Nonlinear asymptotic homogenization and the effective behavior of layered thermoelectric composites

Thermoelectric materials are promising in converting heat directly into electricity, and composite materials are often used to enhance thermoelectric figure of merit. In this work, we develop a nonlinear asymptotic homogenization theory to analyze the effective behavior of layered thermoelectric composite with coupled transport of electricity and heat. The nonlinearly coupled thermoelectric transport equations are homogenized using asymptotic analysis, from which the macroscopic field distributions are derived with local fluctuation averaged out, and overall thermoelectric conversion efficiency is established using an idealized thermoelectric module. It is discovered 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. Furthermore, it is noted that while the effective thermoelectric properties of the composite can be defined through a set of equivalency principle, these effective properties depend on specific boundary conditions, resulting in effective figure of merit that is not correlated with thermoelectric conversion efficiency directly. The analysis thus sheds considerable insight into the effective behavior of thermoelectric composites for their design and optimization.