Abstract In this paper, a formula for estimating the effective thermal conductivity of lotus-type porous materials (LTPM) combining an analytical formula with a mean-field homogenisation technique is developed and validated. LTPMs are considered multi-phase materials in which each phase is defined by the pore shape. To estimate the effective thermal conductivities of multi-phase LTPMs, a two-step mean-field homogenisation method is implemented and validated. The validation is applied by comparing the results obtained with those of the representative volume element based finite element homogenisation method, which has been taken as a reference. The proposed formula is applied by replacing the first step of the two-step mean field homogenisation method using a formula for estimating the effective thermal conductivity of two-phase lotus-type materials. The good agreement between the results of the proposed formula and the reference results indicates that the proposed formula ensures an accurate estimation of the effective macroscopic thermal conductivities of multi-phase lotus-type porous materials.

中文翻译：

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空隙形状对莲花型多孔材料有效导热系数的影响建模

摘要 在本文中，结合解析公式和平均场均化技术，开发并验证了一种用于估算莲花型多孔材料 (LTPM) 有效热导率的公式。LTPM 被认为是多相材料，其中每个相都由孔形状定义。为了估计多相 LTPM 的有效热导率，实施并验证了两步平均场均化方法。通过将获得的结果与基于代表性体积元的有限元均匀化方法的结果进行比较来应用验证，该方法已被用作参考。通过使用用于估计两相莲花型材料的有效热导率的公式代替两步平均场均匀化方法的第一步，应用所提出的公式。所提公式的结果与参考结果吻合良好，表明所提公式保证了对多相莲花型多孔材料宏观有效热导率的准确估计。