Lattice Boltzmann simulation of momentum and energy transfer in a porous medium

The fluid flow and heat transfer in porous media has wide applications in oil industry and air conditioning system. In this study the momentum and energy transport processes in a porous medium are numerically simulated. The Brinkman-Forchheimer-extended Darcy equations and energy equation are solved using single lattice-Boltzmann method (LBM). As a first attempt, a benchmark problem is studied, i.e., momentum and energy transfer in a rectangular enclosure with differentially heated vertical walls. The effect of permeability on the critical Rayleigh numbers, the temperature distribution and flow field is discussed.