(224h) On the Derivation of Damped Wave Conduction and Relaxation Equation by Five Methods

The motivation to seek a generalized Fourier's law of heat conduction is sixfold: Contradiction with the microscopic principle of reversibility, singularities in the description of transient temperature and heat flux in cartesian, cylinder and spherical coordinates, semi-infinite, infinite, and finite media, light speed barrier

and Landau's observation, empirical development of the law, overprediction of theory to experiment in a number of processes such as fluidized bed heat transfer to immersed surfaces, chromatography, CPU overheating and thermal management, adsorption, gel electrophoresis, restriction mapping, laser heating, drug delivery systems, etc and Casimir limit for heat conduction at nanoscales.

Altough Cattaneo and Vernotte hypothesized the non-Fourier heat conduction law very little work has been reported in the derivation of the law and the ramifications of them thereof. In this study the generalized Fourier's law of heat conduction is derived by the following methods;

1) Free Electron Theory

2) Stokes-Einstein Theory

3) Boltzmann Transport Equation

4) Kinetic Theory of Gases

5) Viscoelastic Theory

The ramifications of the derivations and the interpretation of the relaxation time property is discussed. The velocity of the accelerating electron, the velocity of the diffusing molecule in a liquid under a chemical potential difference, elaticity of heat, accumulation term in kinetic theory, and ballistic transport in the BTE are the interpretation to the velocity of heat during transient heat conduction.

How it was called the wave transport is also discussed. Under what conditions does the heat conduction become wavy is presented. Some of the misconceptions about ubiquitous occurence of waves is cleared. The reality of the conditions under which the subcritical damped oscillations under some conditions of high relaxation time materials are derived.