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
Your Session has timed out. Please sign back in to continue.


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.
Beck,  J. V., Litkouhi,  B., and St. Clair,  C. R., 1982, “Efficient Sequential Solution of the Nonlinear Inverse Heat Conduction Problem,” Numer. Heat Transfer, 5, pp. 275–286.
Raynaud,  M., and Bransier,  J., 1986, “A New Finite-Difference Method for the Nonlinear Inverse Heat Conduction Problem,” Numer. Heat Transfer, 9, pp. 27–42.
Jarny,  Y., Özişik,  M. N., and Bardon,  J. P., 1991, “A General Optimization Method Using Adjoint Equation for Solving Multidimensional Inverse Heat Conduction,” Int. J. Heat Mass Transf., 34, pp. 2911–2919.
Alifanov, O. M., 1994, Inverse Heat Transfer Problems, Springer-Verlag.
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.


Grahic Jump Location
Schematic of the problem for: (a) a plate; (b) a ring.
Grahic Jump Location
CCT diagram for SAE 52100 steel
Grahic Jump Location
Cooling curve used in this study
Grahic Jump Location
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.
Grahic Jump Location
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.
Grahic Jump Location
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.
Grahic Jump Location
Comparison of the numerically computed convective heat transfer coefficient with constant (“linear”) and temperature-dependent (“nonlinear”) thermal conductivity (Fo−1=0.07,r=4)




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In