An Enhanced Mathematical Model for Phase Change Problems with Natural Convection

The enthalpy-porosity technique is commonly used for modeling phase change problems with natural convection. In most applications however, this technique is restricted to equal thermophysical properties of solid and liquid phases. In this paper, an enhanced formulation based on the enthalpy-porosity method is proposed where the different thermophysical properties between the two phases can be easily taken into account. Accurate temporal and spatial discretizations are also presented for solving the proposed formulation. Numerical simulations on pure gallium melting and a comparison between experimental and numerical results for water solidification are presented to illustrate the performance of the proposed model and numerical methodology.