A transient inverse heat conduction problem focused on gas quenching of steel plates and rings is posed and solved, both analytically and numerically. The quenching objective is to calculate the transient convective heat transfer coefficient which would produce an optimized phase transformation cooling curve. The governing nonlinear heat equation is nondimensionalised, and a small parameter, the reciprocal of the Fourier number, is identified. This allows the construction of an analytic solution in the form of an asymptotic series. For higher values of the reciprocal Fourier number, a numerical scheme incorporating the function specification and Keller Box methods is used to generate solutions. Comparison of the results proves favorable, and suggests that for this inverse problem asymptotic methods provide an attractive alternative to solely numerical ones.
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Some Analytical and Numerical Solutions to Inverse Problems Applied to Optimizing Phase-Transformation Tracking in Gas Quenching
Michael Vynnycky,
Michael Vynnycky
Faxe´nLaboratoriet, KTH, 100 44 Stockholm, Sweden
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Je´ro^me Ferrari,
Je´ro^me Ferrari
Faxe´nLaboratoriet, KTH, 100 44 Stockholm, Sweden
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Noam Lior
Noam Lior
Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104-6315
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Michael Vynnycky
Faxe´nLaboratoriet, KTH, 100 44 Stockholm, Sweden
Je´ro^me Ferrari
Faxe´nLaboratoriet, KTH, 100 44 Stockholm, Sweden
Noam Lior
Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104-6315
Contributed by the Heat Transfer Division for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received by the Heat Transfer Division May 30, 2001; revision received August 5, 2002. Associate Editor: G. S. Dulikravich.
J. Heat Transfer. Feb 2003, 125(1): 1-10 (10 pages)
Published Online: January 29, 2003
Article history
Received:
May 30, 2001
Revised:
August 5, 2002
Online:
January 29, 2003
Citation
Vynnycky , M., Ferrari, J., and Lior, N. (January 29, 2003). "Some Analytical and Numerical Solutions to Inverse Problems Applied to Optimizing Phase-Transformation Tracking in Gas Quenching ." ASME. J. Heat Transfer. February 2003; 125(1): 1–10. https://doi.org/10.1115/1.1517271
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