Time fractional dual-phase-lag heat conduction equation

doi:10.1088/1674-1056/24/3/034401

›› 2015, Vol. 24 ›› Issue (3): 34401-034401.doi: 10.1088/1674-1056/24/3/034401

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇下一篇

Time fractional dual-phase-lag heat conduction equation

续焕英^{a b}, 蒋晓芸^a

a School of Mathematics, Shandong University, Jinan 250100, China;
b School of Mathematics and Statistics, Shandong University, Weihai 264209, China

收稿日期:2014-07-24 修回日期:2014-10-02 出版日期:2015-03-05 发布日期:2015-03-05
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11102102, 11472161, and 91130017), the Natural Science Foundation of Shandong Province, China (Grant No. ZR2014AQ015), and the Independent Innovation Foundation of Shandong University, China (Grant No. 2013ZRYQ002).

Time fractional dual-phase-lag heat conduction equation

Xu Huan-Ying (续焕英)^{a b}, Jiang Xiao-Yun (蒋晓芸)^a

a School of Mathematics, Shandong University, Jinan 250100, China;
b School of Mathematics and Statistics, Shandong University, Weihai 264209, China

Received:2014-07-24 Revised:2014-10-02 Online:2015-03-05 Published:2015-03-05
Contact: Jiang Xiao-Yun E-mail:wqjxyf@sdu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11102102, 11472161, and 91130017), the Natural Science Foundation of Shandong Province, China (Grant No. ZR2014AQ015), and the Independent Innovation Foundation of Shandong University, China (Grant No. 2013ZRYQ002).

摘要/Abstract

摘要： 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.

关键词: fractional dual-phase-lag model, thermal wave, non-Fourier heat conduction, analytical solution

Abstract: 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.

Key words: fractional dual-phase-lag model, thermal wave, non-Fourier heat conduction, analytical solution

中图分类号: (Heat conduction)

44.10.+i

44.05.+e (Analytical and numerical techniques) 45.10.Hj (Perturbation and fractional calculus methods)

续焕英, 蒋晓芸. Time fractional dual-phase-lag heat conduction equation[J]. , 2015, 24(3): 34401-034401.

Xu Huan-Ying (续焕英), Jiang Xiao-Yun (蒋晓芸). Time fractional dual-phase-lag heat conduction equation[J]. Chin. Phys. B, 2015, 24(3): 34401-034401.

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Time fractional dual-phase-lag heat conduction equation

Time fractional dual-phase-lag heat conduction equation

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