ABSTRACT Phonon mean free path (MFP) spectra are essential for the accurate prediction and utilization of the classical size effect. Rebuilding an MFP spectrum from experimental data remains challenging. It requires solving the thermal transport phenomenon of a heat source of a given shape across the entire size range. Herein, to do this for a heat source embedded in an infinite medium, we derive a new set of modified ballistic–diffusive equations by analyzing the cause of the erroneous results observed in a steady-state solution of the original ballistic-diffusive equations. We demonstrate their ease and accuracy by obtaining the effective thermal conductivity for a spherical nanoparticle embedded in an infinite medium in an explicit closed-form and comparing it with that obtained by the Boltzmann transport equation (differences estimated as <3%).

中文翻译：

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用于从弹道热阻获得声子平均自由程谱的修正弹道扩散方程：I. 方程的介绍和验证

摘要 声子平均自由程 (MFP) 光谱对于经典尺寸效应的准确预测和利用至关重要。从实验数据重建 MFP 频谱仍然具有挑战性。它需要解决给定形状的热源在整个尺寸范围内的热传输现象。在这里，为了对嵌入在无限介质中的热源做到这一点，我们通过分析在原始弹道扩散方程的稳态解中观察到的错误结果的原因，推导出一组新的修正弹道扩散方程。我们通过获得以显式封闭形式嵌入无限介质中的球形纳米颗粒的有效热导率并将其与通过玻尔兹曼传输方程获得的热导率进行比较（差异估计为 <