The Cattaneo-type time fractional heat conduction equation for laser heating

被引：77

作者：

Qi, Hai-Tao ^{[1
,2
,3
]}

Xu, Huan-Ying ^{[1
]}

Guo, Xin-Wei ^{[1
]}

机构：

[1] Shandong Univ, Sch Math & Stat, Weihai 264209, Peoples R China

[2] Peking Univ, Coll Engn, State Key Lab Turbulence & Complex Syst, Beijing 100871, Peoples R China

[3] Peking Univ, Coll Engn, Dept Mech & Aerosp Engn, Beijing 100871, Peoples R China

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2013年 / 66卷 / 05期

基金：

中国国家自然科学基金;

关键词：

Non-Fourier heat conduction; Laser heating; Fractional derivative; Fox's H-function; PROPAGATION; DIFFUSION; LEQUATION;

D O I：

10.1016/j.camwa.2012.11.021

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the laser short-pulse heating of a solid surface is considered. The time fractional Cattaneo model is used as the heat conduction model and the corresponding fractional heat conduction equation with a volumetric heat source is built. The analytical solution for the temperature distribution is obtained using the Laplace transformation method. Finally, the numerical results are presented graphically for various values of model parameters, and their effects on the speed of heat conduction propagation are discussed. (C) 2012 Elsevier Ltd. All rights reserved.

引用

页码：824 / 831

页数：8

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