Determination of the temperature field of the thermoelectric element when it cools down

Abstract

In this paper, the question of finding the temperature field of a rectangular thermoelectric element under boundary conditions of the third kind with an adibatically-isolated side is considered. Based on the Fourier method, the distribution of the temperature field of the thermoelectric element is obtained. The solution itself is obtained in the form of a series containing trigonometric and exponential functions. The reliability of the obtained result is confirmed by the fact that one of the special cases leads the problem to a problem with boundary conditions of the first kind, when the surface temperature is constant. The presented analysis of the main characteristics of thermoelectric converters makes it possible to determine the criteria for selecting materials and temperature conditions in order to increase the efficiency of such converters.