Heat Conduction Paradox Involving Second-Sound Propagation in Moving Media

Abstract

In this Letter, we revisit the Maxwell-Cattaneo law of finite-speed heat conduction. We point out that the usual form of this law, which involves a partial time derivative, leads to a paradoxical result if the body is in motion. We then show that by using the material derivative of the thermal flux, in lieu of the local one, the paradox is completely resolved. Specifically, that using the material derivative yields a constitutive relation that is Galilean invariant. Finally, we show that under this invariant reformulation, the system of governing equations, while still hyperbolic, cannot be reduced to a single transport equation in the multidimensional case.