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

被引：63
|
作者：
Voller, V. R. [1 ]
机构：
[1] Univ Minnesota, Dept Civil Engn, Minneapolis, MN 55455 USA
来源：
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER | 2010年 / 53卷 / 23-24期
关键词：
Stefan problem; Anomalous diffusion; Fractional derivative; DENDRITIC GROWTH; ENTHALPY METHOD; SIMULATION; CONVECTION; FRONT; MODEL;
D O I：
10.1016/j.ijheatmasstransfer.2010.07.038
中图分类号：
O414.1 [热力学];
学科分类号：
摘要：
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 < beta <= 1 and a fractional space derivative for the flux of order 0 < alpha <= 1. Solution of this fractional Stefan problem predicts that the melt front advance as s = t(gamma), gamma = beta/alpha+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. (C) 2010 Elsevier Ltd. All rights reserved.
引用
收藏
页码：5622 / 5625
页数：4
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