Macroscopic model for solidification in porous media

A macroscopic model for solidification of pure metal in porous media is derived using the volume averaging method. Solidification starts when the infiltration of the porous mould is completed and therefore the phase change problem involving three phases (liquid and solid metal, mould) is governed by diffusion. The upscaled model is first characterized by the local thermal equilibrium assumption (LTE) between the liquid and the solid metallic phases leading to one energy conservation equation for the equivalent metallic phase. On the other hand, local thermal non-equilibrium (LTNE) between the equivalent continuous metallic phase and the mould is considered, giving rise to two coupled energy conservation equations. The associated closure problems are derived and numerically solved allowing for the determination of the effective transport properties. Numerical solutions of the macroscopic model are qualitatively compared with available experiments.