Suscripción a Biblioteca: Guest

ISSN Online: 2377-424X

ISBN Print: 978-1-56700-421-2

International Heat Transfer Conference 15
August, 10-15, 2014, Kyoto, Japan

Thermomass-Based General Law for Ballistic-Diffusive Heat Conduction in Nanostructures

Get access (open in a dialog) DOI: 10.1615/IHTC15.cnd.009021
pages 1357-1368

Sinopsis

The classical Fourier’s heat conduction law works well only for diffusive transport under normal conditions, and several typical models, such as Cattaneo-Vernotte, dual-phase-lagging and thermomass models, have been developed for thermal wave transport of transient conditions in recent decades. Heat transports in a ballistic-diffusive way in nanostructures where the phonon mean free path is comparable to the characteristic length. Previous studies show that the thermal conductivity of low-dimensional systems increases with the characteristic length increasing. However, few models are available for the thermal transport processes thus far. In this paper we show that the general heat conduction law based on the thermomass theory can be extended to the phonon ballistic-diffusive transport with modification of boundary conductions. First, we analyze the diffusive and ballistic transport processes from the viewpoint of the thermomass theory. The diffusive transport is that thermal energy drifts in a body with the resistance proportional to the drift velocity, just like fluid flows in porous media. The resistance of the ballistic transport is zero with temperature jump at boundaries. Second, we derive the boundary condition for the ballistic-diffusive heat conduction from the phonon Boltzmann transport equation. The temperature jump at the boundaries is found to be linearly related to the Knudsen number, defined as the ratio of the phonon mean free path to the characteristic length, the temperature gradient and the temperature relaxation rate. Third, Monte Carlo simulations of heat conductions in silicon nanofilms are performed to confirm the theoretical models. Good agreements between the theoretical predictions and simulations are obtained for the temperature profiles, boundary temperature jump and length-dependent thermal conductivity. We demonstrate that the thermomass-based general heat conduction law can be successfully extended to the ballistic-diffusive transport in nanostructures with the boundary condition modification we developed based on the phonon Boltzmann transport equation.