Abstract Present work performs a numerical study about the energy removal in a heated tubular array submitted to an external flow. Taking into account that a large variety of tubular arrangements can exists, in this work it is developed a tubular array that does not use any kind of initial predefined arrangement. Using the principles of Constructal Theory (or Law) and a positioning function dependent on the velocity and temperature fields, it is calculated, in a deterministic way, the location where each tube should be positioned. Pressure drop is not taken in to account in this first algorithm implementation as a performance indicator. In order to validate the proposed methodology, the Constructal Array is compared with standard aligned and staggered arrangements suggested in literature. The minimum distance between tubes (p) is considered as a degree of freedom. Four variations are studied: p = 1D, p = 1.25D, p = 1.5D and p = 2D, where D is the tube diameter. It is considered here the simulation of a transient, incompressible and laminar flow of a Newtonian fluid in a two-dimensional domain with forced convection and Prandtl number equal to 0.71. Results are computed when the flow reaches to the steady state condition. It is evaluated three values for Reynolds number: ReD = 10, 50 and 100. Thermal analysis of the formed patterns has shown that best thermal performance was not obtained with p = 1D, neither with p = 2D, i.e., tube distance has an influence on its formation and, consequently, on the heat transfer exchange. In all performed analyzes, Constructal arrays configuration showed higher energy removal (up to 71%) than the aligned and staggered arrangements, which highlights the capacity of proposed method. Constructal Array for p = 1.5D showed the most homogeneous distribution and proved to be the most effective in 4 of the six studied cases.

中文翻译：

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使用构造理论对受外流影响的管状布置进行热分析

摘要 目前的工作对受外流作用的加热管阵列中的能量去除进行了数值研究。考虑到可以存在多种管状排列，在这项工作中开发了一种不使用任何类型的初始预定义排列的管状阵列。使用构造理论（或定律）的原理和依赖于速度和温度场的定位函数，以确定性的方式计算每个管应定位的位置。在这个第一个算法实现中没有考虑压降作为性能指标。为了验证所提出的方法，将构造阵列与文献中建议的标准对齐和交错排列进行比较。管之间的最小距离 (p) 被视为一个自由度。研究了四种变体：p = 1D、p = 1.25D、p = 1.5D 和 p = 2D，其中 D 是管直径。此处考虑在强制对流和普朗特数等于 0.71 的二维域中模拟牛顿流体的瞬态、不可压缩和层流。当流量达到稳态条件时计算结果。对雷诺数的三个值进行了评估：ReD = 10、50 和 100。形成的图案的热分析表明，p = 1D 和 p = 2D 都没有获得最佳热性能，即管距有影响关于它的形成，因此，关于传热交换。在所有进行的分析中，结构阵列配置显示出比对齐和交错排列更高的能量去除（高达 71%），这突出了所提出方法的能力。p = 1.5D 的构造阵列显示出最均匀的分布，并在六个研究案例中的四个案例中证明是最有效的。