Homogenization for thermoconductivity in a porous medium with periods of different orders in the different directions

Abstract

We study here the problem of heat transfer in a porous medium consisting of a homogeneous isotropic material. We assume that the period of the medium is not the same in the two directions and that the ratio of these two periods tends to zero. We find the explicit representation of the coefficients of the averaged equations and prove strong convergence to the solution of the averaged problem.