弹道扩散导热的热质模型

Abstract

The classical Fourier heat conduction law only works well for diffusive transport under normal conditions. Several typical non-Fourier models, such as the Cattaneo-Vernotte, dual-phase-lagging, and thermomass models, have been developed for thermal wave transport under transient conditions in recent decades. In addition, some recent studies have shown that the thermal conductivity of lowdimensional systems increases with increasing characteristic length because heat is transported in a ballistic-diffusive manner in nanostructures, in which the phonon mean free path (MFP) is comparable to the characteristic length. However, few models have become available for such thermal transport processes to date. In this work, we show that the general heat conduction law can be extended to phonon ballistic-diffusive transport by modification of the boundary conditions. First, we analyze the diffusive and ballistic transport processes from a thermomass theory viewpoint. Diffusive transport is transport in which thermal mass drifts in a body with a resistance proportional to the drift velocity, similar to fluid flows in porous media, and the current general heat conduction law can be derived from the thermomass balance equations, in which the heat inertia is considered. However, when the MFP is comparable with the characteristic length, the rarefied effect of the thermomass occurs, which corresponds to ballistic heat transport. In this regime, temperature jumps occur at the boundaries. It is noted here that the effects of ballistic heat transport are not covered in the current general heat conduction law. Therefore, modified boundary conditions that consider ballistic transport are applied to extend the general heat conduction law. We derive these modified boundary conditions from the phonon Boltzmann transport equation. The phonon distribution function is expanded with respect to the Knudsen number ( Kn ), and the continuous heat flux condition is used to obtain the modified boundary conditions. In addition, heat conduction in silicon nanofilms at room temperature is studied numerically, and comparisons with Monte Carlo simulations are also conducted to confirm the proposed theoretical models. It is found that our model can predict the temperature distributions well within silicon nanofilms with different Knudsen numbers. The size-dependent thermal conductivity can also be obtained using our model.