Abstract
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 ε3 (the critical size of perforations for the Navier-Stokes system) and when the ratio of the fluid/solid conductivities is of order ε6, 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.
Acknowledgment
This work was done during the visit of Fadila Bentalha and Dan Polişevschi at the I.R.M.A.R.'s Department of Mechanics (University of Rennes 1) whose support is gratefully acknowledged.