Abstract
Several experimental and theoretical investigations confirm the failure of the classical Fourier's law in low-dimensional systems and ultrafast thermal transport. Hydrodynamic heat transport has been recently considered as a promising avenue to thermal management and phonon engineering in graphitic materials. Non-Fourier features are therefore required to describe and distinguish the hydrodynamic regime from other heat transport regimes. In this work, we provide an efficient framework for the identification of hydrodynamic heat transport and second sound propagation in graphene at 80 and 100 K. We solve both the dual-phase-lag model and the Maxwell-Cattaneo-Vernotte equation based on the finite element method with ab initio data as inputs. We emphasize on the detection of thermal wave-like behavior using macroscopic quantities including the Knudsen number and second sound velocity beyond Fourier's law. We present a clear observation of the crossover phenomena from the wave-like regime to diffusive heat transport predicted in terms of mesoscopic equations. This present formalism will contribute to a clear and deeper understanding of hydrodynamic heat transport in condensed systems for future experimental detection of second sound propagation above 80 K.