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

Journal title

Bulletin of the Polish Academy of Sciences Technical Sciences






No 2


Divisions of PAS

Nauki Techniczne






DOI: 10.1515/bpasts-2017-0022 ; ISSN 2300-1917


Bulletin of the Polish Academy of Sciences: Technical Sciences; 2017; 65; No 2; 179-186


Jain (2010), and Rizwan - uddin An exact analytical solution for two - dimensional unsteady multilayer heat conduction in spherical coordinates of Heat and Mass Transfer, International Journal, 53, 2133. ; Lu (2006), An analytical method to solve heat conduction in layered spheres with time - dependent boundary conditions A, Physics Letters, 351. ; Lucena (2008), da Solutions for a fractional diffusion equation with spherical symmetry using Green function approach, Chemical Physics, 344. ; Ning (2011), Analytical solution for the time - fractional heat conduction equation in spherical coordinate system by the method of variable separation, Acta Mechanica Sinica, 27, 994, ; Haji (2002), Sheikh and Temperature solution in multi - dimensional multi - layer bodies of Heat and Mass Transfer, International Journal, 45. ; Siedlecka (2014), Radial heat conduction in a multilayered sphere of Applied Mathematics and, Journal Computational Mechanics, 13, 109. ; Sierociuk (1990), Modelling heat transfer in heterogeneous media using fractional calculus Phil, Trans, 371. ; Haubold (2011), Mittag - Leffler functions and their applications of Applied Mathematics paper ID, Journal, 298628. ; Povstenko (2012), Central symmetric solution to the Neumann problem for a time - fractional diffusion - wave equation in a sphere Nonlinear Analysis : Real, World Applications, 13, 1229, ; Abbas (2015), Eigenvalue approach on fractional order theory of thermoelastic diffusion problem for an infinite elastic medium with a spherical cavity Modelling, Applied Mathematical, 39. ; Bayat (2012), Analytical and numerical analysis for the FGM thick sphere under combined pressure and temperature loading of, Archive Applied Mechanics, 82, 229, ; Povstenko (2011), Solutions to time - fractional diffusion - wave equation in spherical coordinates et, Acta Mechanica Automatica, 5, 108. ; Siedlecka (2015), A solution to the problem of time - fractional heat conduction in a multi - layer slab of Applied Mathematics and, Journal Computational Mechanics, 14, 95. ; Povstenko (2013), Fractional heat conduction in an infinite medium with a spherical inclusion, Entropy, 15, 4122, ; Raslan (2016), Application of fractional order theory of thermoelasticity to a problem for a spherical shell of and, Journal Theoretical Applied Mechanics, 54, 295, ; Lenzi (2006), da Fractional diffusion equation and Green function approach : Exact solutions, Physica A, 360. ; Pawar (2014), Dynamic behavior of functionally graded sphere subjected to thermal load of, Journal Mathematics, 9, 43. ; Žecová (2015), Heat conduction modeling by using fractional - order derivatives and, Applied Mathematics Computation, 257. ; Ishteva (2005), On the Caputo operator of fractional calculus and functions Research, Mathematical Sciences Journal, 9, 161. ; Lu (2006), Transient analytical solution to heat conduction in composite circular cylinder of Heat and Mass Transfer, International Journal, 49. ; Dzieliński (2010), Some applications of fractional order calculus, Bull Tech, 58.