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Mathematical Problems in EngineeringVolume 2013 2013, Article ID 205169, 11 pages

Research ArticleCollege of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China

Received 6 July 2013; Revised 26 August 2013; Accepted 2 September 2013

Academic Editor: Herb Kunze

Copyright © 2013 Shiqin Lyu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The inverse heat conduction problem on the heat transfer characteristics ofcooled-heated laminar flows through finite length thick-walled circular tubes is studied, usingtemperature 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 estimatethe unknown temperature on the external surface of the circular pipe. The main idea of theproposed 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 temperaturemeasurement for the inverse problem, and during the calculation, the Tikhonov regularizationand L-curve methods are employed to solve the inverse problem. Therefore, this study also considersthe influence of errors in these measurements upon the precision of the estimated resultsas 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 improvedby 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 whenerrors in the temperature measurements are present.

Autor: Shiqin Lyu, Can Wu, and Sufang Zhang



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