Mass Nature of Heat and Its Applications I: Motion of Thermomass Fluid and General Heat Conduction Law

The concept of thermomass is defined as the equivalent mass of thermal energy according to the Einstein’s mass-energy relation. Hence, the phonon gas in dielectrics can be regarded a weighty, compressible fluid. Heat conduction in the medium, where the rest mass lattices or molecules acts the porous framework, resembles the gas flow through the porous medium. Newton mechanics has been applied to establish the equation of state and the equation of motion for the phonon gas as in fluid mechanics, since the drift velocity of a phonon gas is normally much less than the speed of light. The momentum equation of the thermomass gas, including the driving, inertial and resistant forces, is a damped wave equation, which is in fact the general conduction law. This is because it reduces to the CV (Cattaneo-Vernotte) model or the single phase-lag model as the heat flux related inertial terms are neglected, and reduces to Fourier’s heat conduction law as all inertial terms are neglected. Therefore, the underlying physics of Fourier’s heat conduction law is the balance between the driving force and the resistant force of the heat motion, and Fourier’s law will break down when the inertial force is comparable to the resistant force, for instance, in the case of ultra-short pulse laser heating or heat conduction in carbon nanotubes at ultra-high heat flux.