Model of two-temperature convective transfer in porous media
Résumé
In this paper, we study the asymptotic behaviour of the solution of a convective heat transfer boundary problem in an "-periodic domain which consists of two interwoven phases, solid and fluid, separated by an interface. The fluid flow and its dependence with respect to the temperature are governed by the Boussinesq approximation of the Stokes equations. The tensors of thermal di↵usion of both phases are "-periodic, as well as the heat transfer coecient which is used to describe the first-order jump condition on the interface. We find by homogenization that the two-scale limits of the solutions verify the most commonly system used to describe local thermal non-equilibrium phenomena in porous media (see [11] and [17]). Since now, this system was justified only by volume averaging arguments. Mathematics Subject Classification (2010). 35B27; 76M50; 76Rxx; 74F10; 74Q05.
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