An inverse forced convection problem was studied in this paper. The unknown space-dependent heat flux at the outer boundary of a circular pipe was identified from the temperature measurements within the flow using the algorithm based on an improved conjugate gradient method, which is a combination of the modified inverse algorithm proposed by Ozisik et al. (Huang and Ozisik, 1992, “Inverse Problem of Determining Unknown Wall Heat Flux in Laminar Flow Through a Parallel Plate Duct,” Numer. Heat Transfer, Part A 21, pp. 2615–2618) and the general inverse algorithm based on the conjugate gradient method. The effects of the convection intensity, the number of thermocouples, the location of the thermocouples, and the measurement error on the performance of the modified inverse algorithm method and the improved inverse algorithm were studied thoroughly through three examples. It is shown that the improved inverse algorithm can greatly improve the solution accuracy in the entire computation domain. The accuracy and stability of both the modified inverse algorithm method and the improved inverse algorithm are strongly influenced by the Reynolds number and the shape of the unknown heat flux. Those functions, which contain more high-frequency components of Fourier series, are more sensitive to the increase in the Reynolds number.

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# Estimation of Unknown Boundary Heat Flux in Laminar Circular Pipe Flow Using Functional Optimization Approach: Effects of Reynolds Number

Peng Ding,

Peng Ding

School of Energy and Power Engineering,

Xi’an Jiaotong University

, Xi’an 710049, China
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Wen-Quan Tao

Wen-Quan Tao

School of Energy and Power Engineering,

e-mail: wqtao@mail.xjtu.edu.cn
Xi’an Jiaotong University

, Xi’an 710049, China
Search for other works by this author on:

Peng Ding

School of Energy and Power Engineering,

Xi’an Jiaotong University

, Xi’an 710049, China
Wen-Quan Tao

School of Energy and Power Engineering,

Xi’an Jiaotong University

, Xi’an 710049, Chinae-mail: wqtao@mail.xjtu.edu.cn

*J. Heat Transfer*. Feb 2009, 131(2): 021701 (9 pages)

**Published Online:**December 12, 2008

Article history

Received:

September 16, 2007

Revised:

September 12, 2008

Published:

December 12, 2008

Citation

Ding, P., and Tao, W. (December 12, 2008). "Estimation of Unknown Boundary Heat Flux in Laminar Circular Pipe Flow Using Functional Optimization Approach: Effects of Reynolds Number." ASME. *J. Heat Transfer*. February 2009; 131(2): 021701. https://doi.org/10.1115/1.3013825

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