Thermal flow through a porous radiant of low conductivity (Q1596384)

The author considers the homogenization of the Stokes-Boussinesq flow of a heat conducting incompressible viscous fluid through a porous medium with a small periodicity \(\varepsilon >0\). Under the assumption that the Rayleigh number and the ratio of the solid and fluid conductivity is of the order \(\varepsilon^{-2}\) and \(\varepsilon^2\), respectively, a macroscopic model is obtained. This model is similar to the Darcy-Boussinesq system with an extra radiation term. It is found that the temperature is no longer the solution of the macroscopic system; it must be added a term being the product of the radiation source with a certain capacity of the solid matrix.