Lattice Boltzmann simulation of natural convection dominated melting in a rectangular cavity filled with porous media

A thermal lattice Boltzmann model is developed for the melting with natural convection in porous media at the representative elementary volume scale. An evolution equation of the temperature distribution function is constructed through selecting the equilibrium distribution function and non-linear source term properly. Simulations of melting with natural convection in a cavity with and without a porous matrix are performed using the present model. Numerical results show good agreement with previous analytical, experimental and numerical solutions. In addition, the analysis of the melting process over a wider range of dimensionless parameters indicates that for conditions of high Darcy number and high porosity the effect of natural convection on the melting becomes stronger, and the Rayleigh number based on porous media (Ram) proposed in the previous studies may not be appropriate to correlate the average hot wall Nusselt number independently. The present model is also suitable for simulating freezing and solidification in porous media without modification.