Analysis of thermoelectric energy conversion efficiency with linear and nonlinear temperature dependence in material properties

A novel approach to estimate energy conversion efficiency for a power-generating thermoelectric element, whose material properties possess both linear (first order) and nonlinear (second order) dependence on temperature, is developed by solving the differential equation governing its temperature distribution, which includes both the Joule heat and the Thomson effect. In order to obtain analytic expressions for power output and energy conversion efficiency, several steps of simplification are taken. Most notably, the material properties are evaluated with a linear temperature profile between the hot and cold ends. The model is further applied to a high-performance n-type half-Heusler alloy, matching the results of direct numerical analysis. The close correspondence between the proposed model and the numerical solution indeed proves that the approximations we have made are valid. The effect of linear and nonlinear components in the temperature dependence of material properties on the energy conversion efficiency is analyzed both qualitatively and quantitatively with the model. The results suggest that the accurate inclusion of the Thomson effect is essential to understand even the qualitative behavior of thermoelectric energy conversion.