A novel transient heat conduction phenomenon to distinguish the hydrodynamic and (quasi) ballistic phonon transport

Abstract

Many studies have predicted the failure of Fourier's law of thermal conduction due to the existence of wave like propagation of heat. This non-Fourier thermal transport phenomenon can appear in both the hydrodynamic and (quasi) ballistic regimes. Hence, it is not easy to clearly distinguish these two non-Fourier regimes only by the wave like propagation of heat. In this work, the transient heat propagation in homogeneous thermal system is studied based on the phonon Boltzmann transport equation (BTE) under the Callaway model. Given a quasi-one or quasi-two dimensional thermal system with homogeneous environment temperature, at initial moment, a heat source is added suddenly at the center of the system with high temperature, then the heat propagates from the center to the outer. Numerical results show that in quasitwo dimensional thermal system, the transient temperature will be lower than the lowest value of initial temperature in the hydrodynamic regime within a certain range of time and space. This phenomenon appears only when the normal scattering dominates heat conduction. Besides, it disappears in quasi-one dimensional thermal system. Similar phenomenon is also observed in thermal system with time varying heat source. This peculiar heat propagation phenomenon of hydrodynamic phonon transport distinguishes it well from (quasi) ballistic phonon transport.