The inverse problem of estimating surface temperatures and fluxes from simulated transient temperature measured within a semitransparent slab is studied. A space-marching technique, whose performance is already known for the solution of the inverse heat conduction problem (IHCP), is adapted to solve an inverse heat conduction-radiation problem (IHCRP). An iterative algorithm is proposed. Different values of the conduction-to-radiation parameter are considered in order to show, with benchmark test cases, the effects of the radiative heat transfer mode on the performance of the inverse method.
Issue Section:
Heat Conduction
1.
Andre, S., and Degiovanni, A., 1992, “An Extension of the Flash Technique in the 300 K to 800 K Temperature Range: Application to Thermal Diffusivity Measurement of Semi-transparent Materials,” Proceedings of the Third UK National Heat Transfer Conference, Rugby, United Kingdom, Paper No. 153, Vol. 2, pp. 1197–1203.
2.
Beck, J. V., and Arnold, K. J., 1977, Parameter Estimation in Engineering and Science, Wiley, New York.
3.
Beck
J. V.
Litkouhi
B.
St. Clair
C. R.
1982
, “Efficient Sequential Solution of the Nonlinear Inverse Heat Conduction Problem
,” Numerical Heat Transfer
, Vol. 5
, pp. 275
–286
.4.
Beck, J. V., Blackwell, B., and St. Clair, C. R., Jr., 1985, Inverse Heat Conduction: Ill-Posed Problems, Wiley, New York.
5.
D’Souza, N., 1975, “Numerical Solution of One-Dimensional Inverse Transient Heat Conduction by Finite Difference Method,” ASME Paper No. 75-WA/HT-81.
6.
Field
R. E.
Viskanta
R.
1993
, “Measurements and Prediction of Dynamic Temperatures in Unsymmetrically Cooled Glass Windows
,” AIAA Journal of Thermophysics and Heat Transfer
, Vol. 7
, No. 4
, pp. 616
–623
.7.
Hensel
E. H.
Hills
R. G.
1986
, “An Initial Value Approach to the Inverse Heat Conduction Problem
,” ASME JOURNAL OF HEAT TRANSFER
, Vol. 108
, pp. 248
–256
.8.
Hensel, E. H., 1991, Inverse Theory and Applications for Engineers, Prentice-Hall, Englewood Cliffs, NJ.
9.
Hills
R. G.
Raynaud
M.
Hensel
E.
1986
, “Surface Variance Estimates Using an Adjoint Formulation for a One-Dimensional Nonlinear Inverse Heat Conduction Technique
,” Numerical Heat Transfer
, Vol. 10
, pp. 441
–461
.10.
Huang
C. H.
O¨zis¸ik
M. N.
1992
, “Inverse Problem of Determining Unknown Wall Heat Flux in Laminar Flow Through a Parallel Plate Duct
,” Numerical Heat Transfer
, Part A, Vol. 21
, pp. 55
–70
.11.
Li
H. Y.
O¨zis¸ik
M. N.
1993
, “Inverse Radiation Problem for Simultaneous Estimation of Temperature Profile and Surface Reflectivity
,” AIAA Journal of Thermophysics and Heat Transfer
, Vol. 7
, No. 1
, pp. 88
–93
.12.
Mann
D.
Viskanta
R.
1995
, “An Inverse Method for Determining Transient Temperature Distribution in Glass Plates
,” Inverse Problems in Engineering
, Vol. 1
, pp. 273
–291
.13.
Matthews
L. K.
Viskanta
R.
Incropera
F. P.
1984
, “Development of Inverse Methods for Determining Thermophysical and Radiative Properties of High-Temperature Fibrous Materials
,” International Journal of Heat and Mass Transfer
, Vol. 27
, No. 4
, pp. 487
–495
.14.
Murio, D. A., 1993, The Mollification Method and the Numerical Solution of Ill-Posed Problems, Wiley, New York.
15.
Nicolau
V. P.
Raynaud
M.
Sacadura
J. F.
1994
, “Spectral Radiative Properties Identification of Fiber Insulating Materials
,” International Journal of Heat and Mass Transfer
, Vol. 37
, Suppl. 1, pp. 311
–324
.16.
O¨zis¸ik, M. N., 1973, Radiative Transfer and Interactions With Conduction and Convection, Wiley, New York.
17.
Raynaud, M., 1986, “Combination of Methods for the Inverse Heat Conduction Problem With Smoothing Filters,” AIAA Paper No. 86-1243.
18.
Raynaud
M.
Bransier
J.
1986
a, “A New Finite Difference Method for the Nonlinear Inverse Heat Conduction Problem
,” Numerical Heat Transfer
, Vol. 9
, No. 1
, pp. 27
–42
.19.
Raynaud, M., and Bransier, J., 1986b, “Experimental Validation of a New Space Marching Finite Difference Algorithm for the Inverse Heat Conduction Problem,” Proceedings of the Eighth International Heat Transfer Conference, San Francisco, CA.
20.
Raynaud
M.
Beck
J. V.
1988
, “Methodology for Comparison of Inverse Heat Conduction Methods
,” ASME JOURNAL OF HEAT TRANSFER
, Vol. 110
, pp. 30
–37
.21.
Ruperti, N. J. Jr., Raynaud, M., and Sacadura, J. F., 1995, “Influence of Radiation on the Coupled Inverse Heat Conduction-Radiation Problem,” ASME HTD-Vol. 312, pp. 79–86.
22.
Sakami, M., and Lallemand, M., 1993, “Retrieval of Absorption and Temperature Profiles in Axisymmetric and Non-axisymmetric Emitting-Absorbing Media by Inverse Radiative Methods,” Proceedings of the First International Conference on Inverse Problems in Engineering: Theory and Practice, Palm Coast, FL, pp. 259–266.
23.
Tseng
C. J.
Chu
H. S.
1992
, “Transient Combined Conduction and Radiation in an Absorbing, Emitting and Anisotropically-Scattering Medium With Variable Thermal Conductivity
,” International Journal of Heat and Mass Transfer
, Vol. 35
, No. 7
, pp. 1844
–1847
.24.
Viskanta
R.
Hommert
P. J.
Groninger
G. L.
1975
, “Spectral Remote Sensing of Temperature Distribution in Semitransparent Solids Heated by an External Radiation Source
,” Journal of Applied Optics
, Vol. 14
, No. 2
, pp. 428
–437
.
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