This research is devoted to geometrical optimization of internal longitudinal fins based on constructal theory. These fins are extended inward from the pipe perimeter to a prescribed radius and would have an optimal length, determined analytically by means of constructal theory. The effective parameters of the current study are the ratio of high conductivity to low conductivity, volume fraction of the fins, and the number of the fins. For a round tube with two thermal boundary conditions, i.e., constant heat flux and constant temperature, the optimization length and also the corresponding thickness of fins for a known material ratio are determined parametrically ensuring maximum heat transfer and thermal efficiency In addition, dominancy of conduction heat transfer between fins and convection in the core of pipe are the main assumptions of this research. Finally, our analytical results are verified with their corresponding numerical counterparts.

中文翻译：

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基于构造理论的管内纵向鳍设计与优化

这项研究致力于基于构造理论的内部纵向鳍的几何优化。这些散热片从管道周边向内延伸到规定的半径，并具有最佳长度，这是通过构造理论解析确定的。当前研究的有效参数是高电导率与低电导率之比，鳍片的体积分数以及鳍片的数量。对于具有两个热边界条件（即恒定的热通量和恒定的温度）的圆管，通过参数确定最优化长度以及相应的散热片厚度，以确保最大的热传递和热效率。翅片之间的传热传热和管道中心的对流占主导地位是本研究的主要假设。最后，我们的分析结果与相应的数值对应物进行了验证。