A numerical method for the Rubinstein binary-alloy problem in the presence of an under-cooled liquid

A fixed grid solution for tracking a moving solidification front controlled by coupled heat and mass transport in the presence of an under-cooled liquid is developed. A known closed form similarity solution for the solidification of a binary alloy in a one-dimensional domain is outlined. A previously reported enthalpy based model for this problem is presented and a novel numerical solution devised. Comparisons with the analytical solution show that the proposed numerical solution can produce high-fidelity predictions across a wide range of conditions including cases where the liquid becomes under-cooled.