Lattice Boltzmann method for heat transfer of melting in porous media with high Darcy number

The Brinkmann-Forchheimer-Darcy equation is used to characterize the flow in porous media.An evolution equation of the temperature distribution function is developed through selecting the equilibrium distribution function and nonlinear source term properly.The melting with natural convection in a cavity with and without porous matrix is simulated using the present model.Numerical results agree well with previous solutions,so the accuracy of the present model is verified.The simulation results indicate that the effect of natural convection on the melting process becomes much stronger with the increases of the Rayleigh number and the Darcy number.Under the conditions with high Darcy number,the effect of increasing the Rayleigh number on heat transfer is greater than that of increasing the Darcy number,due to non-Darcy effect.