Second Order Corrector in the Homogenization of a Conductive-Radiative Heat Transfer Problem ∗

This paper focuses on the contribution of the so-called second order corrector in periodic homogenization applied to a conductive-radiative heat transfer problem. More precisely, heat is diffusing in a periodically perforated domain with a non-local boundary condition modelling the ra-diative transfer in each hole. If the source term is a periodically oscillating function (which is the case in our application to nuclear reactor physics), a strong gradient of the temperature takes place in each periodicity cell, corresponding to a large heat flux between the sources and the perfo-rations. This effect cannot be taken into account by the homogenized model, neither by the first order corrector. We show that this local gradi-ent effect can be reproduced if the second order corrector is added to the reconstructed solution. Key words: periodic homogenization, correctors, heat transfer, radiative transfer.