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TECHNICAL PAPERS: Conduction

Some Analytical and Numerical Solutions to Inverse Problems Applied to Optimizing Phase-Transformation Tracking in Gas Quenching

[+] Author and Article Information
Michael Vynnycky, Jéro⁁me Ferrari

FaxénLaboratoriet, KTH, 100 44 Stockholm, Sweden

Noam Lior

Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104-6315

J. Heat Transfer 125(1), 1-10 (Jan 29, 2003) (10 pages) doi:10.1115/1.1517271 History: Received May 30, 2001; Revised August 05, 2002; Online January 29, 2003
Copyright © 2003 by ASME
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References

Thuvander, A., Melander, A., Lind, M., Lior, N., and Bark, F., 1999, “Prediction of Convective Heat Transfer Coefficients and Their Effects on Distortion and Mechanical Properties of Cylindrical Steel Bodies Quenched by Gas Cooling,” Paper AJTE99-6289, presented at ASME/JSME Joint Thermal Engng. Conf., San Diego, CA, March 15–19, 1999.
Burggraf,  O. R., 1964, “An Exact Solution of the Inverse Problem in Heat Conduction Theory and Applications,” ASME J. Heat Transfer, 86C, pp. 373–382.
Özişik, M. N., and Orlande, H. R. B., 2000, Inverse Heat Transfer, Taylor & Francis, New York.
http://www.maplesoft.com
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Beck, J. V., Blackwell, B., and St. Clair, C. R., Jr., 1985, Inverse Heat Conduction-III Posed Problems, Wiley, New York.
Cebeci, T., and Bradshaw, P., 1984, Physical and Computational Aspects of Convective Heat Transfer, Springer, Berlin.
Archambault,  P., and Azim,  A., 1995, “Inverse Resolution of the Heat-Transfer Equation: Application to Steel and Aluminum Alloy Quenching,” J. Mater. Eng. Perform., 4, pp. 730–736.
Archambault,  P., Denis,  S., and Azim,  A., 1997, “Inverse Resolution of the Heat-Transfer Equation With Internal Heat Source: Application to the Quenching of Steels With Phase Transformations,” J. Mater. Eng. Perform., 6, pp. 240–246.
Matsevityi,  Y. M., Multanovskii,  A. V., and Nemirovskii,  I. A., 1991, “Optimization of the Heat-Engineering Processes Involving Utilization of Control and Identification Methods,” J. Eng. Phys., 59, pp. 1055–1063.

Figures

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Schematic of the problem for: (a) a plate; (b) a ring.
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CCT diagram for SAE 52100 steel
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Cooling curve used in this study
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The required convective heat transfer coefficient, h(t), as calculated by the analytical method using 1, 2, and 3 series expansion terms, and by a numerical method: (a) Fo−1=0.02; (b) Fo−1=0.1; and (c) Fo−1=0.2.
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Selected quantities as numerically computed for 3, 4, and 5 future time steps in the model (Fo−1=0.07): (a) the convective heat transfer coefficient, h(t), at x=L; (b) the temperature, Tw(t), at x=0; (c) the surface temperature at x=L; and (d) the surface heat flux at x=L.
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The convective heat transfer coefficient, h(t), at x=L for Fo−1=0.07 with: (a) Δτ=1/100,r=3, 4, 5; and (b) Δτ=1/300,r=5, 6, 7.
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Comparison of the numerically computed convective heat transfer coefficient with constant (“linear”) and temperature-dependent (“nonlinear”) thermal conductivity (Fo−1=0.07,r=4)

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