Phonon hydrodynamics for nanoscale heat transport at ordinary temperatures

Abstract

The classical Fourier's law fails in extremely small and ultrafast heat conduction even at ordinary temperatures due to strong thermodynamic nonequilibrium effects. In this work, a macroscopic phonon hydrodynamic equation beyond Fourier's law with a relaxation term and nonlocal terms is derived through a perturbation expansion to the phonon Boltzmann equation around a four-moment nonequilibrium solution. The temperature jump and heat flux tangential retardant boundary conditions are developed based on the Maxwell model of the phonon-boundary interaction. Extensive steady-state and transient nanoscale heat transport cases are modeled by the phonon hydrodynamic model, which produces quantitative predictions in good agreement with available phonon Boltzmann equation solutions and experimental results. The phonon hydrodynamic model provides a simple and elegant mathematical description of non-Fourier heat conduction with a clear and intuitive physical picture. The present work will promote deeper understanding and macroscopic modeling of heat transport in extreme states.