Exact solution of a Stefan problem in a nonhomogeneous cylinder

The exact solution is found for the Stefan problem of inwards freezing of a nonhomogeneous cylinder whose specific heat and latent heat depend upon the inverse square of the radial distance. The freezing time for the corresponding annular cylinder is found exactly. The validity of the pseudo-steady-state approximation for the solvable cylinder problem is verified explicitly. It is argued that the exact solution for the solvable cylinder problem may be used as a small-time start-up solution for numerical procedures for general axi-symmetric cylinder problems and for general Stefan numbers. KeywordsStefan problem, Moving boundary, Freezing, Cylinder, Annulus, Pseudo-steady-state, Small-time. ________________________________ The author gratefully acknowledges the hospitality of the School of Mathematics and the Centre in Statistical Science and Industrial Mathematics at the Queensland University of Technology, Gardens Point, Brisbane, where this work was initiated during an Outside Studies Program. Useful discussions with Professor Sean McElwain and Dr Fawang Liu are also acknowledged.