Analysis of One-Dimensional Hyperbolic Heat Conduction in a Functionally Graded Thin Plate

This paper presents the analytical solution of one-dimensional non-Fourier heat conduction problem for a finite plate made of functionally graded material. To investigate the influence of material properties variation, exponential space-dependant functions of thermal conductivity and specific heat capacity are considered. The problem is solved analytically in the Laplace domain, and the final results in the time domain are obtained using numerical inversion of the Laplace transform. The trial solution method with collocation optimizing criterion has been applied to solve the hyperbolic heat conduction equation based on polynomial shape function approximation. Due to the reflection and interaction of the thermal waves, the temperature peak happens on the insulated wall of the FGM plate, so the major aim of this paper is to find the amount of temperature peak and the time at which it happens. It has been shown that the dimensionless temperature peak and its happening time increase along with an increase in the dimensionless relaxation time. The results are validated by comparison with the results from an exact available solution solved at special case which shows a close agreement.