Closed-Form Approximate Solution for Thermo-Mechanical Performance Analysis of Thermoelectric Generators with Temperature-Dependent Material Properties by Differential Transform Method

Abstract

Thermoelectric materials play a significant role in the electronic industry and energy production. However, temperature-dependent material properties make the theoretical analysis challenging. This paper investigates the thermo-mechanical performance of thermoelectric generators with temperature-dependent material properties by differential transform method (DTM). The nonlinear distribution of temperature-dependent thermal conductivity, Seebeck coefficient, and electric resistivity are considered. DTM is used to construct analytical approximate solutions of the nonlinear differential equation governing the temperature distribution of the thermoelectric element. The thermal performance of the thermoelectric element including temperature distribution, temperature gradient, heat flux, power output per area, and energy conversion efficiency are predicted by DTM. And, the proposed method is utilized to analyze the thermal stress of the thermoelectric element. Compared with numerical solutions, the results indicate that DTM has a fast convergence speed and a high accuracy. The findings reveal that the maximum energy conversion efficiency and thermal stress enhance with the increase of temperature difference.