The radial thermal rectification in the concentric silicon ring from ballistic to diffusive regime is investigated based on the phonon Boltzmann transport equation. In the ballistic and diffusive limits, the analytical solutions prove that there is no thermal rectification. In the ballistic-diffusive regime, the heat flux prefers to flow from the inner boundary to the outer boundary. Furthermore, as the characteristic length (the distance between two circular boundaries) increases from tens of nanometers to tens of microns, the thermal rectification ratio enhances first and then fades away gradually. It attributes to that as the direction of the temperature gradient changes, the average phonon mean free path changes. The difference of the average phonon mean free path finally leads to the change of the heat flux or thermal conductivity. As the temperature decreases, the maximum thermal rectification ratio decreases. In addition, as the radius ratio between the inner and outer boundary increases, the thermal rectification ratio decreases for a given characteristic length.

中文翻译：

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同心硅环中从弹道到扩散状态的径向热整流

基于声子玻尔兹曼传输方程研究了同心硅环中从弹道到扩散区的径向热整流。在弹道和扩散极限中，解析解证明没有热整流。在弹道扩散状态下，热通量更倾向于从内边界流向外边界。此外，随着特征长度（两个圆形边界之间的距离）从几十纳米增加到几十微米，热整流比先增加然后逐渐消失。它归因于随着温度梯度方向的变化，平均声子平均自由程发生变化。平均声子平均自由程的差异最终导致热通量或热导率的变化。随着温度降低，最大热整流比降低。此外，随着内边界和外边界之间的半径比增加，对于给定的特征长度，热整流比降低。