Effective Interfacial Thermal and Electrical Resistances of a Microcracked Interface with Applications to Thermoelectrics

Abstract

This work develops an analytical model to estimate the effective interfacial thermal and electrical resistances of an interface with an array of periodic microcracks between two dissimilar materials. The theoretical model and the numerical results for a Bi2Te3/PbTe bimaterial system indicate that the interfacial thermal and electrical resistances increase linearly with increasing crack length when the crack length per unit interface length (specific crack length) is fixed. The interfacial resistances depend strongly on the specific crack length and go to infinity when the specific crack length approaches unity. Moreover, higher thermal and electrical conductivities of the bulk dissimilar materials lead to lower interfacial resistances. Based on the developed interfacial resistance model, it is found that the influence of the microcracks at the interface between the two segments on the energy efficiency of a segmented Bi2Te3/PbTe thermoelectric material is insignificant when the specific crack length is not close to 1. The effects of the microcracks become pronounced when the specific crack length is close to 1.