Melting and Solidification of Binary Alloy Subjected to Cyclic Temperature and Heat Flux Boundary Condition

Abstract

An enthalpy based Fixed-Grid method is developed for modeling phase change in a binary alloy subjected to periodic boundary condition. A two-dimensional model is developed for the melting and solidification cycle a gallium-tin (eutectic) alloy. The model also includes the natural convection effect in the liquid zone. Two cases are studied: (1) one of the boundaries is subjected to periodic variation of the temperature and (2) the same boundary subjected to periodic variation of heat flux. An enthalpy based fixed grid approach is used to solve the energy equation. The SIMPLER algorithm of Patankar is used to calculate the flow variables from continuity and momentum equations. The Tri-Diagonal-Matrix-Algorithm is used to solve the algebraic discrete equations. The melting and solidification fronts are captured implicitly by calculating the latent heat content at each control volume. An iterative update procedure is developed to update the latent heat content at each control volume. The proposed methodology is very simple to implement as the grid size is fixed. Since the grid size is fixed, hence the computational domain is also fixed. The domain is discretized once at the beginning of computation. The results obtained using the proposed enthalpy method is being validated with the available experimental results for melting of pure gallium. It is seen that, the solidification front takes a rather more regular shape, than the melting front. This is because of the rapid dissipation of temperature gradients in the melt. Hence, the movement of the solidification front is not modified by the fluid flow.