Abstract The present work is guided by the Constructal theory to identify the best shapes for the cavity inserted in a cylindrical solid body with a constant heat generation rate. From the assertion that a system must evolve to persist in time, an evolution of the elemental (I-shaped) cavity to a tree-shaped cavity with two branches added to a single branch is proposed. With these modifications, two restrictions (area occupied by the trunk and area occupied by the branches of the cavity) and seven degrees of freedom are used to represent the geometry. The study focused on investigating the effect of the degrees of freedom associated with the cavity branches and the number of cavities. Results show that the optimization of each new degree reduces the maximum excess of temperature. However, the results obtained with a more complex cavity were similar to those obtained by the elemental cavity in reducing the maximum excess temperature. In practical terms, the results are similar. Despite the similarity between the present results and those achieved with a most simple shape. The increase of performance with the increase of degrees of freedom studied here indicates that for complete optimization, the performance of complex shapes can surpass that of the simplest cavity.

中文翻译：

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树形空腔插入圆柱体发热结构设计

摘要 目前的工作以构造理论为指导，以确定插入具有恒定发热率的圆柱形固体中的空腔的最佳形状。从系统必须进化以在时间上持续存在的断言，提出了将基本（I 形）腔演化为树形腔，在单个分支上添加两个分支。通过这些修改，使用两个限制（树干占据的面积和腔分支占据的面积）和七个自由度来表示几何形状。该研究的重点是研究与空腔分支和空腔数量相关的自由度的影响。结果表明，每个新度数的优化减少了最大的温度过剩。然而，使用更复杂的空腔获得的结果与使用元素空腔获得的结果在降低最大过量温度方面的结果相似。实际上，结果是相似的。尽管目前的结果与用最简单的形状获得的结果相似。这里研究的随着自由度的增加性能的增加表明，对于完全优化，复杂形状的性能可以超过最简单腔的性能。