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Thermoelasticity Based on Time-Fractional Heat Conduction Equation in Polar Coordinates

  • Yuriy PovstenkoEmail author
Chapter
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 219)

Abstract

The fundamental solutions to the first and second Cauchy problems and to the source problem are obtained for axisymmetric time-fractional heat conduction equation in an infinite plane in polar coordinates. Radial heat conduction in a cylinder and in an infinite solid with a cylindrical cavity is investigated. The Dirichlet boundary problems with the prescribed boundary value of temperature and the physical Neumann boundary problems 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. Figures show the characteristic features of temperature and stress distribution and represent the whole spectrum of order of time-derivative.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Institute of Mathematics and Computer ScienceJan Długosz UniversityCzęstochowaPoland

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