Chin. Phys. B ›› 2013, Vol. 22 ›› Issue (1): 14401-014401.doi: 10.1088/1674-1056/22/1/014401

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

Fractional Cattaneo heat equation in a semi-infinite medium

续焕英a, 齐海涛a b, 蒋晓芸c   

  1. a School of Mathematics and Statistics, Shandong University (Weihai), Weihai 264209, China;
    b State Key Laboratory for Turbulence and Complex Systems and Department of Mechanics and Aerospace Engineering,College of Engineering, Peking University, Beijing 100871, China;
    c School of Mathematics, Shandong University, Jinan 250100, China
  • 收稿日期:2012-04-20 修回日期:2012-06-18 出版日期:2012-12-01 发布日期:2012-12-01
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 11102102, 11072134, and 91130017), the Natural Science Foundation of Shandong Province, China (Grant No. ZR2009AQ014), and the Independent Innovation Foundation of Shandong University, China (Grant No. 2010ZRJQ002).

Fractional Cattaneo heat equation in a semi-infinite medium

Xu Huan-Ying (续焕英)a, Qi Hai-Tao (齐海涛)a b, Jiang Xiao-Yun (蒋晓芸)c   

  1. a School of Mathematics and Statistics, Shandong University (Weihai), Weihai 264209, China;
    b State Key Laboratory for Turbulence and Complex Systems and Department of Mechanics and Aerospace Engineering,College of Engineering, Peking University, Beijing 100871, China;
    c School of Mathematics, Shandong University, Jinan 250100, China
  • Received:2012-04-20 Revised:2012-06-18 Online:2012-12-01 Published:2012-12-01
  • Contact: Qi Hai-Tao E-mail:htqi@sdu.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 11102102, 11072134, and 91130017), the Natural Science Foundation of Shandong Province, China (Grant No. ZR2009AQ014), and the Independent Innovation Foundation of Shandong University, China (Grant No. 2010ZRJQ002).

摘要: To better describe the phenomenon of non-Fourier heat conduction, the fractional Cattaneo heat equation is introduced from the generalized Cattaneo model with two fractional derivatives of different orders. The anomalous heat conduction under the Neumann boundary condition in a semi-infinity medium is investigated. Exact solutions are obtained in series form of the H-function by using the Laplace transform method. Finally, numerical examples are presented graphically when different kinds of surface temperature gradient are given. The effects of fractional parameters are also discussed.

关键词: Caputo fractional derivative, non-Fourier heat conduction, Cattaneo equation, H-function

Abstract: To better describe the phenomenon of non-Fourier heat conduction, the fractional Cattaneo heat equation is introduced from the generalized Cattaneo model with two fractional derivatives of different orders. The anomalous heat conduction under the Neumann boundary condition in a semi-infinity medium is investigated. Exact solutions are obtained in series form of the H-function by using the Laplace transform method. Finally, numerical examples are presented graphically when different kinds of surface temperature gradient are given. The effects of fractional parameters are also discussed.

Key words: Caputo fractional derivative, non-Fourier heat conduction, Cattaneo equation, H-function

中图分类号:  (Heat conduction)

  • 44.10.+i
44.05.+e (Analytical and numerical techniques) 02.30.Gp (Special functions)