Modeling the mushy zone during the melting process under Neumann boundary condition using the improved enthalpy-porosity method

Abstract

Non-isothermal melting phenomenon widely exists in phase change process where mixtures are utilized as phase change materials. It is in the mushy zone that phase transition actually occurs during the melting process. Thus, an in-depth understanding of flow and heat transfer in the mushy zone can provide beneficial ways to improve melting technologies. This article focuses on the evolution of mushy zone for low-Prandtl material under Neumann boundary condition. A two-dimensional model composed of liquid zone, mushy zone, and solid zone is established based on the improved enthalpy-porosity method. The pressure and velocity are coupled with SIMPLER algorithm based on the finite volume method with a Fortran code. The results indicate that the temperature on the heating surface is uneven, which are different from the results under Dirac boundary condition. The existence of mushy zone can supply a buffer to the unsteady melting adjacent to the heating surface initially. And the mushy zone experiences expanding stage and shrinking stage. More time is needed for complete melting and the average temperature on the heating surface gets lower under greater melting temperature range. Increasing Ra can result in augmentation of heat transfer in liquid domain and more inclined interface, and the heat transfer is dominated by heat conduction when liquid phase fraction is less than 20%, and thereafter, it is dominated by natural convection. For the same material, increasing heat flux obviously shortens the total melting time. And the mushy zone is reduced for that greater temperature gradient is produced in the mushy area.