Numerical solution of heat conduction problems with a change of phase

Numerical solutions for the freezing of finite slabs, cylinders, and spheres initially above the fusion temperature subject to boundary conditions of the first, second, and third kind were obtained by utilizing the DuFort-Frankel finite-difference scheme. Illustrative calculations for the transient temperature field, freezing front location, heat flux at the wall, and times for complete freezing were presented for various values of the dimensionless parameters. The ranges of values for the dimensionless parameters for which solutions can be successfully obtained were determined. FORTRAN IV computer programs which can be used to obtain solutions for any conditions within these ranges have been made available. The computer programs were written in such a way as to be easily extended and/or modified to solve other freezing problems.