Manifestation of Acceleration During Transient Heat Conduction

Abstract

The damped wave conduction and relaxation equation is derived from the free electron theory. The relaxation time is a third of the collision time between the electron and the obstacle in a given material. Six different reasons are given to seek a generalized Fourier's law of heat conduction. The hyperbolic governing equation is solved for by four different methods for three different boundary conditions. The reports in the literature of a temperature overshoot are revisited. For a small slab, a < π(ατ r ) 1/2 ,the temperature was shown to exhibit subcritical damped oscillations. In the case of the semi-infinite medium reports in the literature about a wave discontinuity were revisited. A substitution variable that is symmetric in space and time, that is, 11 = r2 - X 2 , is proposed to transform the governing equation into a Bessel differential equation. Three regimes are recognized in the solution: inertial lagging zero transfer regimes, a rising regime, and a third falling regime. The manifestation of the relaxation time for the case of the periodic boundary condition is studied using the method of complex temperature. The solution is an overdamped system. The storage coefficient is defined and found to be a critical parameter in the analysis.