Abstract
In the current study, the problem of two-dimensional (2-D) heat transfer on a long cylindrical vessel made of functionally graded material (FGM) whose material properties vary according to a power function is investigated. Functionally graded materials are materials with special production processes in which different thermophysical properties can be gradually changed. To conduct the research, the analytical method is exploited. The exact solution is obtained using the separation of variable (SOV) method. Boundary conditions in the inner radius of this cylinder are provided by solar energy (renewable energies). Heat conduction equations are assumed to change in two directions based on the power-law function. The presented analytical solution is verified using numerical results. After validating the obtained exact solution, some parametric studies using a practical example are considered. The obtained solution is capable of handling various combinations of homogenous and inhomogeneous boundary conditions. It is shown that more flexible attitudes in terms of temperature distribution are seen by using functionally graded material. Through one illustrative example, the effect of different boundary conditions along with various parameters such as material constants, conductive coefficient, and convection coefficient on temperature distribution is analyzed. By increasing the σ number from 0.1 to 0.7, the temperature in the cylinder radius decreases by 6.1%. On the other hand, it has also been observed that by increasing the number τ from 1 to 4, the temperature increases by 3.9%.