# Classical two-phase Stefan problem for spheres

McCue, Scott W., Wu, Bisheng, & Hill, James M.
(2008)
Classical two-phase Stefan problem for spheres.
*Proceedings of the Royal Society of London. Series A*, *464*(2096), pp. 2055-2076.

## Abstract

The classical Stefan problem for freezing (or melting) a sphere is usually treated by assuming that the sphere is initially at the fusion temperature, so that heat flows in one phase only. Even in this idealized case there is no (known) exact solution, and the only way to obtain meaningful results is through numerical or approximate means. In this study, the full two-phase problem is considered, and in particular, attention is given to the large Stefan number limit. By applying the method of matched asymptotic expansions, the temperature in both the phases is shown to depend algebraically on the inverse Stefan number on the first time scale, but at later times the two phases essentially decouple, with the inner core contributing only exponentially small terms to the location of the solid–melt interface. This analysis is complemented by applying a small-time perturbation scheme and by presenting numerical results calculated using an enthalpy method. The limits of zero Stefan number and slow diffusion in the inner core are also noted.

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ID Code: | 14099 |
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Item Type: | Journal Article |

Additional Information: | An open access copy of this article can be accessed from the publisher's website - see DOI link above. |

Keywords: | two, phase Stefan problem, formal asymptotics, large Stefan number limit, zero Stefan number solution, slow diffusion limit, small, time behaviour, enthalpy method, solidification, melting, sphere |

DOI: | 10.1098/rspa.2007.0315 |

ISSN: | 1471-2946 |

Subjects: | Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > OTHER MATHEMATICAL SCIENCES (019900) > Mathematical Sciences not elsewhere classified (019999) Australian and New Zealand Standard Research Classification > PHYSICAL SCIENCES (020000) > OTHER PHYSICAL SCIENCES (029900) > Physical Sciences not elsewhere classified (029999) Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > PURE MATHEMATICS (010100) > Pure Mathematics not elsewhere classified (010199) |

Divisions: | Current > Schools > School of Curriculum Past > QUT Faculties & Divisions > Faculty of Science and Technology |

Copyright Owner: | Copyright 2008 Royal Society of London |

Deposited On: | 18 Jul 2008 |

Last Modified: | 25 Mar 2013 08:07 |

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