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The present work deals with the derivation of corrector estimates for thetwo-scale homogenization of a thermo-diffusion model with weak thermal couplingposed in a heterogeneous medium endowed with periodically arrangedhigh-contrast microstructures. The terminology "weak thermal coupling" refershere to the variable scaling in terms of the small homogenization parameter ofthe heat conduction-diffusion interaction terms, while the "high-contrast" isthought particularly in terms of the heat conduction properties of thecomposite material. As main target, we justify the first-order terms of themultiscale asymptotic expansions in the presence of coupled fluxes, induced bythe joint contribution of Sorret and Dufour-like effects. The contrasting heatconduction combined with cross coupling lead to the main mathematicaldifficulty in the system. Our approach relies on the method of periodicunfolding combined with a priori estimates for the thermal and concentrationfields and for their coupled fluxes.

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