Abstract The present study deals with the design and analysis of an array of constructal fork-shaped fins adhered to a circular tube and operating under fully wet conditions. Fork-shaped fin arrays with two and three numbers of branches are considered in the current work. The mass transfer process is calculated by using a cubic relation between the humidity ratio of saturated air and the corresponding fin surface temperature. The governing equations are highly non-linear and hence they are solved by using a semi-analytical technique called Homotopy Perturbation method. The optimisation is done by maximising the net heat transfer rate of the fin array and un-finned surface and by imposing certain constraints. The constraints are taken such that the radial space limitations fin material limitations, as well as the minimum fin gap considerations, are taken into account. As the present problem involves a large number of design parameters as well as the interrelated constraints, a bio-inspired metaheuristic algorithm called the Firefly Algorithm has been employed for obtaining the optimum condition. The analysis has been performed for different operating conditions and the results have been compared with the corresponding rectangular fin array. From the study, it has been seen that the heat transfer rate from the optimum fork-shaped fin array with two branches is higher than that from the optimum rectangular fin array. However, in a few cases, it has been found that there is marginal difference in heat transfer rate between the optimum fork-shaped fin array with two branches and the rectangular fin array but the total length of each fin for the former case is found to be smaller and hence fork-shaped fin array with two branches would be a better selection than the rectangular fin array. However, increasing the number of branches of the fork-shaped fins from two to three does not provide any benefit in terms of either lower fin length or higher heat transfer rate.

中文翻译：

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空间受限情况下同时传热传质应用的新型优化构造叉形翅片阵列设计

摘要 本研究涉及一系列结构叉形翅片的设计和分析，这些翅片附着在圆管上并在完全潮湿的条件下运行。在当前的工作中考虑了具有两个和三个分支数量的叉形鳍阵列。传质过程是利用饱和空气的湿度比与相应的翅片表面温度之间的三次关系计算的。控制方程是高度非线性的，因此通过使用称为同伦微扰法的半解析技术来求解它们。优化是通过最大化翅片阵列和非翅片表面的净传热率并施加某些约束来完成的。采取约束使得径向空间限制翅片材料限制以及最小翅片间隙考虑，被考虑在内。由于目前的问题涉及大量的设计参数以及相互关联的约束，因此采用了一种称为萤火虫算法的仿生元启发式算法来获得最佳条件。对不同的操作条件进行了分析，并将结果与​​相应的矩形翅片阵列进行了比较。从研究中可以看出，具有两个分支的最佳叉形翅片阵列的传热率高于最佳矩形翅片阵列的传热率。然而，在少数情况下，已经发现，具有两个分支的最佳叉形翅片阵列与矩形翅片阵列之间的传热率存在边际差异，但发现前一种情况下每个翅片的总长度更小，因此是叉形翅片。具有两个分支的鳍阵列将是比矩形鳍阵列更好的选择。然而，将叉形翅片的分支数量从两个增加到三个在翅片长度更短或传热率更高方面没有任何好处。