An analytical solution to the problem of time-fractional heat conduction in a composite sphere

Bulletin of the Polish Academy of Sciences. Technical Sciences

S. KuklaCorresponding authorInstitute of Mathematics, Czestochowa University of Technology, 21 Armii Krajowej Ave., 42-201 Cz?stochowa, PolandEmailOther articles by this author:De Gruyter OnlineGoogle Scholar¹  U. SiedleckaInstitute of Mathematics, Czestochowa University of Technology, 21 Armii Krajowej Ave., 42-201 Cz?stochowa, PolandOther articles by this author:De Gruyter OnlineGoogle Scholar¹ 

[1] Institute of Mathematics, Czestochowa University of Technology, 21 Armii Krajowej Ave., 42-201 Cz?stochowa, Poland

关键词: Keywords: heat conduction;    multilayered sphere;    Caputo fractional derivative;   

DOI  :  10.1515/bpasts-2017-0022

学科分类：工程和技术（综合）

来源: Polska Akademia Nauk * Centrum Upowszechniania Nauki / Polish Academy of Sciences, Center for the Advancement of Science

【 摘 要 】

An analytical solution to the problem of time-fractional heat conduction in a sphere consisting of an inner solid sphere and concentric spherical layers is presented. In the heat conduction equation, the Caputo time-derivative of fractional order and the Robin boundary condition at the outer surface of the sphere are assumed. The spherical layers are characterized by different material properties and perfect thermal contact is assumed between the layers. The analytical solution to the problem of heat conduction in the sphere for time-dependent surrounding temperature and for time-space-dependent volumetric heat source is derived. Numerical examples are presented to show the effect of the harmonically varying intensity of the heat source and the harmonically varying surrounding temperature on the temperature in the sphere for different orders of the Caputo time-derivative.

【 授权许可】

Unknown