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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Heat Flux Estimation in a Nonlinear Inverse Heat Conduction Problem With Moving Boundary
Hosein Molavi,
Hosein Molavi
Researcher
Department of Mechanical Engineering,
e-mail: hn.molavi@gmail.com
Tarbiat Modares University
, Tehran 14115-143, Iran
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Ramin K. Rahmani,
Ramin K. Rahmani
Affiliate Research Scholar
Department of Mechanical, Industrial and Manufacturing Engineering,
e-mail: rkhrahmani@yahoo.com
University of Toledo
, Toledo, OH 43606
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Alireza Pourshaghaghy,
Alireza Pourshaghaghy
Assistant Professor
Department of Industrial and Mechanical Engineering,
Islamic Azad University of Qazvin
, Qazvin 34197, Iran
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Ebrahim Sharifi Tashnizi,
Ebrahim Sharifi Tashnizi
Assistant Professor
Department of Industrial and Mechanical Engineering,
Tafresh University
, Tafresh 39518-79611, Iran
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Ali Hakkaki-Fard
Ali Hakkaki-Fard
Graduate Student
Department of Mechanical Engineering,
McGill University
, Montreal, QC, H3A2T5, Canada
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Hosein Molavi
Researcher
Department of Mechanical Engineering,
Tarbiat Modares University
, Tehran 14115-143, Irane-mail: hn.molavi@gmail.com
Ramin K. Rahmani
Affiliate Research Scholar
Department of Mechanical, Industrial and Manufacturing Engineering,
University of Toledo
, Toledo, OH 43606e-mail: rkhrahmani@yahoo.com
Alireza Pourshaghaghy
Assistant Professor
Department of Industrial and Mechanical Engineering,
Islamic Azad University of Qazvin
, Qazvin 34197, Iran
Ebrahim Sharifi Tashnizi
Assistant Professor
Department of Industrial and Mechanical Engineering,
Tafresh University
, Tafresh 39518-79611, Iran
Ali Hakkaki-Fard
Graduate Student
Department of Mechanical Engineering,
McGill University
, Montreal, QC, H3A2T5, CanadaJ. Heat Transfer. Aug 2010, 132(8): 081301 (10 pages)
Published Online: May 20, 2010
Article history
Received:
March 4, 2009
Revised:
January 15, 2010
Online:
May 20, 2010
Published:
May 20, 2010
Citation
Molavi, H., Rahmani, R. K., Pourshaghaghy, A., Tashnizi, E. S., and Hakkaki-Fard, A. (May 20, 2010). "Heat Flux Estimation in a Nonlinear Inverse Heat Conduction Problem With Moving Boundary." ASME. J. Heat Transfer. August 2010; 132(8): 081301. https://doi.org/10.1115/1.4001305
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