Asymptotic thermal flow around a highly conductive suspension
Résumé
Radiant spherical suspensions have a periodic distribution in a three dimensional incompressible viscous fluid governed by the Stokes-Boussinesq system. We study the border case when the radius of the spheres is of the third power order of the period and the ratio of the solid/fluid conductivities is converging to infinity when the peruod tends to zero. We apply a homogenization procedure by adapting the energy method introduced by Cioranescuand Murat and developed by Bellieud and Bouchitté on one hand, Allaire on the other hand. The macroscopic behavior is described by a nonlocal law of Brinkman-Boussinesq type and two heat equations, where the radiation and a certain capacity of the vanishing suspensions appear. This result completes those obtained for the thermal flow through an periodic solid matrix having a non-vanishing macroscopic porosity, see Ene and Polisvski.