Fractional heat conduction in multilayer spherical bodies

• Autorzy: Kukla S. , Siedlecka U.

Identyfikatory

DOI

10.17512/jamcm.2016.4.09

• Języki publikacji: EN

Abstrakty

EN

In this paper an analytical solution of the time-fractional heat conduction problem in a spherical coordinate system is presented. The considerations deal the two-dimensional problem in multilayer spherical bodies including a hollow sphere, hemisphere and spherical wedge. The mathematical Robin conditions are assumed. The solution is a sum of time-dependent function satisfied homogenous boundary conditions and of a solution of the steady-state problem. Numerical example shows the temperature distributions in the hemisphere for various order of time-derivative.

Słowa kluczowe

EN

heat conduction; multilayer bodies; Caputo derivative; spherical coordinate

PL

przewodnictwo cieplne; pochodna Caputo; współrzędna sferyczna

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2016
• Tom: Vol. 15, nr 4
• Strony: 83--92
• Opis fizyczny: Bibliogr. 12 poz., rys.

Twórcy

autor

Kukla S.

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

autor

Siedlecka U.

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

Bibliografia

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• [3] Jain P.K., Singh S., Rizwan-uddin, An exact analytical solution for two-dimensional, unsteady, multilayer heat conduction in spherical coordinates, International Journal of Heat and Mass Transfer 2010, 53, 2133-2142.
• [4] Diethelm K., The Analysis of Fractional Differential Equations, Springer-Verlag, Berlin Heidelberg 2010.
• [5] Podlubny I., Fractional Differential Equations, Academic Press, San Diego 1999.
• [6] Povstenko Y., Linear Fractional Diffusion-wave Equation for Scientists and Engineers, Birkhäuser, New York 2015.
• [7] Ning T.H., Jiang X.Y., Analytical solution for the time-fractional heat conduction equation in spherical coordinate system by the method of variable separation, Acta Mechanica Sinica 2011, 27(6), 994-1000.
• [8] Kukla S., Siedlecka U., An analytical solution to the problem of time-fractional heat conduction in a composite sphere, Bulletin of the Polish Academy of Sciences, Technical Sciences (in print).
• [9] Žecová M., Terpák J., Heat conduction modeling by using fractional-order derivatives, Applied Mathematics and Computation 2015, 257, 365-373.
• [10] Povstenko Y., Fractional heat conduction in an infinite medium with a spherical inclusion, Entropy 2013, 15, 4122-4133.
• [11] Ishteva M., Scherer R., Boyadjiev L., On the Caputo operator of fractional calculus and C-Laguerre functions, Mathematical Sciences Research Journal 2005, 9(6), 161-170.
• [12] Haubold H.J., Mathai A.M., Saxena R.K., Mittag-Leffler functions and their applications, Journal of Applied Mathematics, Article ID 298628, 2011.

Uwagi

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