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RESEARCH PAPERS: Forced Convection

Estimation of Time-Varying Inlet Temperature and Heat Flux in Turbulent Circular Pipe Flow

[+] Author and Article Information
Cha’o-Kuang Chen

Department of Mechanical Engineering, National Cheng Kung University, Tainan 70101, Taiwan, Republic of Chinackchen@mail.ncku.edu.tw

Li-Wen Wu, Yue-Tzu Yang

Department of Mechanical Engineering, National Cheng Kung University, Tainan 70101, Taiwan, Republic of China

J. Heat Transfer 128(1), 44-52 (Jul 16, 2005) (9 pages) doi:10.1115/1.2130402 History: Received September 30, 2004; Revised July 16, 2005

This study addresses the conjugate heat transfer problem of hydrodynamically developed turbulent flow in a circular pipe. An inverse method is used to estimate the time-varying inlet temperature and the outer-wall heat flux simultaneously on the basis of temperature measurements taken at two different locations within the pipe flow. The present approach rearranges the matrix forms of the governing differential equations and then applies a whole domain estimation with the function specification method and the linear least-squares-error method to determine the two boundary conditions of the pipe flow. The dimensionless temperature data obtained from the direct problem are used to simulate the temperature measurements. The influence of temperature measurement errors upon the precision of the estimated results is investigated. The proposed method provides several advantages compared to traditional methods: (1) it yields a solution within a single computational iteration, (2) no prior information is required regarding the functional form of the quantities of interest, (3) no initial guesses of the unknown parameter values are required, and (4) the inverse problem can be solved in a linear domain. This study also considers the influence of the location of the temperature measurement sensors upon the accuracy of the calculated results. The numerical results confirm that the proposed method provides an efficient, robust, and accurate means of estimating the inlet temperature and outer-wall heat flux simultaneously in turbulent pipe flow.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

System under consideration. Note that the velocity profile is fully developed and that the inlet temperature is constant. [q(t) and f(t) denote the outer-wall heat flux function and the inlet temperature function, respectively].

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Figure 2

Estimated dimensionless outer-wall heat flux distributions with and without wall conduction for measurement error of σ=0% and r=3

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Figure 3

Estimated dimensionless inlet temperature distributions for different values of future-time parameter with measurement errors of σ=1% and 3%

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Figure 4

Estimated dimensionless outer-wall heat flux distributions for different values of future-time parameter with measurement errors of σ=1% and 3%

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Figure 5

Comparison between variation of deterministic bias with future-time parameter of: (a) inlet temperature, ΔdΘ, and (b) outer-wall heat flux, ΔdQ, for measurement errors of σ=0% and 3%

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Figure 6

Comparison between variation of maximum nonlinear bias with future-time parameter of: (a) inlet temperature, [ΔnΘ]max, and (b) outer-wall heat flux, [ΔnQ]max, for measurement errors of σ=0% and 3%

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Figure 7

Effects of sensor locations 10ΔX and 15ΔX on accuracy of estimated inlet temperature for measurement error of σ=3% and r=14

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Figure 8

Effects of measuring point location on variation of ΔdΘ with future-time parameter for measurement error of σ=3%

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