Axisymmetric Problems in Cylindrical Coordinates

Problems of fractional thermoelasticity based on the time-fractional heat conduction equation are considered in cylindrical coordinatesCylindrical coordinates. Heat conduction in a long cylinderCylinder, in an infinite solid with a long cylindrical cavity and in a half-space is investigated. The solutions to the fractional heat conduction equationFractional heat conduction equation under the Dirichlet boundary conditionDirichlet 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 obtained. Different kinds of integral transforms (Laplace, Fourier and Hankel) are used. Associated thermal stresses are investigated. The representations of stresses in terms of the displacement potentialDisplacement potential and the biharmonic Love function allow us to satisfy the prescribed boundary conditionBoundary condition for the stress tensor.