多孔材料具有孔隙率高、密度小和比表面积大等特征,在消声、减震、隔热和电磁屏蔽等应用方面具备多种优异性能。由于其在气孔中存在低热导率的空气介质,可以用作绝热材料。与其他相应材料相比,它具有耐高温和强度高的优点,已被广泛应用于航空航天、原子能和交通运输等行业。本文研究了热辐射效应对圆柱形空腔多孔材料传热性能的影响,推导了多孔材料局部有效热导率的方便工程应用的封闭公式。与已有理论结果比较,给出了本文公式的精度。数值算例揭示了孔洞对于热传输的有意义的影响规律。多孔材料的局部有效热导率可以分为两部分：一部分由固相和气相的纯传导引起,无量纲化的传导热导率不依赖于温度和孔径;另一部分由热辐射引起,随温度和孔径的变化而剧烈变化。在温度较低和孔径较小的情形下,辐射影响可以忽略不计。

Porous materials possess superior mechanical and thermal performances, and have been widely used in aeronautics, astronautics, atomic energy, transportation etc industries. The effect of the radiation for the heat transfer property of the porous materials with the cylindrical cavities is studied. The micromechanics methods, ie dilute, self-consistent and Mori-Tanaka methods, are extended to predict the effective thermal conductivity of porous materials accounting for the radiation effect at high temperature. The compact closed form formula of the local effective thermal conductivity is derived, which is very convenient for engineering application. A comparison with available theoretical predictions is made to demonstrate the accuracy of the present formula. The dilute and self-consistent methods give unreasonable predictions for the relative high porosity. The Mori-Tanaka predicts reasonable solutions. Numerical examples reveal a lot of interesting interaction phenomena of pores on heat transfer. It is seen that the local effective thermal conductivity divides into two parts: one attributes to conduction and the dimensionless conductivity by pure conduction is independent of temperature and pore size, whereas the other is due to thermal radiation in the pores and strongly depends on temperature and pore size, which is negligible at low temperature and in the case of small pores.