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.

中文翻译：

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纳米级径向弹道扩散热传导

摘要 半径方向的热传导对于二维材料的使用和实验具有重要意义。在本文中，通过声子蒙特卡罗（MC）方法和声子玻尔兹曼传输方程研究了纳米尺度的径向弹道扩散热传导。我们发现由于二维性质，径向传热由两个参数主导，包括克努森数（Kn）和两个同心边界的半径比，前者定义为声子的比值到两个边界的距离的平均自由路径。与一维情况相比，径向弹道输运不仅导致边界温度跳跃和有效热导率的尺寸效应，而且导致对数半径坐标中的非线性温度分布，内外边界温度跳跃的差异，更强的尺寸效应，以及系统内不均匀的局部热导率。当 Kn 的值远小于 1 时，扩散传输占主导地位，半径比的影响可以忽略不计。然而，当 Kn 等于或大于 1 时，与扩散传输相比，弹道传输的强度将随着半径比的减小而显着增加。此外，温度分布模型和有效热导率模型分别通过极限解的插值和先前模型的修改推导出来。与声子 MC 模拟的良好一致性证明了它们的有效性。以及系统内不均匀的局部热导率。当 Kn 的值远小于 1 时，扩散传输占主导地位，半径比的影响可以忽略不计。然而，当 Kn 等于或大于 1 时，与扩散传输相比，弹道传输的强度将随着半径比的减小而显着增加。此外，温度分布模型和有效热导率模型分别通过极限解的插值和先前模型的修改推导出来。与声子 MC 模拟的良好一致性证明了它们的有效性。以及系统内不均匀的局部热导率。当 Kn 的值远小于 1 时，扩散传输占主导地位，半径比的影响可以忽略不计。然而，当 Kn 等于或大于 1 时，与扩散传输相比，弹道传输的强度将随着半径比的减小而显着增加。此外，温度分布模型和有效热导率模型分别通过极限解的插值和先前模型的修改推导出来。与声子 MC 模拟的良好一致性证明了它们的有效性。当 Kn 等于或大于 1 时，与扩散传输相比，弹道传输的强度将随着半径比的减小而显着增加。此外，温度分布模型和有效热导率模型分别通过极限解的插值和先前模型的修改推导出来。与声子 MC 模拟的良好一致性证明了它们的有效性。当 Kn 等于或大于 1 时，与扩散传输相比，弹道传输的强度将随着半径比的减小而显着增加。此外，温度分布模型和有效热导率模型分别通过极限解的插值和先前模型的修改推导出来。与声子 MC 模拟的良好一致性证明了它们的有效性。