Heterogeneous media with several spatial scales are often found in heat transfer applications. For instance, two-phase nanofluids made of nanoparticles immersed in a fluid containing both individual particles and clusters, which exhibit at least three structural scales, have shown improved thermal conductivity over the individual constituents. In this work, a problem for the Fourier heat equation with periodic and rapidly oscillating coefficients is studied via a reiterated homogenization method. The constituent phases are assumed to be in imperfect thermal contact, so there is a thermal barrier at the interfaces. The formal procedure to derive the homogenized problem, local problems, and effective coefficients is described for a general three-dimensional problem. The influence of volume fractions, phase conductivities, and interfacial thermal resistances on the effective behavior is exemplified for the case of laminated composites. An application of a simple model for the study of nanofluids is explained. Improvement of the effective conductivity and its dependence on the interfacial resistance is analyzed.

中文翻译：

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适用于具有界面热阻的纳米流体的重复均质化

在传热应用中经常发现具有几种空间尺度的非均质介质。例如，由纳米颗粒制成的两相纳米流体浸入包含单个颗粒和团簇的流体中，该流体表现出至少三个结构尺度，与单个组分相比，其导热性得到了改善。在这项工作中，通过反复均化方法研究了具有周期性和快速振荡系数的傅立叶热方程的问题。假定组成相之间的热接触不完善，因此界面处存在热障。对于一般的三维问题，描述了导出均化问题，局部问题和有效系数的形式化过程。体积分数，相电导率，对于层压复合材料的情况，举例说明了界面热阻对有效性能的影响。解释了一种用于研究纳米流体的简单模型的应用。分析了有效电导率的提高及其对界面电阻的依赖性。