Homogenization of parabolic nonlinear coupled problem in heat exchange

This work deals with the homogenization of heat transfer nonlinear parabolic problem in a periodic composite medium consisting in two-component (fluid/solid). This problem presents some difficulties due to the presence of a nonlinear Neumann condition modeling a radiative heat transfer on the interface between the two parts of the medium and to the fact that the problem is strongly coupled. In order to justify rigorously the homogenization process, we use two scale convergence. For this, we show first the existence and uniqueness of the homogenization problem by topological degree of Leray-Schauder, Then we establish the two scale convergence, and identify the limit problems.