Fins are surface extensions used to increase the rate of heat transfer from a heated surface to the surrounding cooler fluid or from a heated fluid to the surface. In this article, we describe new families of straight and pin fins for which the temperature distribution along the fin as well as fin effectiveness and efficiency can be computed in closed form. The profile of the new straight fin is a circular arc centered on the fin’s longitudinal axis, while the profile of the new pin fin is a more complex concave parametric curve. Although the pattern of temperature distribution in these fins is remarkably similar to that in the classic straight and pin fins of constant thickness, the geometry of the new fins is strikingly different; in particular, the maximum length of the new fins is finite. We also discovered that both classic fins of constant thickness and novel fins described in this work have the following equivalence property: if the ratio of the heat transfer coefficient on the fin’s tip to that on the lateral surface is not too high, then the temperature distribution for a fin with a non-adiabatic boundary condition at the tip is identical to that for a longer fin of the same kind with adiabatic tip. Our analysis of heat transfer by fins is only based on standard homogeneity, steady-state, and one-dimensionality assumptions. In particular, we completely dispense with the “length-of-arc” assumption that underlies most of the previous works.

中文翻译：

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新系列直翅片和针翅片的传热：精确解决方案

翅片是表面延伸，用于增加从受热表面到周围较冷流体或从受热流体到表面的热传递速率。在本文中，我们描述了直翅片和针翅片的新系列，它们沿翅片的温度分布以及翅片效率和效率可以以封闭形式计算。新直翅的轮廓是以翅纵轴为中心的圆弧，而新针翅的轮廓是更复杂的凹形参数曲线。尽管这些翅片的温度分布模式与经典的等厚直翅片和针翅片非常相似，但新翅片的几何形状却截然不同；特别是，新鳍的最大长度是有限的。我们还发现，本文中描述的等厚经典翅片和新型翅片都具有以下等效性：如果翅片尖端与侧面的传热系数之比不太高，则温度分布对于尖端具有非绝热边界条件的翅片，与具有绝热尖端的同类较长翅片的边界条件相同。我们对翅片传热的分析仅基于标准均匀性、稳态和一维假设。特别是，我们完全摒弃了之前大多数作品所基于的“弧长”假设。如果翅片顶端的传热系数与侧面的传热系数之比不太高，则在顶端具有非绝热边界条件的翅片的温度分布与较长翅片的温度分布相同。与绝热尖端相同。我们对翅片传热的分析仅基于标准均匀性、稳态和一维假设。特别是，我们完全摒弃了之前大多数作品所基于的“弧长”假设。如果翅片顶端的传热系数与侧面的传热系数之比不太高，则在顶端具有非绝热边界条件的翅片的温度分布与较长翅片的温度分布相同。与绝热尖端相同。我们对翅片传热的分析仅基于标准均匀性、稳态和一维假设。特别是，我们完全摒弃了之前大多数作品所基于的“弧长”假设。