A conductive line inclusion in thermoelectric materials : the thermoelectric fields and the effective thermoelectric properties

This paper studies a finite thermoelectric (TE) medium with an internal line inclusion which is electrically and thermal conductive. Exact solutions are obtained for the coupling and nonlinear thermoelectric fields. Based on the derived thermal and electrical fields, the effective thermoelectric properties (including thermal conductivity, electrical conductivity, Seebeck coefficient and figure-of-merit) of the inclusion/TE-medium system are expressed in explicit forms. It is found that there are upper bounds of the effective thermoelectric properties that the inclusion can enhance. Specifically, the effective thermal and electrically conductivities can be increased by 100%, the effective Seebeck coefficient and the figure-of-merit can be increased by 18% and 38%, respectively, by the inclusion. Since all the results are given in closed and explicit forms, they can be applied to the optimization of thermoelectric performance of thermoelectric materials in an effective and convenient way.