A similarity solution for solidification of an under-cooled binary alloy

A similarity solution for solidification of an under-cooled binary alloy melt in a semi-infinite, one-dimensional, insulated slot is developed. It is shown that this solution is a generalization of the known similarity solution for the solidification of an under-cooled pure melt, and is a special case of the similarity solution for solidification of a binary alloy previously presented in the literature. The new solution is used to quantify the effect of the Lewis number (ratio of thermal to solutal diffusivity) on the behavior of solidification. Limits on the amount of under-cooling that will admit a physically meaningful solution are obtained.