An exact solution of a limit case Stefan problem governed by a fractional diffusion equation

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Abstract

An anomalous diffusion version of a limit Stefan melting problem is posed. In this problem, the governing equation includes a fractional time derivative of order 0 < β ≤ 1 and a fractional space derivative for the flux of order 0 < α ≤ 1. Solution of this fractional Stefan problem predicts that the melt front advance as s=tγ,γ=βα+1. This result is consistent with fractional diffusion theory and through appropriate choice of the order of the time and space derivatives, is able to recover both sub-diffusion and super-diffusion behaviors for the melt front advance.

Original languageEnglish (US)
Pages (from-to)5622-5625
Number of pages4
JournalInternational Journal of Heat and Mass Transfer
Volume53
Issue number23-24
DOIs
StatePublished - Nov 2010

Bibliographical note

Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.

Keywords

  • Anomalous diffusion
  • Fractional derivative
  • Stefan problem

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