The Effective Behavior of Thermoelectric Composites

Abstract

Thermoelectric materials have attracted significant interests recently for their capability in converting heat directly into electricity and vice versa, and thus promise a wide range of energy and environmental applications. Despite their importance, there have been only very limited theoretical effort towards the analysis and understanding of effective behavior of thermoelectric composites. In this work, we develop * a rigorous continuum analysis on both bi-layered and core-shell thermoelectric composites, in which the distribution of temperature, electric potential, and heat flux are solved from the governing equations, and the effective thermoelectric properties defined through an equivalency principle; * a conversion efficiency analysis of thermoelectric composites, using an idealized thermoelectric module; * a non-linear asymptotic homogenization theory to understand the effective behavior of both one-dimensional and two-dimensional thermoelectric composites without macroscopic heterogeneity. We establish the unit cell problem, for which, the two dimensional numerical solution are obtained by a finite element method. The nonlinearly coupled thermoelectric transport equations are further homogenized, from which the macroscopic field distributions are derived with local fluctuation averaged out, and overall thermoelectric conversion efficiency is established. Through analysis, we * demonstrate that higher figure of merit of thermoelectric composite than any of its constituents is indeed possible, excluding size and interfacial effects; * find out that the thermoelectric conversion efficiency of a composite can be enhanced by its constituents, with the mechanism responsible for the enhancement identified, and the upper bound established; * discover that the thermoelectric field distributions in the composite are different from those in a homogeneous material, and they are difficult to be fitted by homogeneous solution. We conclude that energy conversion efficiency of a thermoelectric composite is not bounded, and can be higher than all its constituents in the absence of size and interface effects. Furthermore, it is noted the effective properties defined by a set of equivalency principle depend on specific boundary conditions, resulting in effective figure of merit that is not correlated with thermoelectric conversion efficiency directly. The analysis thus points toward a new route for developing high-performance thermoelectric materials, and provides considerable insight into the effective behavior of thermoelectric composites in terms of both design and optimization.