A thermal lattice Boltzmann model for natural convection in porous media under local thermal non-equilibrium conditions

A thermal lattice Boltzmann model for natural convection in porous media under local thermal non-equilibrium conditions is proposed through an appropriate selection of equilibrium distribution functions and discrete source terms. In this model, two new distribution functions are introduced to simulate the temperature fields of the fluid and solid matrix phases in addition to the density distribution function for the velocity field. The macroscopic energy equations are recovered from the corresponding lattice Boltzmann equations by the Chapman–Enskog procedure. Detailed numerical tests of the proposed model are carried out for three different cases under both steady state and transient conditions. The influence of various parameters such as ratio of solid-to-fluid thermal conductivities, interstitial Nusselt number, Rayleigh number, and Darcy number on the thermal and flow fields is investigated. The present numerical results agree well with the solutions reported in previous studies. Therefore, it is verified that the present model can be served as a feasible and efficient tool for non-equilibrium natural convection problems in porous media.