Time fractional thermoelastic problem of a thick cylinder with non homogeneous material properties

Abstract

In this article, we assume a two dimensional thermoelastic problem of nonhomogeneous thick hollow cylinder within the context of fractional order derivative of order 0 < α ≤ 2. Convective heat exchange boundary conditions are applied at the curved surface, whereas the lower surface and the upper surface of the cylinder are considered at zero temperature. Furthermore cylinder is subjected to a sectional heating at the outer curved surface of cylinder. Let the material properties of the cylinder except Poisson’s ratio and density are considered to be expresses by a simple power law in axial direction. The solution of the thermoelastic problem is obtained in terms of trigonometric and Bessel’s functions. Both the thermal and mechanical behavior is analyzed by the influence of inhomogeneity. Numerical computations are carried out for a mixture of copper and tin metals for both homogeneous and nonhomogeneous cases. Results of numerical solutions are illustrated graphically for temperature distribution and thermal stresses for all the different values of the fractional-order parameter α with the help of Mathematica software.