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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hn.molavi@gmail.com

rkhrahmani@yahoo.com
Department of Industrial and Mechanical Engineering,

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August 2010

Research Papers

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

Hosein Molavi,

Hosein Molavi

Researcher

Department of Mechanical Engineering,

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,

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, Iranhn.molavi@gmail.com

Ramin K. Rahmani
Affiliate Research Scholar

Department of Mechanical, Industrial and Manufacturing Engineering,

University of Toledo

, Toledo, OH 43606rkhrahmani@yahoo.com

Alireza Pourshaghaghy
Assistant Professor

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, Canada*J. 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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