An analytical solution for asymmetric non-Fourier heat conduction in a long solid orthotropic cylinder

In this paper, an analytical solution for the asymmetric temperature distribution in a long orthotropic cylinder, by considering the Cattaneo theory, is presented. The temperature distribution, due to the non-axisymmetric initial condition, is obtained by using the separation of variable method. In order to verify the analytical results, the governing equations are solved numerically by using finite difference method. In presented results, the effect of the heat wave travelling from the outer wall and simultaneously from the center into the cylinder as well as their interference on the temperature distribution is discussed thoroughly. Additionally, the effect of lay up angle on the temperature distribution in both radial and circumferential directions is investigated. The time history of the non-Fourier temperature has a wavy form in contrast to the Fourier one. According to the results, the non-Fourier temperature distribution does not converge to the Fourier one before reaching to the steady state.