurately. Huang et al. [17], [18] and Chen et al. [19] studied the influence of Thomson effect in the thermoelectric cooler system and found that the Thomson effect influence the energy efficiency and cooling power output of the system. Manikandan and Kaushik [20] studied the thermoelectric generator operated thermoelectric cooler combined system for low cooling power applications with maximum power point tracking technique and found that the maximum power point tracking technique in combined system can improve the energy efficiency and cooling power output of the system.

Sahin and Yilbas [21] and Ali et al. [22] studied the thermoelectric couple with trapezoidal geometry and found that the energy conversion efficiency is higher than the flat plate geometry of thermoelectric couple. Shen et al. [23] studied the annular thermoelectric generator without considering the Thomson effect and found that the energy efficiency of annular thermoelectric generator is lower when compared with flat plate thermoelectric generator. Meng et al. [24], [25] have studied the transient behaviour of thermoelectric cooler and thermoelectric generator using three dimensional heat transfer and electric potential coupling model and found that, at lower currents the model with constant property also perform better but at higher currents the model with temperature dependent property has remarkable effect in the dynamic response.

Cvahtet and Strnad [26] analysed the ideal thermoelectric heat engine and heat pump and compared it with the actual systems based on the entropy generation concept and found that the second law of thermodynamics is useful in predicting the performance of the thermoelectric system. Nuwayhid et al. [27] and Wang et al. [28] have analysed the thermoelectric system based on entropy generation minimization method and derived analytical solution for the entropy generation in different modes of operation (TEG and TEC). Sharma et al. [29] carried out simple exergy analysis in the single and multistage exoreversible flat plate thermoelectric cooling system and found that the exergy analysis should be performed in thermoelectric system to identify and quantify the irreversibilities. Tipsaenporm et al. [30] have proposed thermodynamic analysis in thermoelectric cooler and found out second law efficiency is less than the first law (energy) efficiency and second law analysis is useful in the design of thermoelectric cooling systems. Kaushik et al. [31] have performed detailed exergy analysis of a thermoelectric heat pump system and found that the exergy analysis is useful to identify actual irreversibilities in the thermoelectric systems because, exergy analysis provides true measure of efficiency since it takes into considerations of first and second law of thermodynamics. Kaushik and Manikandan [32] studied the influence of Thomson effect in the performance optimization of the two stage thermoelectric cooler and found that the Thomson effect increases the performance of the thermoelectric cooler and it influence the optimization of number of thermocouples in the first and second stage of the thermoelectric cooler. Kaushik and Manikandan [33] studied the energetic and exergetic performance of an annular thermoelectric generator considering Thomson effect and concluded that Thomson effect decreases the performance of thermoelectric generator system. The basis of exergy analysis in different thermal systems for power generation, cooling and other industrial processes have been detailed in [34], [35], [36], [37]. With this technique the actual exergy destruction in the system can be located so that the avoidable exergy losses can be reduced by taking corrective actions.

If the fluid flowing through a pipe is to be cooled, then the design of heat exchanger using flat plate thermoelectric cooler may have structural challenges. Therefore, in such applications ATEC will be best suited because of its annular structure. Chen et al. [38] found that the cooling power and energy efficiency of a thermoelectric cooler will improve if the total heat transfer area is increased. In ATEC system the total heat transfer area is higher than the flat plate thermoelectric cooler and the hot side heat transfer area can be increased using annular fins and the design/integration of hot side heat exchanger will be simple. Therefore, an annular shaped thermoelectric cooler has been introduced in this paper.

Based on the literature survey, it is found that the annular shaped thermoelectric cooler has not been modelled and analysed. Moreover, the energy and exergy analysis in annular thermoelectric cooler systems has not been carried out. The effect of electrical contact resistance and the Thomson effect in energy/exergy efficiency of ATEC are also not studied. It is also found from the literature survey that the exergy analysis is useful in analysing the thermoelectric system. Therefore, it is desirable to carryout energy and exergy analysis in the annular thermoelectric cooler system to identify and quantify the irreversibilities happening in the system.

In this study the authors have derived dimensionless cooling power output, energy/exergy efficiency and dimensionless irreversibilities of the thermoelectric cooler and then analysed the effect of annular shape factor (S_r) and dimensionless temperature ratio (θ-theta) on the performance of ATEC system.

Section snippets

Thermodynamic modelling of ATEC

A typical ATEC with two thermoelectric couple is shown in Fig. 1, unlike flat plate thermoelectric cooler the cross section area A(r) of the thermoelectric couple increases in the radial direction (r).

Certain assumptions were made in the thermodynamic modelling and analysis of ATEC, that are as follows:

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One dimensional steady state heat transfer along the radial direction is considered for the analysis.
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The thickness (δ) of the thermoelectric couple is constant,
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Convection heat transfer from the

Results and discussion

The energy and exergy analysis of annular thermoelectric cooler has been carried out for various operating conditions in MATLAB Simulink environment. The Simulink block diagram of the annular thermoelectric cooler system is shown in Fig. 3.

The hot side temperature (T_h) of the ATEC is fixed at 300 K and the cold side temperature (T_c) is varied from 250 K to 290 K to calculate the performance parameters such as cooling power, energy efficiency, exergy efficiency and irreversibilities in the system.

Conclusions

In this study the concept of annular thermoelectric cooler has been introduced. The energy and exergy analyses of the annular thermoelectric cooler system considering Joule heating, Fourier Heat and Thomson effect have also been carried out. This study provides characteristics of the energy/exergy efficiency and the irreversibilities in an annular thermoelectric cooler system. The following conclusions can be drawn from this study:

•
Analytical expression for the temperature distribution,

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