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

• Autorzy: Kukla S. , Siedlecka U.

Identyfikatory

DOI

10.1515/bpasts-2017-0022

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

heat conduction; multilayered sphere; Caputo fractional derivative

PL

przewodzenie ciepła; powłoka wielowarstwowa; pochodna ułamkowego rzędu Caputo

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2017
• Tom: Vol. 65, nr 2
• Strony: 179--186
• Opis fizyczny: Bibliogr. 31 poz., rys., wykr., tab.

Twórcy

autor

Kukla S.

• Institute of Mathematics, Czestochowa University of Technology, 21 Armii Krajowej Ave., 42-201 Częstochowa, Poland

autor

Siedlecka U.

• Institute of Mathematics, Czestochowa University of Technology, 21 Armii Krajowej Ave., 42-201 Częstochowa, Poland

Bibliografia

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Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).