Simulating transient heat transfer in graphene at finite Knudsen number via the Boltzmann transport equation and molecular dynamics

The phonon Boltzmann transport equation (BTE) with the relaxation time approximation (RTA) scattering model is used to calculate transient temperature profiles in graphene, and the results are compared to analogous molecular dynamics (MD) simulations. For the BTE calculations, the phonon dispersion relation and frequency-dependent scattering rates are obtained from a combination of MD data and semi-empirical power-law expressions for the normal and Umklapp phonon lifetimes. The dimensions and initial temperature conditions of graphene are varied to study the size and temperature dependence of thermal transport physics at the mesoscopic scale. Good quantitative agreement to within 5% is found between the BTE and MD results, over a wide range of temperatures and lengthscales of the temperature variation in the graphene sheet. Small differences are attributed to the inaccuracy of the RTA as applied to graphene, and to neglecting four-phonon scattering in the BTE simulations. The present results may further understanding in applications such as the transient heating of nanoelectronics.