A review on thermoelectric cooling parameters and performance

doi:10.1016/j.rser.2014.07.045

Renewable and Sustainable Energy Reviews

Volume 38, October 2014, Pages 903-916

https://doi.org/10.1016/j.rser.2014.07.045 Get rights and content

Abstract

This paper deals with a review of the main research aspects concerning the formulation of the parameters indicating the characteristics and performance of thermoelectric cooling devices, with particular reference to a number of recent publications. The specific aspects addressed include some practical considerations referring to the thermoelectric figure of merit, the characterization of the cooling capacity, and the assessment of the coefficient of performance (COP). The contribution of this paper starts by categorizing the topics addressed by recent review papers, showing that these reviews generally had a wide focus and provided little specific details on thermoelectric cooling parameters and performance. Then, the dimensionless thermoelectric figure of merit is addressed by focusing on its conventional and modified definitions and indicating the values obtained for different thermoelectric cooling materials. Furthermore, the expressions of the cooling capacity for single-stage and multi-stage thermoelectric coolers are reviewed. Concerning the COP, its dedicated expressions are constructed starting from the classical formulation and introducing additional factors or modifications in order to take into account the Thomson effect, the dependence on temperature of the thermoelectric materials, and the effects of the electrical contact resistance, thermal resistance, thermoelement length and current. Finally, on the basis of the indications taken from the literature, further considerations are included on the COP values found in thermoelectric cooling applications, as well as on how to obtain COP improvements.

Introduction

The thermoelectric devices used in thermoelectric refrigeration (or thermoelectric coolers) are based on the Peltier effect to convert electrical energy into a temperature gradient [1]. A conventional thermoelectric cooler is composed of a number of N-type and P-type semiconductor junctions connected electrically in series by metallic interconnects (conducting strips, in general made of copper) and thermally in parallel, forming a single-stage cooler [2]. If a low-voltage DC power source is applied to a thermoelectric cooler, heat is transferred from one side of the thermoelectric cooler to the other side. Therefore, one face of the thermoelectric cooler is cooled and the opposite face is heated.

Fig. 1 depicts a thermoelectric cooling module considered as a thermoelectric refrigerator, in which the electrical current flows from the N-type element to the P-type element [3]. The temperature $T_{c}$ of the cold junction decreases and the heat is transferred from the environment to the cold junction at a lower temperature. This process happens when the transport electrons pass from a low energy level inside the P-type element to a high energy level inside the N-type element through the cold junction. At the same time, the transport electrons carry the absorbed heat to the hot junction which is at temperature $T_{h}$ . This heat is dissipated in the heat sink, whilst the electrons return at a lower energy level in the P-type semiconductor (the Peltier effect). If there is a temperature difference between the cold junction and hot junction of N-type and P-type thermoelements, a voltage (called Seebeck voltage) directly proportional to the temperature difference is generated [4], [5]. The other parameters appearing in Fig. 1 are introduced in Section 3.2.

The quality of a thermoelectric cooler depends on parameters such as the electric current applied at the couple of N-type and P-type thermoelements, the temperatures of the hot and cold sides, the electrical contact resistance between the cold side and the surface of the device, the thermal and electrical conductivities of the thermoelement, and the thermal resistance of the heat sink on the hot side of the thermoelectric cooler [6]. The number of thermoelements in a thermoelectric module mainly depends on the required cooling capacity and the maximum electric current [7].

The characteristics and performance of a thermoelectric refrigerator are described by parameters like the figure of merit, the cooling capacity, and the coefficient of performance [4]. This review is specifically focused on these parameters, addressing the concepts in a different way with respect to various review papers appearing on thermoelectric cooling in the past years. Specific aspects such as thermoelectric cooling system design, experimental assessment, numerical analysis and simulation are outside the scope of this review.

The remainder of this paper is organized as follows. Section 2 presents a synthetic overview of recent review papers dedicated to aspects relevant to thermoelectric materials, applications and parameters. Section 3 recalls the basic definitions of figure of merit, cooling capacity, and coefficient of performance. Section 4 addresses some analytical formulations and experimental results referring to the thermoelectric figure of merit. Section 5 presents an assessment of the relevant concepts and literature concerning the cooling capacity. Section 6 deals with the coefficient of performance, starting from its classical expression and introducing specific formulations including the impact of the Thomson effect, the dependence on temperature of the characteristics of the materials, the effect of electrical contact resistances and thermal resistances on the $C O P$ , with some indications on $C O P$ improvement. The last section contains the concluding remarks.

