© 1986 by Oxford University Press
ON A MULTIPHASE STEFAN PROBLEM
( Department of Mathematics, The University of Wollongong Wollongong, N.S.W., Australia )
The multiphase Stefan problem describing the melting (freezing) of a material with two distinct phase-change temperatures is considered. The material is assumed initially to be uniformly at the lowest (highest) fusion temperature. For spherical, cylindrical and planar geometries an integral formulation is obtained which generalizes results for the idealized single-phase Stefan problem. From this integral formulation a new non-trivial integral relating the motions of the moving boundaries is deduced. Further, the enthalpy of the material is found to occur in this integral relation, allowing the result to be derived and extended to an n-phase material. The presence of the enthalpy makes it an extremely simple matter to evaluate the integral in a numerical enthalpy scheme so that it may be used as an independent gauge or check on the accuracy of the numerical scheme. Numerical results confirm the accuracy of a simple explicit enthalpy scheme. The pseudo steady-state approximation for the problem is discussed, and the analytical difficulties inherent in obtaining the approximate boundary motions for cylindrical and spherical geometries are noted. An examination of the pseudo steady-state approximation for planar geometry reveals that it is valid in cases where the sensible heats of the phases are very small in comparison to their latent heats of fusion.