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.

热电模块可以将热能转换为电能，反之亦然，并且它们在众多冷却应用中越来越受欢迎。热电冷却器没有活动部件，并且可能会成为使用寿命长的免维护且无噪音的冰箱。

根据先前的研究，在热电冷却系统中优化热电模块的热阻很重要。不适当的热匹配会降低热电冷却系统的性能，降低其效率，并增加其尺寸和重量，而不会提供足够的冷却功率。

在这项研究中，我们开发了近似公式，用于估算在给定的室温热界面条件下，热电模块的最佳热阻。这些公式是使用级数展开和截断技术获得的。另外，分析了从这些公式获得的估计值中的相对误差，以提供每个公式的有效范围。我们的近似公式可用于在设计的早期阶段快速估算热阻匹配的条件，这可能会降低热电冷却产品的整体开发成本。