具有高导热和辐射悬浮体的热流的渐近性
Asymptotics of a thermal flow with highly conductive and radiant suspensions
摘要：
在Stokes-Boussinesq系统控制的三维不可压缩粘性流体中，辐射球形悬浮液具有$\veps$周期性分布。当固体球的半径为$\veps^3$（Navier-Stokes系统的穿孔的临界尺寸）和流体/固体电导率的比为$\veps^6$（悬浮液的总体积的数量级）时，我们执行均匀化程序。适应小夹杂物的研究中使用的方法，我们证明了宏观行为是由一个Brinkman-Boussinesq型法律和两个耦合的热方程，其中出现的悬浮液和辐射源的某些能力。
英文摘要：
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.
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