Derivation of a Convection Process in a Steady Diffusion-Transfer Problem by Homogenization

TL;DR

This paper derives a homogenized model for steady diffusion in a heterogeneous medium with a periodic barrier, revealing the emergence of convective terms through two-scale convergence analysis.

Contribution

It introduces a homogenization approach for a diffusion problem with a barrier, showing the development of convective terms in the effective equations.

Findings

Effective conductivity is derived using two-scale convergence.

Homogenized equations include convective terms of order one.

The model captures the impact of the barrier on macroscopic flow.

Abstract

We study the homogenization of a steady diffusion equation in a highly heterogeneous medium made of two subregions separated by a periodic barrier through which the flow is proportional to the jump of the temperature by a layer conductance of the same order of magnitude of the materials in consideration. The macroscopic governing equations and the effective conductivity of the homogenized model are obtained by means of the two scale convergence technique. We show that under some hypothesis the homogenized systems contain convective terms of order one.