Analytical Approach for Study of Transient Performance of Thermoelectric Coolers

A solid-state thermoelectric device uses the Peltier effect to create a heat flux differential between the junctions of two different types of materials. By applying electrical energy, a thermoelectric cooler can transport heat from the cool side of the device to the heat sink. The purpose of this paper is to develop an analytical tool that can be readily implemented by design engineers in the field of thermoelectric cooler technology. The relatively complicated partial differential equation governing energy transport within the semiconductor elements is reduced to a conventional heat diffusion equation with the aid of a special function and then solved analytically using the integral-transformation technique. The temperature distributions within the semiconductor elements, the Seebeck effect, the thermal conductivity, the cooling load, and the system coefficient of performance for a thermoelectric cooler are determined and analyzed. The transient behavior of a thermoelectric cooler can be used as an optimization tool for various design configurations in meeting specific packaging requirements.