Homogenization of a conductive suspension in a Stokes–Boussinesq flow

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.

Keywords:

• Stokes–Boussinesq system
• Homogenization
• Non-local effects

Keywords:

• 2000 Mathematics Subject Classifications: 35B27
• 76D07
• 76S05

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.