Micromechanics-based theoretical prediction for thermoelectric properties of anisotropic composites and porous media

By employing a mean-field homogenization theory to an anisotropic thermoelectric composite involving spherical fillers, we obtain analytical predictions of the effective Seebeck coefficient, effective electrical conductivity, and effective thermal conductivity in the presence of interfacial electrical and thermal resistances. First, we validate the thermoelectric Eshelby tensor and concentration tensor for an anisotropic matrix in the presence of interfacial resistance using finite element analysis (FEA) results and subsequently demonstrate that the predicted effective thermoelectric properties match well with the FEA up to a filler volume fraction of less than 20%. Based on the homogenization theory, we investigate the effect of filler size and filler properties on the effective thermoelectric properties of a composite. An interesting observation is that the porosity, which was known not to affect the effective Seebeck coefficient in isotropic materials, noticeably affects the effective Seebeck coefficient in anisotropic materials. Under strong anisotropy, there was a mismatch between the Seebeck coefficients of the porous medium obtained from numerical simulation and theoretical prediction. We discuss the origin of such phenomena in terms of the thermoelectric eddy current existing in an anisotropic medium: as the electric field is not conservative anymore, there is a circulating current in the porous anisotropic materials.