Chebyshev pseudospectral analysi̇s of the functi̇onal gradi̇ng of the cyli̇nder i̇n transi̇ent regi̇me

Transient analysis of functionally graded infinite length hollow cylinder is performed using non-Fourier hyperbolic heat conduction model. Except the thermal relaxation time, the material properties are assumed to change exponentially in the radial direction. Since an infinite-length cylinder is considered, the effects at the upper and lower ends of the cylinder are neglected. Under these conditions, a linear partial differential equation based on the radial and time variable is obtained. This partial differential equation is solved numerically by Laplace-Pseudospektral Chebyshev-Durbin combined method. The transient dynamic responses of temperature and heat flux are investigated by taking a special metal-ceramic mixture and examining various relative temperature changes. The behavior of temperature distribution and heat flux at different times is shown in the form of graphs. The solutions available in the literature are used to demonstrate the accuracy of this combined method. The combined method used in this study has been shown to be a well structured, simple and effective.