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Axisymmetric steady temperature field in FGM cylindrical shells with temperature-dependent heat conductivity and arbitrary linear boundary conditions
Arch. Mech. 67 (3), 233-251, 2015
Keywords: heat conduction; temperature-dependent heat conductivity; functionally graded material; hollow cylinder; perturbation method
Abstract
An approximate analytical solution to the axisymmetric heat conduction equation for a hollow cylinder made of functionally graded material with temperature-dependent heat conductivity is presented. General linear boundary conditions are considered. The Poincaré method for regular perturbation problems is employed to obtain an analytical closed-form approximate solution for the temperature field. The hierarchical asymptotic problems are solved up to the second-order approximation. A numerical example is worked out, i.e., the one-dimensional heat conduction in the radial direction with prescribed temperatures at the boundaries. The approximate temperature profiles are compared with a numerical solution of the full nonlinear problem which provides the reference “exact” solution. A good agreement between the approximate and reference solutions is established. The convergence of the asymptotic series as well as the properties of the temperature field are studied.