It is very difficult to characterize the transport properties of porous media due to the disorder of pores distribution in porous media. In this paper, we study heat conduction through porous media with randomly fractures which are considered as tree-like networks. An expression for effective thermal conductivity (ETC) of saturated dual-porosity media is derived based on the fractal characteristics of pores diameter and fractures size. It is shown that the ETC is a function of structure parameters of the fractal dimension (Dg), the porosity (ϕg), the tortuous fractal dimension (Dt) and the maximum diameter (λmax) for the porous matrix; the fractal dimension (Df), the porosity (ϕf), the maximum diameter (d0max), the diameter ratio (β), the length ratio (α) and the branching levels (n) for the fracture networks. The dependence of structure parameters on the ETC is studied in detail. The results of our model are compared with the available experiments, which show good agreement. The proposed model for the ETC does not contain empirical parameters. The model is useful for predicting the heat conduction of materials.

中文翻译：

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具有随机分布的树状网络的双孔介质有效热导率的分形模型

由于多孔介质中孔隙分布的无序性，很难表征多孔介质的输运特性。在本文中，我们研究了通过随机裂缝的多孔介质的热传导，这些裂缝被认为是树状网络。根据孔隙直径和裂缝尺寸的分形特征，推导了饱和双孔隙介质有效热导率（ETC）的表达式。结果表明，ETC 是分形维数结构参数的函数 (DG), 孔隙率 (φG), 曲折的分形维数 (D吨) 和最大直径 (λ最大限度) 用于多孔基体；分形维数 (DF), 孔隙率 (φF), 最大直径 (d0最大限度), 直径比 (β), 长度比 (α) 和分支级别 (n) 用于断裂网络。详细研究了结构参数对ETC的依赖性。我们的模型的结果与可用的实验进行了比较，显示出良好的一致性。为 ETC 提出的模型不包含经验参数。该模型可用于预测材料的热传导。