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

TL;DR

This paper derives corrector estimates for a complex thermo-diffusion model with high-contrast microstructures, addressing coupled heat and mass transfer in heterogeneous media using homogenization techniques.

Contribution

It provides the first rigorous justification of first-order asymptotic expansions for a coupled thermo-diffusion system with high contrast and weak thermal coupling.

Findings

Established corrector estimates for the model.

Addressed mathematical challenges due to high contrast and coupling.

Validated the asymptotic expansion approach in complex media.

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.