Unsteady temperature distribution in a cylinder made of functionally graded materials under circumferentially-varying convective heat transfer boundary conditions

Abstract

A novel model on 2D unsteady conductive heat transfer in an infinite hollow cylinder is proposed. The cylinder is made of functionally graded material (FGM) that has variable properties both in radial and angular directions. Volumetric heat capacity and thermal conductivity coefficient are changed according to the power function of the radius. In the presence of variable coefficients, the governing equations of unsteady heat transfer in FGMs have caused the complexity. The Laplace transform method is used to transfer the energy equation from time to frequency domain whereas the meromorphic function is used for the inverse Laplace transform to obtain the desired solutions. The closed form solutions have been well validated and the results have been presented for different values of functionally graded indices for thermal conductivity coefficients and volumetric heat capacity. Two different FGM cases with different complicated thermal boundary conditions have been investigated. The first case has a constant temperature in the inner radius and a variable heat flux along with the convection condition in the outer radius. In the second case, the inner radius has a specific harmonic temperature and the outer radius is exposed to the convective conditions. It was observed that in both cases, the temperature value in the cylinder decreases with the increase of the FG index for the conductivity coefficient. The presented analytical solution provides a good tool for validating unsteady numerical solutions presented in the field of heat transfer in FGMs.