Exact Relations Satisfied by the Effective Tensors of Two-Dimensional Two-Phase Thermoelectric Composites

Abstract

Thermoelectric materials have been used for cooling and heating systems for over a hundred years. Today practical applications of thermoelectric devices include cooling car seats, power generation, and refrigeration. Thermoelectric materials are special for their ability to convert temperature imbalances into electricity. Their applications can inform the discourse about the transition to renewable energy sources---something that our Earth most desperately needs. The goal of this dissertation is to describe how the effective tensors of two-dimensional thermoelectric composites made from two isotropic materials depend on thermoelectric parameters of the constituents. Using the theory of exact relations and links developed by Grabovsky and his collaborators, we describe all equations satisfied by the thermoelectric effective tensor of a composite without the explicit knowledge of its microstructure. In some special cases, the effective tensor can be determined completely. Even in the general case, four out of 10 components of the two-dimensional thermoelectric tensor can be expressed in terms of the remaining 6, regardless of the microstructure. We started with special cases and worked our way up to the more general ones.