Thermal and electrical electrode/punch problem of thermoelectric materials

This paper studies the problem of a thermal and electrical electrode/punch on a thermoelectric material layer within the framework of fully coupled, nonlinear thermoelectricity model. The resultant thermal flux and energy current on the electrode/punch are prescribed. Explicit expressions for the thermal/electrical fields at the electrode/punch tip are obtained and are seen to be singular. For infinite layer thickness the thermoelectrical fields are obtained in closed-form. For finite layer thickness, the relationship between the applied flux/current and the voltage/temperature underneath the electrode/punch are obtained numerically by a singular integral equation technique. Effect of layer thickness is discussed. The results are helpful in measuring the thermoelectric coupling properties of thermoelectric materials by electrode/punch experiments.