Exact Solution of a Stefan Problem in a Nonhomogeneous Cylinder.
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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.
Applied Mathematics Letters
Copyright 2002 Elsevier. This is the author-manuscript version of this paper. Reproduced in accordance with the copyright policy of the publisher. Please refer to the journal's website for access to the definitive, published version.