ABSTRACT In this paper, we examine the application of an ideal phonon-hydrodynamic material as the heat transfer medium between two diffuse-gray boundaries with a finite temperature difference. We use the integral-equation approach to solve a modified phonon Boltzmann transport equation with the displaced Bose–Einstein distribution as the equilibrium distribution between two boundaries perpendicular to the heat transfer direction. When the distance between the boundaries is smaller than the phonon normal scattering mean free path, our solution converges to the ballistic limit as expected. In the other limit, we find that, although the local thermal conductivity in the bulk of the hydrodynamic material approaches infinity, the thermal boundary resistance at the interfaces becomes dominant. Our study provides insights into both the steady-state thermal characterization of phonon-hydrodynamic materials and the practical application of phonon-hydrodynamic materials for thermal management.

中文翻译：

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垂直于漫灰色边界的流体动力学声子传输

摘要 在本文中，我们研究了理想声子流体动力学材料作为具有有限温差的两个扩散灰色边界之间的传热介质的应用。我们使用积分方程方法来求解修正的声子玻尔兹曼输运方程，其中位移玻色-爱因斯坦分布作为垂直于传热方向的两个边界之间的平衡分布。当边界之间的距离小于声子法向散射平均自由程时，我们的解决方案按预期收敛到弹道极限。在另一个限制中，我们发现，尽管大部分流体动力材料的局部热导率接近无穷大，但界面处的热边界电阻变得占主导地位。