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 language||English (US)|
|Number of pages||4|
|Journal||International Journal of Heat and Mass Transfer|
|State||Published - Nov 2010|
Copyright 2011 Elsevier B.V., All rights reserved.
- Anomalous diffusion
- Fractional derivative
- Stefan problem