Exact Transient Heat Conduction of Functionally Graded Thick Structures

Closed form solution of the transient thermal analysis in functionally graded cylindrical and spherical bodies under different thermal loads are presented. It is assumed that the material properties change according to the different inhomogeneity parameters according to the power-law in the radial direction. In the partial differential equation obtained under these conditions, the time dependence is eluted with the Laplace transform and transformed into Bessel differential equation in Laplacian space. This equation, which is solved with Bessel functions in Laplacian space, is transformed into physical space with the modified inverse Durbin method. Behaviors of cylindrical and spherical bodies under constant, convective and time-dependent boundary conditions are investigated. Besides, it is aimed to obtain benchmark solutions for these structures to the literature.