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2015 | OriginalPaper | Buchkapitel

5. Thermoelasticity Based on Time-Fractional Heat Conduction Equation in Spherical Coordinates

verfasst von : Yuriy Povstenko

Erschienen in: Fractional Thermoelasticity

Verlag: Springer International Publishing

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Abstract

The fundamental solutions to the first and second Cauchy problems and to the source problem are obtained for central symmetric time-fractional heat conduction equation in an infinite medium in spherical coordinates. Radial heat conduction in a sphere and in an infinite solid with a spherical cavity is investigated. The Dirichlet boundary problem with the prescribed boundary value of temperature and the physical Neumann boundary problem with the prescribed boundary value of the heat flux are solved using the integral transform technique. The associated thermal stresses are studied. The numerical results are illustrated graphically for the whole spectrum of order of fractional derivative.

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Vorheriges Kapitel Axisymmetric Problems in Cylindrical Coordinates

Nächstes Kapitel Thermoelasticity Based on Space-Time-Fractional Heat Conduction Equation

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Titel: Thermoelasticity Based on Time-Fractional Heat Conduction Equation in Spherical Coordinates
verfasst von: Yuriy Povstenko
Verlag: Springer International Publishing
Buch: Fractional Thermoelasticity
Print ISBN: 978-3-319-15334-6

Electronic ISBN: 978-3-319-15335-3

Copyright-Jahr: 2015
DOI: https://doi.org/10.1007/978-3-319-15335-3_5

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