  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
quasi-two 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.
