Thomson Power in the Model of Constant Transport Coefficients for Thermoelectric Elements

Abstract

The analytical expressions derived using simple models provide clear insights on the processes in thermoelectric coolers. The model of constant transport coefficients (CTC) considers that the thermal conductivity, the electrical resistivity and the Thomson coefficient are constants. The version of the CTC model that has become standard in the description of the global energy balance may yield grossly inaccurate predictions for thermoelectric cooling applications. We show that these failures can be avoided by accurately describing the Thomson effect in the energy balance. Calculations for bismuth telluride semiconductors show that deviations as large as a factor of three in the Thomson power contribution to the global balance may be found under conditions of practical interest. Compared to the standard version (valid only for moderate temperature gradients), the improved version (valid for highly nonlinear temperature distributions) of the CTC model predicts that a larger fraction of the power released by the electric current leaves the thermoelectric element through the hot boundary. Significant differences in the estimations of the cooling capacity and the coefficient of performance of the thermoelectric cooler are also observed.