The effective thermal conductivity of unsaturated porous media is of interest in a number of applications of heat transfer. In this paper, a novel fractal solution for effective thermal conductivity is derived based on the fractal distribution of surface roughness and pore size in unsaturated porous media with roughened surfaces. The proposed fractal model explicitly relates the effective thermal conductivity to the microstructural parameters (relative roughness, porosity and fractal dimensions). The proposed fractal model is verified by a satisfying agreement of the effective thermal conductivity predicted by our model and that reported as existing experimental data in the literature. A parametric study is also elaborated to investigate the influences of the microstructural parameters on the effective thermal conductivity. The results demonstrate that our proposed fractal model improves our understanding of the physical mechanisms of heat transport through unsaturated porous media with roughened surfaces. One advantage of our fractal analytical model is that it contains no empirical constant, while it is usually required in previous models.

中文翻译：

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粗糙表面不饱和分形多孔介质的有效热导率研究

不饱和多孔介质的有效热导率在许多传热应用中都很重要。在本文中，基于粗糙表面的不饱和多孔介质的表面粗糙度和孔径的分形分布，推导了一种新的有效热导率分形解。所提出的分形模型明确地将有效热导率与微观结构参数（相对粗糙度、孔隙率和分形维数）联系起来。所提出的分形模型通过我们模型预测的有效热导率与文献中现有实验数据的令人满意的一致性得到验证。还进行了参数研究，以研究微观结构参数对有效热导率的影响。结果表明，我们提出的分形模型提高了我们对通过具有粗糙表面的不饱和多孔介质的热传输物理机制的理解。我们的分形分析模型的一个优点是它不包含经验常数，而以前的模型通常需要它。