Homogenization of a conductive suspension in a Stokes-Boussinesq flow

ISSN： 0003-6811

Source： Applicable Analysis, Vol.85, Iss.6-7, 2006-06, pp. : 811-830

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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 ε 3 (the critical size of perforations for the Navier-Stokes system) and when the ratio of the fluid/solid conductivities is of order ε 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.