A numerical solution of the multidimensional solidification (or melting) problem

Abstract The purpose of this investigation was to develop a simple numerical technique with which to treat heat-transfer problems involving a change of phase. These problems are nonlinear due to the conditions at the moving interface boundary surface. The numerical scheme presented here solves the pertinent equations for the multidimensional problem and determines the temperature distribution in both media around the liquid-solid interface while at the same time it locates the loci of the latter as time progresses. The types of boundary conditions most frequently encountered in practice are studied in the analysis; the sample problems are selected in such a way as to reflect constant temperature and Newtonian cooling conditions at the boundary of the solidifying substance. The two-dimensional slab and the two- and three-dimensional corners are used to exemplify typical multidimensional geometries. Comparisons of the results obtained in this work with the few existing solutions show satisfactory agreement.