A Heat Transfer Analysis for Solidification of Slabs, Cylinders, and Spheres

The method of strained coordinates is applied to the inward solidification problem. Constant thermal properties are assumed throughout the analysis for the liquid, which is initially at the fusion temperature. A unified approach is adopted that allows the simultaneous treatment of the problem in plane, cylindrical, and spherical geometries for three different types of boundary condition. A general recurrence formula is derived for the determination of the series solutions up to any desired order of the Stefan number. A comparison is made with numerical and regular perturbation solutions in the plane case to illustrate the usefulness and the validity of the method.