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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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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Schematic of the problem for: (a) a plate; (b) a ring.




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