Radial ballistic-diffusive heat conduction in nanoscale

ABSTRACT Heat conduction in radius direction is of great importance to the use of two-dimensional materials and experiments. In this paper, radial ballistic-diffusive heat conduction in nanoscale is investigated by the phonon Monte Carlo (MC) method and phonon Boltzmann transport equation. We find that owing to the two-dimensional nature, the radial heat transport is dominated by two parameters, including the Knudsen number (Kn) and the radius ratio of the two concentric boundaries, the former of which is defined as the ratio of the phonon mean-free-path to the distance of the two boundaries. Compared with the one-dimensional cases, radial ballistic transport not only leads to boundary temperature jumps and the size effect of the effective thermal conductivity, but also results in a nonlinear temperature profile in logarithm radius coordinate, a difference of the inner and outer boundary temperature jumps, a stronger size effect, and a nonuniform local thermal conductivity within the system. When the value of Kn is far less than one, diffusive transport predominates and the effect of the radius ratio is negligible. Whereas, when Kn is comparable to or larger than one, the intensity of ballistic transport compared to diffusive transport will be increased significantly as the radius ratio decreases. In addition, the models for the temperature profile and the effective thermal conductivity are derived by an interpolation of the limit solutions and modification of the previous model, respectively. The good agreements with the phonon MC simulations demonstrate their validity.