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Chin. Phys. B, 2015, Vol. 24(3): 034401    DOI: 10.1088/1674-1056/24/3/034401
ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS Prev   Next  

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
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.
Keywords:  fractional dual-phase-lag model      thermal wave      non-Fourier heat conduction      analytical solution  
Received:  24 July 2014      Revised:  02 October 2014      Accepted manuscript online: 
PACS:  44.10.+i (Heat conduction)  
  44.05.+e (Analytical and numerical techniques)  
  45.10.Hj (Perturbation and fractional calculus methods)  
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

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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