Approximate formulae for thermal resistance matching of thermoelectric coolers operating at room temperature

Abstract

Thermoelectric modules can convert thermal energy into electrical energy or vice versa, and they are becoming increasingly popular in numerous cooling applications. A thermoelectric cooler has no moving parts and may potentially serve as a maintenance-free and noise-free refrigerator with a long life span. According to previous studies, it is important to optimize thermal resistance of the thermoelectric module in a thermoelectric cooling system. Inappropriate thermal matching degrades the performance of the thermoelectric cooling system, decreases its efficiency, and increases its size and weight without providing enough cooling power. In this study, we develop approximate formulae for estimating the optimal thermal resistance of the thermoelectric module under given conditions of thermal interfaces at room temperature. These formulae are obtained using the technique of series expansion and truncation. In addition, the relative error in the estimates obtained from these formulae is analyzed to provide a validity range for each formula. Our approximate formulae can be used to quickly estimate the condition of thermal resistance matching in an early design stage, which may reduce the cost of overall development of thermoelectric cooling products. © 2020 The Author(s).