Corrector estimates for a thermo-diffusion model with weak thermal coupling

Abstract: The present work deals with the derivation of corrector estimates for the two-scale homogenization of a thermo-diffusion model with weak thermal coupling posed in a heterogeneous medium endowed with periodically arranged high-contrast microstructures. The terminology "weak thermal coupling" refers here to the variable scaling in terms of the small homogenization parameter of the heat conduction-diffusion interaction terms, while the "high-contrast" is thought particularly in terms of the heat conduction properties of the composite material. As main target, we justify the first-order terms of the multiscale asymptotic expansions in the presence of coupled fluxes, induced by the joint contribution of Sorret and Dufour-like effects. The contrasting heat conduction combined with cross coupling lead to the main mathematical difficulty in the system. Our approach relies on the method of periodic unfolding combined with a priori estimates for the thermal and concentration fields and for their coupled fluxes.