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

The fundamental solutions to the first and second Cauchy problemsSecond Cauchy problem and to the source problemSource problem are obtained for axisymmetric time-fractional heat conduction equationFractional heat conduction equation in an infinite plane in polar coordinatesPolar coordinates. Radial heat conduction in a cylinderCylinder and in an infinite solid with a cylindrical cavity is investigated. The Dirichlet boundary conditionsDirichlet boundary condition with the prescribed boundary value of temperature and the physical Neumann boundary conditionPhysical Neumann boundary condition with the prescribed boundary value of the heat flux are solved using the integral transform technique. The time-harmonic source term and the time-harmonic boundary conditions are considered. The associated thermal stresses are studied. The numerical results are illustrated graphically. Figures show the distinguishing features of temperature and stress distribution and represent the whole spectrum of order of time-derivative.