Time fractional dual-phase-lag heat conduction equation

We build a fractional dual-phase-lag model and the corresponding bioheat transfer equation, which we use to interpret the experiment results for processed meat that have been explained by applying the hyperbolic conduction. Analytical solutions expressed by H-functions are obtained by using the Lapl...

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Bibliographic Details
Published inChinese physics B Vol. 24; no. 3; pp. 207 - 213
Main Author 续焕英 蒋晓芸
Format Journal Article
LanguageEnglish
Published 01.03.2015
Subjects
Conduction
Construction
Fourier transforms
Heat conduction
Heat transfer
Inverse
Mathematical analysis
Mathematical models
Meat
分数
同时估计
弛豫时间
模型参数
热传导方程
生物传热方程
相位滞后
非线性最小二乘法
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Summary:We build a fractional dual-phase-lag model and the corresponding bioheat transfer equation, which we use to interpret the experiment results for processed meat that have been explained by applying the hyperbolic conduction. Analytical solutions expressed by H-functions are obtained by using the Laplace and Fourier transforms method. The inverse fractional dual-phase-lag heat conduction problem for the simultaneous estimation of two relaxation times and orders of fractionality is solved by applying the nonlinear least-square method. The estimated model parameters are given. Finally, the measured and the calculated temperatures versus time are compared and discussed. Some numerical examples are also given and discussed.
Bibliography:We build a fractional dual-phase-lag model and the corresponding bioheat transfer equation, which we use to interpret the experiment results for processed meat that have been explained by applying the hyperbolic conduction. Analytical solutions expressed by H-functions are obtained by using the Laplace and Fourier transforms method. The inverse fractional dual-phase-lag heat conduction problem for the simultaneous estimation of two relaxation times and orders of fractionality is solved by applying the nonlinear least-square method. The estimated model parameters are given. Finally, the measured and the calculated temperatures versus time are compared and discussed. Some numerical examples are also given and discussed.
Xu Huan-Ying,and Jiang Xiao-Yun（ a） school of Mathematics, Shandong University, Jinan 250100, China; b） School of Mathematics and Statistics, Shandong University, Weihai 264209, China
fractional dual-phase-lag model,thermal wave,non-Fourier heat conduction,analytical solution
11-5639/O4
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:1674-1056
2058-3834
1741-4199
DOI:10.1088/1674-1056/24/3/034401