Effect of cracking on the thermoelectric conversion efficiency of thermoelectric materials

Abstract

Analytical solutions for a rectangular thermoelectric plate with a crack under combined electrical and temperature loadings are obtained. The electric current density and energy flux intensity factors at the crack tip are calculated. The effective thermoelectric properties are obtained. From the results, it is found that both effective electric and heat conductivities are reduced by increasing the crack size. However, the thermoelectric conversion efficiency of the thermoelectric plate is independent of the crack size if the crack face boundary conditions are assumed to be electrically and thermally insulated. In addition, the effect of thermoelectric properties and size of an inclusion on the thermoelectric conversion efficiency is also discussed, and the condition for high efficiency thermoelectric materials is identified. This is the first theoretical paper to study the effect of cracking on the thermoelectric properties by a rigorous inference of mathematics and physics.