Abstract Phonons are the main contributors to thermal energy transfer in thin films. The size dependence of the thermal transport characteristics alters the film properties such as thermal conductivity. Hence, in the present study, three-dimensional, transient phonon transport in dielectric material is studied through the Equation of Phonon Radiative Transport (EPRT) to assess the size dependence of thermal conductivity. The numerical scheme is introduced solving the EPRT in three dimensions and the governing algorithm is described in detail. A parametric study is carried out examining the effect of the Kn \mathrm{Kn} number on the thermal energy transport characteristics in three-dimensional thermally excited film. The formulation and estimation of the effective thermal conductivity tensor is presented and discussed, thereby extending, to some extent, the one-dimensional results obtained earlier. We demonstrate that thermal conductivity changes in all directions, depending on the size effect. In addition, the directions of the temperature gradient and heat flux vectors differ as the Kn \mathrm{Kn} number approaches unity.

中文翻译：

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硅中的三维弹道扩散热传输：瞬态响应和热导率

摘要 声子是薄膜热能传递的主要贡献者。热传输特性的尺寸依赖性改变了薄膜特性，例如热导率。因此，在本研究中，通过声子辐射传输方程 (EPRT) 研究介电材料中的三维瞬态声子传输，以评估热导率的大小依赖性。介绍了在三个维度上求解 EPRT 的数值方案，并详细描述了控制算法。进行了参数研究，研究了 Kn \mathrm{Kn} 数对三维热激发薄膜中热能传输特性的影响。提出和讨论了有效热导率张量的公式和估计，从而扩展，在某种程度上，早先获得的一维结果。我们证明了热导率在各个方向上都会发生变化，这取决于尺寸效应。此外，随着 Kn \mathrm{Kn} 数接近统一，温度梯度和热通量矢量的方向不同。