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

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.