Analytical and Numerical Simulation of a Commercial Thermoelectric Module

Abstract

This work reports a comparison of three different mathematical models used to evaluate the performance of a thermoelectric module: a linear model that relies on the assumption of temperature-independent thermoelectric properties and two nonlinear models that account for the temperature dependence of the properties. The linear model solves analytically the equations for the conservation of energy, electric potential and electric charge. The nonlinear models solve the conservation equations using either the homotopy perturbation method or the finite volume method. The models are applied to a commercial thermoelectric module and compared with the performance data provided by the manufacturer. The results demonstrate that the temperature dependence of the material properties, as well as the electrical contact resistances, must be taken into account to obtain accurate predictions. The assumption of constant properties is reasonable at low temperatures of operation, where the variation of the thermoelectric properties with temperature is negligible, but at high temperatures, this assumption overestimates the performance. Both non-linear models yield a good agreement with each other and with the data obtained from the manufacturer.