Abstract The modification of the Rayleigh number, Ra, has been studied in the past. These studies have shown that the physical interpretation of the modified Rayleigh number which is commonly used is questionable. Moreover, although most of the available correlations work well, their behaviours in extremes (low or high Ra) are not correct where only a few correlations are available in low Ra. Therefore, a numerical simulation of heat transfer from annular circular finned tubes was conducted to present a comprehensive correlation for the modified Rayleigh number. As shown in this study, the flow forms a circular path around the tube. Based on this fact, a new modified Rayleigh number definition and correlation are proposed, which are valid for Nusselt numbers from 1 to 20,000. This range of Ra provides a complete picture of natural convection over circular annular finned tubes, especially at relatively low Ra. Finally, the end behaviours of the proposed correlation were compared with those of existing correlations.

中文翻译：

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基于修正瑞利数的水平环形翅片管自然对流换热

摘要 过去曾研究过瑞利数 Ra 的修正。这些研究表明，常用的修正瑞利数的物理解释是有问题的。此外，尽管大多数可用的相关性工作良好，但它们在极端（低或高 Ra）下的行为是不正确的，因为在低 Ra 下只有少数相关性可用。因此，进行了环形圆形翅片管传热的数值模拟，以呈现修正瑞利数的综合相关性。如本研究所示，流动在管子周围形成圆形路径。基于这一事实，提出了一种新的修正瑞利数定义和相关性，它适用于从 1 到 20,000 的 Nusselt 数。这个 Ra 范围提供了圆形环形翅片管上自然对流的完整图像，尤其是在相对较低的 Ra 下。最后，将所提出的相关性的最终行为与现有相关性的最终行为进行比较。