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Fractional heat conduction in multilayer spherical bodies

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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.
Rocznik
Strony
83--92
Opis fizyczny
Bibliogr. 12 poz., rys.
Twórcy
autor
autor
Bibliografia
  • [1] Özişik M.N., Heat conduction, Wiley, New York 1993.
  • [2] Lu X., Viljanen M., An analytical method to solve heat conduction in layered spheres with time-dependent boundary conditions, Physics Letters A 2006, 351, 274-282.
  • [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.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-df03c26a-0ee7-41f0-a614-c9f7a8327823
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