Solidification of a Liquid Metal with Natural Convection in a Thick-Walled Container

Abstract

ABSTRACTThe solidification of a phase change material (PCM), exemplified by a molten metal, in a thick-walled container is analyzed in this paper. The effects of natural convection and several important controlling parameters are investigated extensively. These parameters include the initial temperature of the PCM, external cooling conditions, thickness and thermal properties of the wall, and the thermal contact resistance at the PCM/wall interface. Two representative configurations are examined in this study. A modified version of the enthalpy formulation in which the sensible heat is separated from the latent heat, is employed to construct the energy equation for the PCM. Vorticity-stream-function approach is adopted for solving the flow field. The governing equations pertinent to the problem are discretized by the weighting function scheme and finally solved by the SIS (Strongly Implicit Solver) algorithm. It is demonstrated that for both configurations natural convection has prominent effect on the temperature distribution of the liquid phase of the PCM; however, the effect of natural convection on the shape of the solid/liquid interface and the overall solid fraction is case dependent. It is also shown that the above-mentioned controlling parameters have a direct impact on the solidification process. Specifically, an increase in the Biot number (from 1 to infinity) and the thermal diffusivity of the mold (from 0.8 to 5) enhances the solidification rate. Reverse effect was found for the other controlling parameters.