ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS |
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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 |
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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.
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Received: 24 July 2014
Revised: 02 October 2014
Accepted manuscript online:
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PACS:
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44.10.+i
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(Heat conduction)
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44.05.+e
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(Analytical and numerical techniques)
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45.10.Hj
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(Perturbation and fractional calculus methods)
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Fund: 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). |
Corresponding Authors:
Jiang Xiao-Yun
E-mail: wqjxyf@sdu.edu.cn
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Cite this article:
Xu Huan-Ying (续焕英), Jiang Xiao-Yun (蒋晓芸) Time fractional dual-phase-lag heat conduction equation 2015 Chin. Phys. B 24 034401
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