Approximate Analytical Method to Stefan Problem for Spheres with Wide Temperature Range of Phase Transition

摘要

The two-dimensional differential transform method is applied to solve the one-dimensional phase-change problem for a solid sphere with time-dependent boundary temperature. The problem assumes that the phase change occurs over a range of temperatures and the initial temperature of the sphere is an arbitrary constant. An approximate analytical (series) solution is derived for the temperature profile in the melting or solidifying sphere. The solution is based on the apparent specific heat method. Numerical results illustrate the effects of the Stefan number, which is the ratio of sensible heat to latent heat, on the transient temperature profile in the sphere.