Homogenization of a conductive suspension in a Stokes-Boussinesq flow

摘要

Radiant spherical suspensions have an ε-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 ε{sup}3 (the critical size of perforations for the Navier-Stokes system) and when the ratio of the fluid/solid conductivities is of order ε{sup}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.