A mushy zone model with an exact solution

Abstract

We propose a very simple model of a mushy zone which admits of an explicit solution. To our knowledge, it is the only instance where an actual observation of the mushy zone width and structure is used as a partial basis for the model definition. The model rests upon two unknown parameters. The first determines the relation between the equilibrium temperature gradient and the mushy zone width. The second depends upon the dendritic structure in the mushy zone, and is related to the solid fraction. Both can be estimated from experiments. We define the model, present its closed form solution, and give tables from which the solution can be found explicitly. It is seen that in most cases the predicted mushy zone is of very small width.