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Application of the RBF Method to the Estimation of Temperature on the External Surface in Laminar Pipe Flow

机译:RBF法在层流管流动中外表面估计的应用

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摘要

The inverse heat conduction problem on the heat transfer characteristics of cooled/heated laminar flows through finite length thick-walled circular tubes is studied, using temperature measurements taken at several different locations within the fluid in this paper. The method of radial basis functions is coupled with the boundary control technique to estimate the unknown temperature on the external surface of the circular pipe. The main idea of the proposed method is to solve the direct problem instead of solving the inverse problem directly. The temperature data obtained from the direct problem are used to simulate the temperature measurement for the inverse problem, and during the calculation, the Tikhonov regularization and L-curve methods are employed to solve the inverse problem. Therefore, this study also considers the influence of errors in these measurements upon the precision of the estimated results as well as the influence of the locations and number of sensors used upon the accuracy of theestimated results. The results indicate that the accuracy of the estimated results is improved by taking temperature measurements in locations close to the the unknown boundary. Finally, the results confirm that the proposed method is capable of yielding accurate results even when errors in the temperature measurements are present.
机译:研究了冷却/加热层流的传热特性的反热传导问题通过有限长度的厚壁圆形管,在本文中的几个不同位置采用温度测量。径向基函数的方法与边界控制技术耦合以估计圆形管的外表面上的未知温度。所提出的方法的主要思想是解决直接问题而不是直接解决逆问题。从直接问题获得的温度数据用于模拟逆问题的温度测量,并且在计算过程中,采用Tikhonov正规和L曲线方法来解决逆问题。因此,本研究还考虑了在这些测量的精度时误差在估计结果的精度以及对所估计结果的准确性的影响的影响和传感器数量的影响。结果表明,通过在靠近未知边界的位置进行温度测量来提高估计结果的准确性。最后,结果证实,即使存在温度测量中的误差,所提出的方法也能够产生精确的结果。

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