Abstract A new anisotropic thermal conductivity equation of h-BN/polymer composites was successfully derived from a series of numerical calculation and mathematical analysis. A simple finite element model of polymer composite filled with oriented hexagonal boron nitride (h-BN) was firstly established to simulate its thermal transportation. This numerical model was validated by other thermal conductive models and experimental data. Then the influence of many factors on the anisotropic thermal conductivity of h-BN/polymer composites was mathematically investigated, including matrix thermal conductivity, h-BN thermal conductivity, size, aspect ratio and oriented angles, interfacial thermal resistance, and non-uniform factors. It is found that thermal conductivity of polymer composites increases with filler content as a power function; decreases with interfacial thermal resistance in a negative power function form; increases almost proportionally with thermal conductivity of polymer matrix; does not change with h-BN thermal conductivity when the in-plane thermal conductivity of h-BN is higher than 100 W·m−1·K−1 and out-of-plane thermal conductivity of h-BN is higher than 2 W·m−1·K−1; and does not change with h-BN size under the same aspect ratio. With the increasing h-BN aspect ratio, in-plane thermal conductivity of composites increases, while out-of-plane thermal conductivity decreases. The change ranges of position and tilt angle correction factors were also obtained.

中文翻译：

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使用有限元分析的 h-BN/聚合物复合材料的新各向异性导热系数方程

摘要 通过一系列的数值计算和数学分析，成功推导出h-BN/聚合物复合材料的各向异性导热系数方程。首次建立了填充有取向六方氮化硼（h-BN）的聚合物复合材料的简单有限元模型，以模拟其热传输。该数值模型得到了其他导热模型和实验数据的验证。然后从数学上研究了多种因素对h-BN/聚合物复合材料各向异性热导率的影响，包括基体热导率、h-BN热导率、尺寸、纵横比和取向角、界面热阻和非均匀因素。 . 发现聚合物复合材料的热导率随着填料含量的增加而增加，作为幂函数；以负幂函数形式随界面热阻减小；与聚合物基体的热导率几乎成比例地增加；当h-BN的面内热导率高于100 W·m-1·K-1和h-BN的面外热导率高于2 W时，h-BN的热导率不随h-BN热导率变化·m-1·K-1；并且在相同的纵横比下不随 h-BN 尺寸变化。随着h-BN纵横比的增加，复合材料的面内热导率增加，而面外热导率降低。还获得了位置和倾斜角校正因子的变化范围。当h-BN的面内热导率高于100 W·m-1·K-1和h-BN的面外热导率高于2 W时，h-BN的热导率不随h-BN热导率变化·m-1·K-1；并且在相同的纵横比下不随 h-BN 尺寸变化。随着h-BN纵横比的增加，复合材料的面内热导率增加，而面外热导率降低。还获得了位置和倾斜角校正因子的变化范围。当h-BN的面内热导率高于100 W·m-1·K-1和h-BN的面外热导率高于2 W时，h-BN的热导率不随h-BN热导率变化·m-1·K-1；并且在相同的纵横比下不随 h-BN 尺寸变化。随着h-BN纵横比的增加，复合材料的面内热导率增加，而面外热导率降低。还获得了位置和倾斜角校正因子的变化范围。