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

页码：5622 / 5625

页数：4

共 50 条

[21] Two-phase Stefan problem as the limit case of two-phase Stefan problem with kinetic condition [J].

Yi, FH ;

Liu, YQ .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2002, 183 (01) :189-207

[22] A self-similar solution to time-fractional Stefan problem [J].

Kubica, A. ;

Ryszewska, K. .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2021, 44 (06) :4245-4275

[23] Fractional diffusion equation and Green function approach:: Exact solutions [J].

Lenzi, EK ;

Mendes, RS ;

Gonçalves, G ;

Lenzi, MK ;

da Silva, LR .

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2006, 360 (02) :215-226

[24] Exact Solutions of a Generalized Multi-Fractional Nonlinear Diffusion Equation in Radical Symmetry [J].

Liu Yan-Qin ;

Ma Jun-Hai .

COMMUNICATIONS IN THEORETICAL PHYSICS, 2009, 52 (05) :857-861

[25] A backward problem for the time-fractional diffusion equation [J].

Liu, J. J. ;

Yamamoto, M. .

APPLICABLE ANALYSIS, 2010, 89 (11) :1769-1788

[26] Boundary value problem for a loaded fractional diffusion equation [J].

Pskhu, Arsen, V ;

Ramazanov, Murat I. ;

Kosmakova, Minzilya T. .

TURKISH JOURNAL OF MATHEMATICS, 2023, 47 (05) :1585-+

[27] Solution for a Space-time Fractional Diffusion Equation [J].

Liu, Qiyu ;

Lv, Longjin .

PROCEEDINGS OF THE 2017 2ND INTERNATIONAL CONFERENCE ON MODELLING, SIMULATION AND APPLIED MATHEMATICS (MSAM2017), 2017, 132 :180-184

[28] Exact solution of the capillary diffusion equation for a three‐component mixture [J].

O. E. Aleksandrov .

Journal of Applied Mechanics and Technical Physics, 2002, 43 (3) :391-396

[29] A SINGULAR LIMIT IN A FRACTIONAL REACTION-DIFFUSION EQUATION WITH PERIODIC COEFFICIENTS [J].

Leculier, Alexis .

COMMUNICATIONS IN MATHEMATICAL SCIENCES, 2019, 17 (02) :565-586

[30] AN INVERSE SOURCE PROBLEM FOR A GENERALIZED TIME FRACTIONAL DIFFUSION EQUATION [J].

Faizi, R. ;

Atmania, R. .

EURASIAN JOURNAL OF MATHEMATICAL AND COMPUTER APPLICATIONS, 2022, 10 (01) :26-39

← 1 2 3 4 5 →