HOMOGENIZATION OF A CONDUCTIVE AND RADIATIVE HEAT TRANSFER PROBLEM

This paper is devoted to the homogenization of a heat conduction problem in a periodically perforated domain with a nonlinear and nonlocal boundary condition modeling radiative heat transfer in the perforations. Because of the critical scaling considered it is essential to use a method of two-scale asymptotic expansions inside the variational formulation of the problem. We obtain a nonlinear homogenized problem of heat conduction with effective coefficients which are computed via a cell problem featuring a radiative heat transfer boundary condition. We rigorously justify this homogenization process for the linearized problem by using two-scale convergence. We perform numerical simulations in two dimensions: we reconstruct an approximate temperature field by adding to the homogenized temperature a corrector term. The computed numerical errors agree with the theoretical predicted errors and prove the effectiveness of our method for multiscale simulation of conductive and radiative heat transfer problems in periodically perforated domains.