Fractional Cattaneo heat equation in a semi-infinite medium  

作　　者：续焕英 齐海涛 蒋晓芸 

机构地区：[1]School of Mathematics and Statistics, Shandong University, Weihai [2]State Key Laboratory for Turbulence and Complex Systems and Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University [3]School of Mathematics, Shandong University

出　　处：《Chinese Physics B》2013年第1期338-343,共6页中国物理B（英文版）

基　　金：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);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.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 

分 类 号：O551.3[理学—热学与物质分子运动论] TQ021.4[理学—物理]