Fractional heat conduction in a sphere under mathematical and physical Robin conditions

• Autorzy: Kukla S. , Siedlecka U.

Identyfikatory

DOI

10.15632/jtam-pl.56.2.339

• Języki publikacji: EN

Abstrakty

EN

In this paper, the effect of a fractional order of time-derivatives occurring in fractional heat conduction models on the temperature distribution in a composite sphere is investigated. The research concerns heat conduction in a sphere consisting of a solid sphere and a spherical layer which are in perfect thermal contact. The solution of the problem with a classical Robin boundary condition and continuity conditions at the interface in an analytical form has been derived. The fractional heat conduction is governed by the heat conduction equation with the Caputo time-derivative, a Robin boundary condition and a heat flux continuity condition with the Riemann-Liouville derivative. The solution of the problem of non-local heat conduction by using the Laplace transform technique has been determined, and the temperature distribution in the sphere by using a method of numerical inversion of the Laplace transforms has been obtained.

Słowa kluczowe

EN

heat conduction; fractional heat equation; Robin boundary condition

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2018
• Tom: Vol. 56 nr 2
• Strony: 339--349
• Opis fizyczny: Bibliogr. 37 poz., rys., tab.

Twórcy

autor

Kukla S.

• Czestochowa University of Technology, Institute of Mathematics, Częstochowa, Poland

autor

Siedlecka U.

• Czestochowa University of Technology, Institute of Mathematics, Częstochowa, Poland

Bibliografia

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Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).