Thermodynamics analysis of thermoelectric materials: Influence of cracking on efficiency of thermoelectric conversion

Abstract

This paper provides a theoretical model to analyze the thermoelectric conversion efficiency of a cracked thermoelectric material with finite height and width based on the nonlinearly coupled transport equations of electricity and heat. The crack is assumed to be filled with air-like medium, and the electric current density in crack is neglected since air is a very good electric insulator. The thickness of crack is very small in general, and the heat conductivity of thermoelectric material is only larger than that of air by 1–3 orders of magnitude, therefore the heat flux on the upper and lower surfaces of the crack is considered. Using Fourier transform technique and singular integral equation method, analytical expressions for the distribution of electric potential and temperature fields, and electric current density and energy flux intensity factors at crack tips are obtained to aid in determination of thermoelectric conversion efficiency. Numerical results show that higher conversion efficiency can be achieved in a cracked thermoelectric material. This paper can be served as a starting point for more sophisticated analytic and computational treatments of defects in thermoelectric materials, and the analysis thus point to a new direction in developing high thermoelectric performance of engineer hybrid composites with inclusion structures.