Time-fractional radial heat conduction in a cylinder and associated thermal stresses

Abstract

The theory of thermal stresses based on the heat conduction equation with the Caputo time-fractional derivative of order 0 < α ≤ 2 is used to investigate axisymmetic thermal stresses in a cylinder. The solution is obtained applying the Laplace and finite Hankel integral transforms. The Dirichlet and two types of Neumann problems with the prescribed boundary value of the temperature, the normal derivative of the temperature, and the heat flux are considered. Numerical results are illustrated graphically. © 2011 The Author(s).