DOWNSCALING PROCEDURE FOR CONVECTIVE HEAT TRANSFER IN PERIODIC POROUS MEDIA

This study proposes a downscaling methodology consisting of describing the convective heat transfer at the pore scale of the porous media from the knowledge of the velocity and temperature fields at the Darcy scale. The analysis is based on the derivation of local deviation equations on a local unit cell. A penalization technique is used to deal with the macroscopic source terms involved in these equations. The partial differential equations system is closed assuming periodic conditions at the boundaries of the unit cell. Numerical simulations illustrate the relevance and the limitations of the downscaling procedure applied to two-dimensional periodic arrays of cylinders.