Abstract Taking interface phonon scattering into consideration, we present a set of thermal conduction interface conditions to simulate the interfacial temperature jump in nanocomposites and consequently obtain closed-form solutions describing thermal fields in the vicinity of a circular nanoinhomogeneity. Our results show that the heat flux inside the inhomogeneity is uniform and that the heat flux in the surrounding matrix can also be made uniform by designing the size or thermal conductivity of the inhomogeneity in the case when the thermal conductivity of the inhomogeneity is higher than that of the matrix. Using our theoretical results, we derive an explicit expression for the effective thermal conductivity of a rectangular region containing a circular nanoinhomogeneity. Furthermore, we undertake a numerical study to further explore the effects of interface phonon scattering on thermal conduction. Our results indicate that interface phonon scattering has the ability to suppress thermal conduction around a nanoinhomogeneity and has thus important applications in improving the performance of a range of functional materials.

中文翻译：

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圆形纳米不均匀性周围的热传导

摘要 考虑到界面声子散射，我们提出了一组热传导界面条件来模拟纳米复合材料中的界面温度跳跃，从而获得描述圆形纳米不均匀性附近热场的封闭形式解。我们的结果表明，不均匀性内部的热通量是均匀的，并且在不均匀性的导热系数高于不均匀性的情况下，通过设计不均匀性的尺寸或导热性，也可以使周围基体中的热通量均匀。的矩阵。使用我们的理论结果，我们推导出包含圆形纳米不均匀性的矩形区域的有效热导率的明确表达式。此外，我们进行了数值研究，以进一步探索界面声子散射对热传导的影响。我们的结果表明，界面声子散射具有抑制纳米不均匀性周围热传导的能力，因此在改善一系列功能材料的性能方面具有重要应用。