A modified lattice Boltzmann model for conjugate heat transfer in porous media

A modified lattice Boltzmann model for conjugate heat transfer in a system containing simultaneously a porous medium and other media is proposed. In this model, the volumetric heat capacity and a new parameter are introduced to the equilibrium temperature distribution function for satisfying the temperature and heat flux continuities at the interface between two phases with different thermal properties (thermal conductivity and volumetric heat capacity), as well as avoiding any correction of distribution functions neighboring the interface. The macroscopic temperature equations are correctly recovered from the corresponding lattice Boltzmann equations by the Chapman-Enskog procedure. Detailed numerical tests of the proposed model are carried out for several benchmark problems including steady-state conjugate heat conduction within two-layer solid medium, transient conjugate heat conduction in infinite composite solid, conjugate natural convection in a cavity partially filled with porous medium and conjugate heat transfer in porous media with a conducting wall. The present numerical results are in excellent agreement with analytical and numerical solutions reported in previous studies. Therefore, it is verified that the present model can be served as a feasible tool for conjugate heat transfer problems in porous media.