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

✍ Scribed by V.R. Voller

• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 204 KB
• Volume: 53
• Category: Article
• ISSN: 0017-9310
• DOI: 10.1016/j.ijheatmasstransfer.2010.07.038

✦ Synopsis

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 < b 6 1 and a fractional space derivative for the flux of order 0 < a 6 1. Solution of this fractional Stefan problem predicts that the melt front advance as s ¼ t c ; c ¼ b aþ1 . 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.