Asymptotics of a thermal flow with highly conductive and radiant suspensions

Abstract

Radiant spherical suspensions have an $\veps$-periodic distribution in a tridimensional incompressible viscous fluid governed by the Stokes-Boussinesq system. We perform the homogenization procedure when the radius of the solid spheres is of order $\veps^3$ (the critical size of perforations for the Navier-Stokes system) and when the ratio of the fluid/solid conductivities is of order $\veps^6$, the order of the total volume of suspensions. Adapting the methods used in the study of small inclusions, we prove that the macroscopic behavior is described by a Brinkman-Boussinesq type law and two coupled heat equations, where certain capacities of the suspensions and of the radiant sources appear.