FEM analysis of binary dilute system solidification using the anisotropic porous medium model of a mushy zone

Finite Element Method (FEM) calculations have been performed to address the problem of the influence of anisotropy of permeability and of thermal conductivity of a mushy region on a temporary flow pattern and temperature during solidification of binary mixtures. Computationally effective FEM algorithm is based on the combination of the projection method, the semi-implicit time marching scheme and the enthalpy-porosity model of the two-phase region. Example calculations are given for two different dilute solutions of ammonium chloride and water. The effect of permeability anisotropy considerably changes the shape of the mushy zone. Three different models of thermal conductivity, the first - based on a mixture theory, the second - fully anisotropic one and the third - the model of isotropic effective conductivity, have been analyzed and mutually compared. It has been found that the impact of the thermal conductivity anisotropy is visible only in the case when this property differs significantly in both phases.