The classical one-phase Stefan problem is presented in dimensionless form with a time-varying heat-power flux boundary condition. The formulating parameters are the Stefan number, Ste, and a generalized form of the Biot number, Bi. The asymptotic solution for Bi -> 0 of the governing equations is of an isothermal phase change material domain, simplifying the model into a moving boundary zero-phase type problem. Exact solutions to the zero-phase model can be found for finite domains in Cartesian, cylindrical and spherical coordinates in one dimension with sign-switching boundary conditions in terms of moving boundary location, or, conversely, melting times. The model can be thought of as an analytical approximation for cases having small but finite Biot numbers. A more general expression that takes the geometry as a parameter is presented. (c) 2007 Elsevier Ltd. All rights reserved.