A continuum theory of thermoelectric bodies and effective properties of thermoelectric composites

TL;DR

This paper develops a continuum mechanics-based theory for thermoelectric materials, deriving linearized equations under small variations, and provides explicit formulas for effective properties of thermoelectric composites with simple microstructures.

Contribution

It introduces a continuum theory for thermoelectric bodies and derives explicit formulas for the effective properties of thermoelectric composites with specific microstructures.

Findings

Linearized equations for thermoelectric bodies under small variations.

Explicit formulas for effective properties of laminates and periodic E-inclusions.

Design principles for engineering thermoelectric composites.

Abstract

We develop a continuum theory for thermoelectric bodies following the framework of continuum mechanics and conforming to general principles of thermodynamics. For steady states, the governing equations for local fields are intrinsically nonlinear. However, under conditions of small variations of electrochemical potential, temperature and their gradients, the governing equations may be reduced to a linear elliptic system, which can be conveniently solved to determine behaviors of thermoelectric bodies. The linear theory is further applied to predict effective properties of thermoelectric composites. In particular, explicit formula of effective properties are obtained for simple microstructures of laminates and periodic E-inclusions, which implies useful design principles for engineering thermoelectric composites.