Electric and heat conductions across a crack in a thermoelectric material

Abstract

The crack problem in a thermoelectric material is studied in this paper. Two kinds of crack surface conditions are discussed. The closed form solutions are derived, based on the complex variable method. The field intensity factors as well as the conversion efficiency are discussed in detail. The results show that the electric current density and thermal flux density exhibit traditional square-root singularity at the crack tip in case 1, while the electric current density has no singularity at the crack tip in case 2. It is proved due to the electric current flow and thermal flux separation, that the thermoelectric conversion efficiency can be higher than the maximum conversion efficiency of one-dimensional thermoelec- tric under the same temperature condition. In the numerical example, the conversion efficiency is increased by 29.6% as compared to the maximum conversion efficiency of one-dimensional thermoelectric.