Inverse solution techniques are applied to the design of heat transfer systems where radiation is important. Various solutions using inverse methods are demonstrated, and it is argued that inverse design techniques provide an alternative to conventional iterative design methods that is more accurate and faster, and can provide a greatly improved first estimate of a thermal design. This estimate can then be used as a trial design in more complete thermal analysis programs for predicting system behavior, eliminating many faulty first design trials. [S0022-1481(00)02703-1]
Issue Section:
Radiative Transfer
1.
Farag, I. H., 1979, “Temperature Profiles in Combustion Gases by Inversion: Review and Approach,” ASME Paper 79-HT-21, ASME, New York.
2.
Matthews
, L. K.
, Viskanta
, R.
, and Incropera
, F.
, 1984
, “Development of Inverse Methods for Determining Thermophysical Properties of High-Temperature Fibrous Materials
,” Int. J. Heat Mass Transf.
, 27
, No. 4
, pp. 487
–495
.3.
Wu, W. J., and Mulholland, G. P., 1989, “Two-Dimensional Inverse Radiation Heat Transfer Analysis Using Monte Carlo Techniques,” Heat Transfer Phenomena in Radiation, Combustion and Fires, R. K. Shah, ed., ASME, New York.
4.
Lin, J.-D., and Tsai, J.-H., 1991, “Comparison of P1 and S-P Two Flux Approximations in Inverse Scattering Problems,” ASME Paper 91-WA-HT-13, ASME, New York.
5.
Subramaniam
, S.
, and Mengu¨c¸
, M. P.
, 1991
, “Solution of the Inverse Radiation Problem for Inhomogeneous and Anisotropically Scattering Media Using a Monte Carlo Technique
,” Int. J. Heat Mass Transf.
, 34
, No. 1
, pp. 253
–266
.6.
Li
, H. Y.
, and O¨ziS¸ik
, M. N.
, 1992
, “Estimation of the Radiation Source Term With a Conjugate-Gradient Method of Inverse Analysis
,” J. Quant. Spectrosc. Radiat. Transf.
, 48
, No. 3
, pp. 237
–244
.7.
Tsai
, J.-H.
, 1993
, “Inverse Scattering Problem With Two Flux Methods
,” Int. Commun. Heat Mass Transfer
, 20
, pp. 585
–596
.8.
Hendricks, T. J., and Howell, J. R., 1994, “Inverse Radiative Analysis to Determine Spectral Radiative Properties Using the Discrete Ordinates Method,” Proc. 10th International Heat Transfer Conference, Vol. 2, Institute of Chemical Engineers, Rugby, U.K., pp. 75–80.
9.
Jones
, M. R.
, Curry
, B. P.
, Brewster
, M. Q.
, and Leong
, K. H.
, 1994
, “Inversion of Light-Scattering Measurements for Particle Size and Optical Constants: Theoretical Study
,” Appl. Opt.
, 33
, No. 18
, pp. 4025
–4041
.10.
Jones
, M. R.
, Tezuka
, A.
, and Yamada
, Y.
, 1995
, “Thermal Tomographic Detection of Inhomogeneities
,” ASME J. Heat Transfer
, 117
, pp. 969
–975
.11.
McCormick, N. J., 1997, “Analytical Solutions for Inverse Radiative Transfer Optical Property Estimation,” Proc. ASME Heat Transfer Division, Vol. 3, ASME, New York, pp. 367–371.
12.
Kudo, K., Kuroda, A., Ozaki, E., and Oguma, M., 1997, “Estimation of Absorption Coefficient Distribution in Two-Dimensional Gas Volume by Solving Inverse Radiative Property Value Problem,” Radiative Transfer-II: Proc. Second Int. Symp. on Radiation Transfer, M. P. Menguc¸, ed., Begell House, New York.
13.
Frankel
, J. I.
, and Keyhani
, M.
, 1996
, “A New Approach for Solving Inverse Solidification Design Problems
,” Numer. Heat Transfer, Part B
, 30
, No. 2
, pp. 161
–177
.14.
Yang
, G. Z.
, and Zabaras
, N.
, 1998
, “The Adjoint Method for an Inverse Design Problem in the Directional Solidification of Binary Alloys
,” J. Comput. Phys.
, 140
, pp. 432
–452
.15.
Franc¸a, F., Morales, J. C., Oguma, M., and Howell, J. R., 1998, “Inverse Design of Radiating Systems Dominated by Radiative Transfer,” Radiative Transfer II:-Proc. Second Int. Symp. Radiative Heat Transfer, M. P. Mengu¨c¸, ed., Begell House, New York.
16.
Franca, F., Morales, J. C., Oguma, M., and Howell, J. R., 1998, “Inverse Design of Thermal Systems With Radiation,” Invited keynote lecture, Heat Transfer 1998, Proc. 11th Int. Heat Transfer Conf., Vol. I, J. S. Lee, ed., Taylor and Francis, New York, pp. 213–221.
17.
