Two-dimensional temperature distribution in FGM sectors with the power-law variation in radial and circumferential directions

This study aimed at presenting a steady-state analytical solution for the two-dimensional heat conduction in a cylindrical segment made of functionally graded materials. It is acquired by taking advantage of the Fourier transform and separation of variables rather than numerical methods. Sturm–Liouville theory is employed to find the proper and adequate Fourier transformation. Continuous variations along the radial and circumferential directions based on the power-law function are taken into account, and non-homogeneous boundary conditions are applied to the problem. The obtained formulation is verified by the available solutions. Through solving an illustrative example, the temperature distribution is deliberated for a combination of boundary conditions. It is to be emphasized that mathematical robustness and generality of the solution are its primary advantage which is not often seen in the previously published literature.