Two exact solutions of a Stefan problem with varying diffusivity

V. R. Voller, F. Falcini

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36 Scopus citations


A one-phase Stefan problem with a variable diffusivity is investigated. For two particular choices of diffusivity - one varying as a power law of position the other as a power function of the potential slope - exact similarity solutions are obtained. Unlike other similarity solutions that involve a time exponent n=12, the derived solutions can exhibit exponents in the range 0 < n < 1. Application of these solutions in the verification of a numerical scheme highlights the importance of a correct numerical treatment for handling variations in diffusivity.

Original languageEnglish (US)
Pages (from-to)80-85
Number of pages6
JournalInternational Journal of Heat and Mass Transfer
Issue number1-2
StatePublished - 2013

Bibliographical note

Funding Information:
This work was supported by the STC program of the National Science Foundation via the National Center for Earth-surface Dynamics under the agreement no. EAR-0120914 . The authors are also grateful to the reviewers useful suggestions.


  • Analytical solution
  • Stefan problem
  • Variable diffusivity


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