Numerical Simulation of Non-Fourier Temperature Behavior of Functionally Graded Materials in a Slab with Surface Radiation

Abstract

Functionally graded materials (FGMs) are used in many applications that presumably produce the wave nature of thermal energy transport. This study investigates the hyperbolic and parabolic heat conduction problem for a solid slab made of FGM numerically. A constant heat flux is considered at both sides of the slab, and boundaries dissipate heat by radiation into an ambient. An exponential space-dependent function of volume fraction is considered. MacCormack's explicit predictor-corrector scheme is used to solve the nonlinear equation in order to handle discontinuities at the wave front quite satisfactorily with small oscillations. Results are compared to the results obtained with the assumption of constant and linear spatial variation of volume fraction function. Further effects of different nondimensional numbers on the temperature distribution is sought. Numerical results are validated by the analytical solution of a special case that shows excellent agreement.