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中文摘要：
对多孔材料辐射-传热耦合计算的数学模型,即Rosseland方程,给出了一种统计的二阶双尺度分析方法,并针对典型问题进行了数值模拟。建立了考虑辐射项的统计二阶双尺度计算公式,给出了统计意义下热流密度极值的预测算法,并通过与理论解的比较对算法进行了验证,利用本文中方法研究了孔洞体分比和空间分布状态对陶瓷多孔材料热传导系数、辐射传导系数和热流密度极值的影响。结果表明：孔洞体积分数的增加将导致有效热传导系数下降;热流密度极值随孔洞体积分数的增加而变大,并且在高温时辐射的作用明显增大;数值试验表明,使用统计二阶双尺度方法及其有限元算法预测孔洞随机分布复合材料结构的热性能是有效的。
英文摘要：
A new statistical second-order two-scale（SSOTS） method was presented for predicting the performances of conduction-radiation coupled heat transfer of porous materials with random distribution of pores.The statistical second-order two-scale formulation for the Rosseland problem of porous materials was discussed,and a statistical prediction algorithm for maximum heat flux density was brought forward.Besides,the validity of the proposed method by comparison with theoretical methods with simple numerical models was verified.Finally,macroscopic thermal properties for the porous ceramic materials with varying probability distribution models including volume fraction and spatial distribution model of pores were shown.The results show that the effective thermal conductivity parameters decrease and maximum heat flux density increases with the pores volume fraction increasing.What is more,the radiation is an important factor for heat transfer at a high temperature.It is also shown that the SSOTS method is valid to predict the performances of conduction-radiation coupled heat transfer of porous materials with random distribution of pores.
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