Second sound of heat conduction in one-dimensional dielectric materials

Abstract

Although recent experiment have shown that second sound can occur in graphite above 200 K, there have been no reports of second sound being observed in low-dimensional materials. In the present work, based on phonon hydrodynamics we found that second sound can occur in a single-walled carbon nanotube (SWCNT) with a length of no less than 2.1333 microns and no more than 2.1209e-4 meters for the initial temperature field with sinusoidal changes in the axial direction. The constraint conditions for relaxation times of the normal and resistive scatterings, as well as the conditions for the axial length and initial temperature distribution required for the occurrence of the second sound in dielectric nanowires are also derived from the Guyer-Krumhansl equations. For both SWCNTs and nanowires it was found that the small normal scattering relaxation time and large resistive scattering relaxation time are beneficial for the occurrence of second sound. Our results show that in comparison with two-dimensional materials, such as graphene, it is easier to experimentally excite second sound in the SWCNTs.