Transient thermal analysis in 2D orthotropic FG hollow cylinder with heat source

A straightforward implementation is applied to solve heat conduction equation for a 2D hollow cylinder made of orthotropic functionally graded material (FGM) in the presence of time-dependent heat source. All material properties are considered to vary continuously within the cylinder along the radial direction with arbitrary law. The transient solution can be obtained by augmented state space method, which leads to carry out the results easily, based on laminate approximation theory in the Laplace domain, and then the results obtained are converted into the time domain by applying the numerical Laplace transform inversion. By this method, the solution of heat conduction problem is obtained for general boundary conditions which can be included various combinations of arbitrary temperature, flux, or convection. Comparison of obtained results with special cases in the literatures shows the capability of the new presented method. Finally, in the presence of time-dependent heat source, the effects of circumferential to the radial thermal conductivity coefficient ratio and heat source size on temperature field are graphically shown.