(671i) Computational Modeling of Thermal Diffusion at the Mesoscale
Heat transfer in crystalline solids occurs through the motion of packets of vibration waves, or phonons. Over sufficiently large length scales, the motion of the phonons is diffusive, local thermal equilibrium is maintained, and the relation between the heat flux and temperature gradient is accurately described by Fourierâs heat law. However, at nanometer length scales or the mesoscale where characteristic lengths are comparable to the phonon mean-free path, phonon transport becomes increasingly ballistic and Fourierâs law is therefore inaccurate. Applications requiring mesoscale simulations of heat transfer include microelectronics devices and improved models for hot spot formation and growth in energetic materials. The phonon Boltzmann transport equation (BTE) is well-suited to these types of problems because it captures behavior over the entire ballistic-diffusive spectrum. In the present work, we assess the feasibility of using molecular dynamics (MD) simulations to obtain the material properties needed to solve the BTE for graphene. We then simulate a graphene sheet subject to different thermal conditions using the BTE and compare the resulting temperature profiles with analogous results obtained by MD. Prepared in part by LLNL under Contract DE-AC52-07NA27344.