Non-Fourier heat conduction analysis of infinite 2D orthotropic FG hollow cylinders subjected to time-dependent heat source

The non-Fourier heat conduction analysis of infinite 2D functionally graded (FG) hollow cylinders subjected to time-dependent heat source is presented. In this study, a new augmented state space method considering laminate approximation theory is introduced. All material properties are assumed to vary continuously within the cylinder along the specified directions following an arbitrary law. We considered acomplicated heat transfer engineering problem that so far has no analytical and/or numerical solution yet. This problem is solved in the Laplace domain, and to convert the obtained results into the time domain, a numerical Laplace transform inversion with consideration of Gibb's phenomenon is employed. This present method is proposed so general that can solve the heat conduction problems time-dependent heat source and general boundary conditions such as heat flux, convection and combinations of arbitrary temperatures. Eventually, our method is superior in correctness and exactness and also has a sufficient computational cost by comparing the obtained results with some available problems in the literatures.