In this paper, considering the structure of the shape factor and the rough element, combined with fractal geometry theory, the shape factor, the relative increase in the heat transfer between the rough surface and the smooth surface in a fractal unit, and the fractal analytical expression of the dimensionless equivalent thermal conductivity caused by convection thermal conductivity are derived. In addition, the relationship between the microstructure parameters of the rough surface and the shape factor, the relative increase in convective heat transfer and the dimensionless equivalent thermal conductivity are studied. It is found that the relative increment of the convective heat transfer and the shape factor are proportional to the ratio of the minimum height and maximum height of the rough element and the fractal dimension, and the dimensionless equivalent thermal conductivity model deduced in this paper is compared with the existing experimental data to verify the validity of the model.

中文翻译：

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粗糙微通道传热特性的分形研究

本文考虑形状因子和粗糙元的结构, 结合分形几何理论, 形状因子, 分形单元中粗糙面和光滑面之间传热的相对增加, 以及分形解析推导了对流热导引起的无量纲等效热导率表达式。此外，还研究了粗糙表面的微观结构参数与形状因子的关系、对流传热的相对增加和无量纲等效热导率。发现对流换热的相对增量和形状因子与粗糙元的最小高度和最大高度与分形维数的比值成正比，