Franc¸a, F., Morales, J. C., Oguma, M., and Howell, J. R., 1998, “Inverse Radiation Heat Transfer Within Enclosures With Participating Media,” Proc. 1998 11th Int. Heat Trans. Conf., J. S. Lee, ed., Taylor and Francis, New York, Vol. 7, pp. 433–438.
18.
Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P., 1992, Numerical Recipes in FORTRAN: The Art of Scientific Computing, Cambridge University Press, New York.
19.
Beck, J. V., Blackwell, B., and St. Clair, Jr., 1995, Inverse Heat Conduction: Ill-Posed Problems, John Wiley and Sons, New York.
20.
Beck, J. V., Alifanov, O. M., Woodbury, K. A., Artyukhin, E. A., and McCormick, N., 1992, “Joint American-Russian NSF Workshop on Inverse Problems in Heat Transfer,” Final Report MSU-ENGR-92-008, Michigan State University.
21.
Alifanov, O. M., 1994, Inverse Heat Transfer Problems, Springer-Verlag, Berlin.
22.
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.
23.
Trujillo, D. M., and Busby, H. R., 1997, Practical Inverse Analysis in Engineering, CRC Press, Boca Raton, FL.
24.
Hansen, P. C., 1998, Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion, SIAM, Philadelphia, PA.
25.
Hansen
, P. C.
, 1992
, “Numerical Tools for Analysis and Solution of Fredholm Integral Equations of the First Kind
,” Inverse Probl.
, 8
, pp. 849
–872
.26.
Tikhonov
, A. N.
, 1963
, “Solution of Incorrectly Formulated Problems and the Regularization Method
,” Sov. Math. Dokl., 4, pp. 1035–1038 (English translation 1963, Dokl. Akad. Nauk. SSSR
, 151
, pp. 501
–504
).27.
Tikhonov, A. N., Goncharsky, A. V., Stepanov, V. V., and Yagola, A. C., 1995, Numerical Methods for the Solution of Ill-Posed Problems, Kulwer Academic, Boston.
28.
Hanke, M., 1995, Conjugate Gradient Type Methods for Ill-Posed Problems, John Wiley and Sons, New York.
29.
Hansen
, P. C.
, Sekii
, T.
, and Shibahashi
, H.
, 1992
, “The Modified Truncated SVD Method for Regularization in General Form
,” SIAM J. Sci. Stat. Comput.
, 13
, No. 5
, pp. 1142
–1150
.30.
Franc¸a, F., and Goldstein, L., 1996, “Application of the Zoning Method in Radiative Inverse Problems,” Brazilian Congress of Engineering and Thermal Sciences, ENCIT 96, Florianopolis, Brazil.
31.
Kudo, K., Kuroda, A., Eid, A., Saito, T., and Oguma, M., 1996, “Solution of the Inverse Radiative Load Problems by the Singular Value Decomposition,” Radiative Transfer–I: Proc. First Int. Symp. on Radiation Transfer, M. P. Menguc¸, ed., Begell House, New York, pp. 568–578.
32.
Matsumura, M., Morales, J. C., and Howell, J. R., 1998, “Optimal Design of Industrial Furnaces by Using Numerical Solution of the Inverse Radiation Problem,” Proc. 1998 Int. Gas Research Conf., San Diego, Nov.
33.
Morales, J. C., Harutunian, V., Oguma, M., and Howell, J. R., 1996, “Inverse Design of Radiating Enclosures With an Isothermal Participating Medium,” Radiative Transfer I:–Proc. First Int. Symp. on Radiative Heat Transfer, M. P. Menguc¸, ed., Begell House, New York, pp. 579–593.
34.
Morales, J. C., Matsumura, M., Oguma, M., and Howell, J. R., 1997, “Computation of Inverse Radiative Heat Transfer Within Enclosures,” Proc. 1997 ASME National Heat Transfer Conference, ASME, New York.
35.
Morales, J. C., 1998, “Radiative Transfer Within Enclosures of Diffuse Gray Surfaces: The Inverse Problem,” Ph.D. dissertation, Department of Mechanical Engineering, The University of Texas at Austin, Austin, TX.
36.
Li
, H. Y.
, 1997
, “Inverse Radiation Problem in Two-Dimensional Rectangular Media
,” AIAA J. Thermophy. Heat Transf.
, 11
, No. 4
, pp. 556
–561
.37.
Matsumura, M., 1997, “Optimal Design of Industrial Furnaces by Using Numerical Solution of the Inverse Radiation Problem,” M.S. thesis, Department of Mechanical Engineering, The University of Texas at Austin, Austin, TX.
38.
Yang, W.-J., Taniguchi, H., and Kudo, K., 1995, “Radiative Heat Transfer by the Monte Carlo Method,” Advances in Heat Transfer, 27, J. P. Hartnett, and T. F. Irvine, eds., Academic Press, San Diego.
39.
Jones
, M. R.
, 1999
, “Inverse Analysis of Radiative Heat Transfer Problems
,” ASME J. Heat Transfer
, 121
, pp. 481
–484
.Copyright © 2000
by ASME
You do not currently have access to this content.