A mathematical model based on minimal thermal resistance and equal law of specific equivalent thermal conductivity is developed to discuss the heat transfer characteristics of ablative thermal insulating material from the mesoscopic scale. Based on the statistical results of mesoscopic parameters, the microstructure unit cell model was established to analyze the influence rule of mesoscopic parameterization which includes the size, distribution, and positional relation of microsphere and fiber. The results show that the equivalent thermal conductivity decreases with the density, size, distribution area, and distance of microsphere and the space distance and volume fraction of fiber decreasing. Besides, the equivalent thermal conductivity will become larger when more quality of heat transfers along the fiber direction. Exploring the relationship between the macroscopic heat transfer process and the microstructure is meaningful for exploring the heat transfer behavior of thermal insulating material and improvement of the processing technology.

中文翻译：

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烧蚀绝热材料传热特性的数学模型

建立了基于最小热阻和比热导率相等律的数学模型，从介观尺度讨论了烧蚀绝热材料的传热特性。基于介观参数的统计结果，建立了微结构单元格模型，分析了介观参数化的影响规律，包括微球和纤维的尺寸，分布和位置关系。结果表明，当量热导率随微球的密度，尺寸，分布面积和距离的增加而减小，纤维的空间距离和体积分数减小。此外，当更多质量的热量沿纤维方向传递时，等效热导率将变大。