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Research Papers: Conduction

Heat Flux Estimation in a Nonlinear Inverse Heat Conduction Problem With Moving Boundary

[+] Author and Article Information
Hosein Molavi

Department of Mechanical Engineering, Tarbiat Modares University, Tehran 14115-143, Iranhn.molavi@gmail.com

Ramin K. Rahmani

Department of Mechanical, Industrial and Manufacturing Engineering, University of Toledo, Toledo, OH 43606rkhrahmani@yahoo.com

Alireza Pourshaghaghy

Department of Industrial and Mechanical Engineering, Islamic Azad University of Qazvin, Qazvin 34197, Iran

Ebrahim Sharifi Tashnizi

Department of Industrial and Mechanical Engineering, Tafresh University, Tafresh 39518-79611, Iran

Ali Hakkaki-Fard

Department of Mechanical Engineering, McGill University, Montreal, QC, H3A2T5, Canada

J. Heat Transfer 132(8), 081301 (May 20, 2010) (10 pages) doi:10.1115/1.4001305 History: Received March 04, 2009; Revised January 15, 2010; Published May 20, 2010; Online May 20, 2010

The estimation of heat flux in the nonlinear heat conduction problem becomes more challenging when the material at the boundary loses its mass due to phase change, chemical erosion, oxidation, or mechanical removal. In this paper, a new gradient-type method with an adjoint problem is employed to predict the unknown time-varying heat flux at the receding surface in the nonlinear heat conduction problem. Particular features of this novel approach are discussed and examined. Results obtained by the new method for several test cases are benchmarked and analyzed using numerical experiments with simulated exact and noisy measurements. Exceedingly reliable estimation on the heat flux can be obtained from the knowledge of the transient temperature recordings, even in the case with measurement errors. In order to evaluate the performance characteristics of the present inverse scheme, simulations are conducted to analyze the effects of this technique with regard to the conjugate gradient method with an adjoint problem and variable metric method with an adjoint problem. The results obtained show that the present inverse scheme distinguishably accelerates the convergence rate, which approve the well capability of the method for this type of heat conduction problems.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Initial-to-final grid comparison

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Figure 2

The exact and estimated values of heat flux (noisy data)

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Figure 3

(a) Reduction histories of the objective function for noise-free data (linear problem). (b) Reduction histories of the objective function for noisy data (linear problem).

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Figure 4

(a) Reduction histories of the objective function for noise-free data (nonlinear problem without moving boundary). (b) Reduction histories of the objective function for noisy data (nonlinear problem without moving boundary).

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Figure 5

The exact and estimated values of heat flux (noisy data)

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Figure 6

The surface recession as a function of time

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Figure 7

The exact and estimated values of heat flux (noisy position measurements)

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Figure 8

The exact and estimated values of heat flux (noisy measured temperatures)

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Figure 9

The exact and estimated values of heat flux (noisy measured temperatures and locations)

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Figure 10

The exact and used values of surface recession rate in this paper

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