A unified approach to Stefan’s problem for spheres and cylinders

The problem of the inward solidification of a spherical or cylindrical body of molten material, initially at its uniform fusion temperature, when the outside is suddenly cooled, is considered. A complete asymptotic theory is developed for the case when the parameter A, which measures the ratio of latent heat to sensible heat of the substance, is large. Uniformly valid approximations to the solution are found everywhere, for all time t*, up to the instant t* = t*e,at which the material is completely frozen. Though many of the results have been obtained previously, the treatment of the final freezing of the central core as t* -> t*e is new. For the cylinder, the novel approach enables asymptotic solutions to be obtained, when t* t*e, for the first time.