A lattice Boltzmann model for thermal flows through porous media

In a three-distribution-function framework, a lattice Boltzmann model was proposed for thermal flows through porous media under local thermal non-equilibrium conditions, in which both viscous dissipation and compression work were considered. In this model, a density distribution function was used to simulate the flow field and two total energy distribution functions were employed to simulate temperature fields for both fluid and solid. Discrete equilibrium density and total energy distribution functions were obtained from Hermite expansions of the corresponding moment equations. Through Chapman-Enskog procedure, macroscopic governing equations could be recovered expediently from the present thermal lattice Boltzmann model. The proposed model was validated by numerical simulations of thermal Poiseuille flow in a planar porous channel and natural convection in a square porous cavity.