An Investigation of the Thermal Stresses Induced in a Thin-Film Thermoelectric Cooler

Abstract

This work aims at investigating the thermal stresses induced within a four-layered thin-film thermoelectric cooler. The one-dimensional (1D) temperature and thermal-stress distributions are firstly analyzed under the consideration of Joule heating, the conduction heat transfer as well as Thomson heating. Followed are two-dimensional (2D) calculations of the thermal stresses with the commercial software ANSYS. The validity of the 1D analytical model is then examined by a comparison of its predicted thermal stresses with the numerical ones obtained from the 2D model. In the 2D model, the thermoelectric element becomes curved due to the shrinkage and the fixed boundary conditions. The latter also causes huge values and rapid changes of thermal stresses near the ends. In the middle portion of the thermoelectric element where the thermal effect dominates, the thermal stresses predicted by the 1D model are not much different from those computed from the 2D model. Quantitative differences arise from the fact that the 1D model does not count the stresses induced by the non-zero Poisson's ratios. In addition, the normal-stress distributions are pretty uniform across the layer thickness (the variation is less than 1MPa within each layer in the worst case). These results verify the possibility of using the 1D model for a preliminary estimate of the thermal stresses induced within the layered thin-film thermoelectric element. The 1D model nonetheless fails to capture the behaviors near the ends of the thermoelectric element.