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首页> 外文期刊>Applied Mathematical Modelling >Smooth and non-smooth optimal pin fin profiles beyond the Schmidt optimality assumption and “length-of-arc” approximation
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Smooth and non-smooth optimal pin fin profiles beyond the Schmidt optimality assumption and “length-of-arc” approximation

机译：超出Schmidt最佳假设和“弧长”近似的平滑和非平滑最佳销鳍轮廓

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摘要

A parametric model of the pin fin shape has been developed. The pin fin profile optimization is performed without adopting the “length-of-arc” approximation. The model is based on the accurate treatment of the arc length. The heat transfer coefficient h is not constant but variable along the length of the pin fin. The objective is to minimize the pin fin volume for given value of the transferred heat flux. Direct optimal control methods are used. The model is validated for a specific case compatible with the application of the Schmidt optimality assumption. Results are shown for pin fins with circular cross section. Both forced convection and natural convection have been considered. Generally, the optimal profile of the pin fin consists of two regions; in the region near the pin fin base, the thickness is constant or decreases almost linearly while in the region near the pin fin tip the thickness is constant or decreases, depending on the thermal load. Including (instead of omitting) in calculation the accurate description of the arc length and using variable (instead of constant) h may yield thinner and shorter pin fins. The main conclusion is that, by including in calculation the accurate treatment of the arc length, non-smooth pin fin profiles may be obtained. Such profiles consist of a series of steps and are more effective than the smooth profiles.
机译：已经开发出销鳍形状的参数模型。在不采用“弧长”近似的情况下执行了鳍鳍轮廓优化。该模型基于对电弧长度的精确处理。传热系数h不是恒定的，而是沿着针状鳍片的长度可变的。目的是在给定的传递热通量值的情况下最小化针翅体积。使用直接最佳控制方法。该模型针对与Schmidt最优性假设的应用兼容的特定案例进行了验证。显示了具有圆形横截面的针状翅片的结果。已经考虑了强制对流和自然对流。通常，针状鳍片的最佳轮廓包括两个区域。在针状鳍片基部附近的区域中，厚度恒定或几乎线性减小，而在针状鳍状片尖端附近的区域中，厚度恒定或减小，这取决于热负荷。在计算中包括（而不是省略）对电弧长度的准确描述，并使用变量（而不是常数）h可以产生更薄，更短的引脚鳍。主要结论是，通过在计算中包括对电弧长度的精确处理，可以获得不光滑的销鳍轮廓。这样的轮廓包含一系列步骤，比平滑轮廓更有效。

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