A shortcoming of the explicit solution for the binary alloy solidification problem

Abstract

It is shown that in certain cases the explicit similarity solution for the binary alloy solidification problem exhibits an artificial mushy zone. Although this solution satisfies all of the explicit mathematical conditions of the problem, there can exist a region just in front of the solid/liquid interface where the temperature and concentration it defines lie in the region between the solidus and liquidus curves. A numerical example is given which shows the mushy region, and a condition on the data is derived whose satisfaction will guarantee its occurrence. The anomaly is interpreted to be a shortcoming of the mathematical formulation, which does not explicity state all of the assumptions.