Modeling of Heat and Mass Transfer for Microflows in Porous Media

In various applications such as vacuum equipment, microdevices or Chemical Vapor Infiltration, there are many situations where non isothermal flow and low pressure are required in porous media and where the pore size may be as low as some micrometers. In this context, we can have situations where the frequency of binary collisions and the frequency of collisions of gas molecules with the boundary of the pores are of the same order. For numerical simulations, we propose a macroscopic model derived by homogenization from a microscopic model based on the Boltzmann equation. This macroscopic model consists in a mass diffusion equation, with thermo-diffusion terms, coupled with heat transfer equation. For this asymptotic transport model, we must compute the effective transport coefficients from the microscopic properties of the material. These coefficients are defined through the solution of auxiliary problems posed on the unit cell of the periodic medium.