Using the constant properties model for accurate performance estimation of thermoelectric generator elements

Abstract

Thermoelectric devices convert thermal energy directly into electrical energy or vice versa. Analytically, the performance (efficiency and power output) of a thermoelectric generator can be quickly estimated using a Constant Properties Model (CPM) suggested by Ioffe. However, material properties in general are temperature dependent and the CPM can yield meaningful estimates only if the constant values of the TE properties used in the formulations are physically appropriate. In this study, a comparison of different averaging modes shows that a combination of integral averaging over the temperature scale for the Seebeck coefficient and spatial averages for the electrical and thermal resistivities proves to be the best among the considered approximations to represent the constant property values. However, averaging spatially requires the knowledge of the exact temperature distribution along the length of the thermoelectric leg (temperature profile), which is usually obtained by Finite Element Method (FEM) calculations. Since FEM is costly and time consuming, a fast and easy way of obtaining a well approximated self-consistent temperature profile is used in this study. The relevance, magnitude and the physical origin of the non-linearity of the temperature profile are visualised by separately plotting the individual contributions to the bending of the temperature profile (Joule, Thomson and Fourier heat contributions). On analyzing the temperature profiles for different highly efficient thermoelectric materials, it is found that the non-constancy of the temperature dependence of the thermal conductivity significantly contributes to the deflection of real temperature profiles from a linear one. This mainly explains the considerable discrepancy of CPM results from exact calculations whereas, so far, the neglect of Thomson heat has been assumed to be the main source of discrepancy and several models with Thomson correction factors have been proposed. With our current view, such models cannot completely remove the discrepancy to CPM unless the T profile is taken into account and can lead to unpredictable error for different material cases and temperatures.