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首页> 外文期刊>International Journal of Mechanical Engineering Education >Approximate analytical treatment of annular fins of rectangular profile for teaching fin heat transfer: Utilization of the mean value theorem for integrals
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Approximate analytical treatment of annular fins of rectangular profile for teaching fin heat transfer: Utilization of the mean value theorem for integrals

机译：矩形传热矩形剖面环形翅片的近似分析方法：用于积分的平均值定理的利用

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摘要

In the teaching of annular fins of rectangular profile, the main obstacle lies in solving the quasi one-dimensional heat conduction equation, the modified Bessel equation of first kind. In the modified Bessel equation, the variable coefficient 1 r multiplying the first order derivative of temperature d T d r is problematic. The principal objective of the present paper on engineering education is to solve the modified Bessel equation of first kind in approximate analytical form. Specifically, we seek to apply the mean value theorem for integrals to the variable coefficient 1 r , viewed as an auxiliary function in the domain of the annular fin extending from the inner radius r 1 to the outer radius r 2 . It is demonstrated in a convincing manner that approximate analytical temperature distributions having exponential functions are easy to obtain without resorting to the exact analytical temperature distribution embodying four modified Bessel functions of first kind. Furthermore, the easiness in calculating heat transfer rates in annular fins of rectangular profile for realistic combinations of the two controlling parameters: the normalized radius ratio and the dimensionless thermo-geometrical parameter is verifiable.
机译：在矩形轮廓的环形翅片的教学中，主要障碍物在于求解准一维导热方程，第一种改进的贝塞尔方程。在修改的Bessel方程中，可变系数1R乘以温度D T D R的第一阶导数是有问题的。本文对工程教育文件的主要目标是解决近似分析形式的改进的贝塞尔方程。具体地，我们寻求将平均值定理应用于变量系数1R，在从内半径R 1延伸到外半径R 2的环形翅片的域中被视为辅助功能。以一种令人信服的方式证明，具有指数函数的近似分析温度分布易于获得，而不借助于体现第一种改进的贝塞尔功能的精确分析温度分布。此外，用于计算矩形轮廓环形翅片的传热速率的容易性，以实现两个控制参数的逼真组合：核实化半径比和无量纲热几何参数是可验证的。

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