Section snippets

Overview of recent literature reviews

A summary of recent review papers is provided in Table 1. The relevant topics addressed are categorized into general aspects, applications and parameters, to show that generally these reviews had a wider scope and dedicated a relatively limited space to the details referring to thermoelectric cooling parameters and formulations of the performance indicators.

Thermoelectric figure of merit

The thermoelectric figure of merit $Z$ indicates if a material is a good thermoelectric cooler. It depends on three material parameters: electrical resistivity $ρ$ (or electrical conductivity $σ = 1 / ρ$ ), Seebeck coefficient $α$ and total thermal conductivity $k$ between the cold and hot sides $Z = \frac{α^{2}}{ρ k} = \frac{α^{2} σ}{k}$

Considering the absolute temperature $T$ (which represents the mean temperature between the cold side and hot side of the thermoelectric module), a widely used parameter is the dimensionless product $Z T$ .

Practical considerations on the dimensionless figure of merit

Starting from the formulation indicated in (1), the dimensionless figure of merit $Z T$ is expressed as $Z T = \frac{α^{2} T}{ρ k} = \frac{α^{2} σ T}{k}$ where

the term $k = k_{φ} + k_{ε}$ is the total thermal conductivity, composed of the phonon (or lattice) component $k_{φ}$ and the electronic component $k_{ε}$ ; the product $α^{2} σ$ is called the electrical power factor and depends on the Seebeck coefficient $α$ and on the electrical conductivity $σ$ [8].

In practice, $Z T$ represents the efficiency of the N-type and P-type materials which compose a thermoelement. A

Cooling capacity for a single thermoelectric cooler

The expression of the cooling capacity per unit area $q$ , taking into account thermal and electrical contact resistances, depends on the thermoelement length l of the module, as reported in [2], [21] $q = \frac{Q_{c}}{S} = \frac{k (Δ T_{\max} - Δ T)}{l + 2 χ y + (χ y / C O P)}$ where y is the thickness of the contact layers (see Fig. 2), $χ$ is the ratio between the thermal conductivity of the thermoelements and the thermal conductivity of the contact layers, and $Δ T_{\max} = Z T_{c}^{2} / 2$ is the maximum temperature difference of a module when the cooling

Classical expression of the COP

The $C O P$ for thermoelectric refrigerators is given by expression (4). The COP values mainly depend on the temperatures at the two sides of the thermoelectric element. This fact is well indicated starting from the definition of the (ideal) Carnot $C O P$ , here indicated as $C O P_{C}$ , that considers the temperatures of the hot source $T_{h}$ and of the cold source $T_{c}$ : $C O P_{C} = \frac{1}{(T_{h} / T_{c}) - 1} = \frac{T_{c}}{T_{h} - T_{c}}$

The classical expression of the $C O P$ , corresponding to the maximum $C O P$ [3] used for sizing the thermoelectric element [7],

Concluding remarks

Thermoelectric cooling is one of the main applications of the thermoelectric devices. This paper has reviewed the formulations of the parameters representing the characteristics and performance of thermoelectric cooling, providing indications on the different formulations of these parameters in order to take into account more detailed effects, and on the values of these parameters found in different applications presented in the recent literature. In particular, on the point of view of the

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A review on thermoelectric cooling parameters and performance

Abstract

Introduction

Section snippets

Overview of recent literature reviews

Thermoelectric figure of merit

Practical considerations on the dimensionless figure of merit

Cooling capacity for a single thermoelectric cooler

Classical expression of the COP

Concluding remarks

Appl Energy

Appl Therm Eng

Appl Therm Eng

Appl Therm Eng

Appl Therm Eng

Renew Sustain Energy Rev

Appl Therm Eng

Appl Therm Eng

Energy Build

Energy Convers Manag

Appl Energy

Energy Convers Manag

Mater Res Bull

Appl Therm Eng

Int J Refrig

Int Commun Heat Mass Transf

Appl Energy

Int J Refrig

Appl Therm Eng

Int J Refrig

Energy

Int J Heat Mass Transf

Sens Actuat. A

Energy Convers Manag

Int J Heat Mass Transf

Appl Energy

Appl Therm Eng

Appl Energy

Microelectron J

Appl Energy

Appl Therm Eng

Cryogenics

Appl Therm Eng

Int J Heat Mass Transf

Int J Refrig

Int J Heat Mass Transf

Appl Therm Eng

Renew Energy

Int J Refrig

Sol Energy

Int J Heat Mass Transf

Appl Therm Eng

Appl Therm Eng

Appl Therm Eng