A closed-form solution for axisymmetric conduction in a finite functionally graded cylinder

An exact general analytical solution is derived for heat conduction problem in an axisymmetric cylinder made of functionally graded material whose thermal conductivity differs in two directions. It is assumed that the thermal conductivity coefficients in radial and longitudinal directions are the power functions of radius. This is accomplished by taking advantage of Sturm-Liouville theory to get a suitable Fourier transformation. The general inhomogeneous thermal boundary conditions are adopted in both radial and longitudinal directions. The obtained solution is adequately verified against available analytical results. Also, two illustrative cases are considered to guarantee the solution's accuracy from a practical perspective. Particularly, the importance of the material constants on temperature distribution in both radial and longitudinal directions is uncovered. The results show that the present exact solution satisfies well the energy equation and arbitrary complex boundary conditions.