A Comparison of Theory and Experiment for a Thermoelectric Cooler

The performance of single-stage Peltier thermocouples was calculated using the experimentally measured values of thermoelectric power, electrical resistivity, and thermal conductivity as functions of temperature. These calculations were made by solving numerically the differential equation for the temperature distributions in the thermoelements. The boundary conditions were the hot junction temperature and the heat flow at the cold junction. The calculated behavior of the thermocouples agreed well with the measured performance in the three cases studied. The measured thermocouple figure of merit agreed with that calculated from the material properties. The effect of temperature variations of the material properties on thermocouple performance was studied by comparing exact calculations with calculations involving one temperature-averaged constant material property. This type of calculation showed that the Thomson effect caused about 4°K of the maximum ΔT of 66°K for one couple studied. The temperature variation of resistivity was found to be the major cause of disagreement between exact calculations and the simpler theory (Ioffe equations).