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TECHNICAL PAPERS: Radiative Heat Transfer

The Application of an Inverse Formulation in the Design of Boundary Conditions for Transient Radiating Enclosures

[+] Author and Article Information
Hakan Ertürk, Ofodike A. Ezekoye, John R. Howell

Department of Mechanical Engineering, The University of Texas at Austin, Austin, TX 78712-1063

J. Heat Transfer 124(6), 1095-1102 (Dec 03, 2002) (8 pages) doi:10.1115/1.1513574 History: Received September 14, 2001; Revised June 10, 2002; Online December 03, 2002
Copyright © 2002 by ASME
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References

Tikhonov, A. N., Goncharsky, A. V., Stepanov, V. V., and Yagola, A. G., 1995, Numerical Methods for Solving Ill-Posed Problems, Kluwer Academic Publishers, Boston, MA.
Beck, J. V., Blackwell, B., and St. Clair, Jr., C. R., 1985, Inverse Heat Conduction, John Wiley and Sons Inc., New York.
Alifanov, O. M., 1994, Inverse Heat Transfer Problems, Springer-Verlag, Berlin.
Alifanov, O. M., Artyukhin, E. A., and Rumyantsev, S. V., 1995, Extreme Methods for Solving Ill-Posed Problems with Applications to Inverse Heat Transfer Problems, Begell House, New York.
Özişik, M. N., and Orlande, H. R. B., 2000, Inverse Heat Transfer, Taylor and Francis, New York.
Kennon,  S. R., and Dulikravich,  G. S., 1985, “The Inverse Design of Internally Cooled Turbine Blades,” ASME J. Eng. Gas Turbines Power, 107(1), pp. 123–126.
Howell,  J. R., Ezekoye,  O. A., and Morales,  J. C., 2000, “Inverse Design Model for Radiative Heat Transfer,” ASME J. Heat Transfer, 122, pp. 492–502.
França,  F. R., Ezekoye,  O. A., and Howell,  J. R., 2001, “Inverse Boundary Design, Combining Radiation and Convection Heat Transfer,” ASME J. Heat Transfer, 123(5), pp. 884–891.
França, F. R., Howell, J. R., Ezekoye, O. A., and Morales, J. C., 2002, “Inverse Design of Thermal Systems,” Advances in Heat Transfer, J. P. Hartnett and T. F. Irvine, eds., 36 , Elsevier, pp. 1–110.
Siegel, R., and Howell, J. R., 2002, Thermal Radiation Heat Transfer, 4th ed., Taylor and Francis, Washington DC.
Farmer, J. T., and Howell, J. R., 1997, “Comparison of Monte Carlo Strategies for Radiative Heat Transfer in Participating Media,” Advances in Heat Transfer, Hartnett, J. P., Irvine, T. F., eds., 31 , Academic Press, New York, pp. 333–425.
Modest, M. F., 1993, Radiative Heat Transfer, McGraw-Hill Book Co, Singapore.
Ertürk, H., Ezekoye, O. A., and Howell, J. R., 2000, “Inverse Solution of Radiative Transfer in Two-Dimensional Irregularly Shaped Enclosures,” Proc. 2000 ASME International Mechanical Engineering Congress and Exhibition, ASME HTD-Vol. 366-1, Orlando, Florida, November 5–10, 2000, pp. 109–117.
Beckman, F. S., 1960, “The Solution of Linear Equations By the Conjugate Gradient Method,” Mathematical Methods For Digital Computers, A. Ralston and H. S. Wilf, eds., John Wiley and Sons, New York, pp. 62–72.
Hansen, P. C., 1998, Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion, SIAM Publications, Philadelphia, PA.
Ertürk,  H., Ezekoye,  O. A., and Howell,  J. R., 2002, “Comparison of Three Regularized Solution Techniques in a Three-Dimensional Inverse Radiation Problem,” J. Quant. Spectrosc. Radiat. Transf., 73, pp. 307–316.

Figures

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The flowchart of the solution algorithm
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The geometry of the furnace
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Desired design surface temperature history
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The errors based on design surface temperature and the design specification
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The temperatures of thirty heater strips along the heating process
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The necessary power input for thirty heater strips
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The L-curve, variation of the solution norm with residual norm for time step 665
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The change in solution accuracy with the CG-step used and time step size
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The geometry of the furnace for the modified case
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The temperatures of thirty heater strips along the heating process for the problem with reflector surfaces having ε=0.5
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The temperatures of thirty heater strips along the heating process for the furnace geometry displayed in Fig. 9.

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