International Scientific Journal


In this paper, an inverse analysis is performed for the estimation of radiative parameters from the measured temperature profile in an absorbing, emitting, and anisotropically scattering medium. The control volume finite element method is employed to solve the direct problem in a 3-D rectangular furnace. The inverse problem is formulated as an optimization problem between the calculated and the experimental data and the Levenberg-Marquardt method is used for its solution. The sensitivity analysis is made in order to determine whether it is possible to identify the parameters. Also, the effects of angular and spatial grid numbers and the initial guesses on the accuracy of the inverse problem are investigated. This method combination, which is applied for the first time to solve 3-D inverse radiation problem, has been found to accurately predict the unknown parameters.
PAPER REVISED: 2009-09-08
PAPER ACCEPTED: 2010-01-18
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2010, VOLUME 14, ISSUE Issue 2, PAGES [373 - 382]
  1. Subramaniam, S., Menguc, M. P., Solution of the Inverse Radiation Problem for Inhomogeneous and Anisotropically Scattering Media Using Monte Carlo Technique, Int. J. Heat Mass Transfer, 34 (1991), 1, pp. 253-266
  2. Kudo, K., et al., Analysis on Inverse Radiative Property Problem in Two-Dimensional Systems, ASME HTD, 340 (1997), 2,pp. 135-140
  3. Siewert, C. E., Inverse Solutions to Radiative-Transfer Problems with Partially Transparent Boundaries and Diffuse Reflection, J. Quantitative Spectroscopy Radiative Transfer, 72 (2002), 4, pp. 299-313
  4. Milandri, A., Asllanaj, F., Jeandel, G., Determination of Radiative Properties of Fibrous Media by an Inverse Method-Comparison with the Mie Theory, J. Quantitative Spectroscopy Radiative Transfer, 74 (2002), 5, pp. 637-653
  5. Kim, K. W., et al., Estimation of Emissivities in a Two-Dimensional Irregular Geometry by Inverse Radiation Analysis Using Hybrid Genetic Algorithm, J. Quantitative Spectroscopy Radiative Transfer, 87 (2004), 1, pp.1-14
  6. Kim, K. W., Baek, S. W., Efficient Inverse Radiation Analysis in a Cylindrical Geometry Using a Combined Method of Hybrid Genetic Algorithm and Finite-Difference Newton Method, J. Quantitative Spectroscopy Radiative Transfer, 108 (2007), 3, pp. 423-439
  7. Qi, H., et al., Inverse Radiation Analysis of a One-Dimensional Participating Slab by Stochastic Particle Swarm Optimizer Algorithm, Int. J. Thermal Sciences, 46 (2008), 7, pp. 649-661
  8. McCormick, N. J., Inverse Radiative Transfer Problems: A Review, Nucl. Sci. Eng., 112 (1992), 3, pp. 185-198
  9. Grissa, H., et al., Three-Dimensional Radiative Transfer Modeling Using the Control Volume Finite Element Method, J. Quantitative Spectroscopy Radiative Transfer, 105 (2007), 3, pp. 388-404
  10. Grissa, H., et al., Nonaxisymmetric Radiative Transfer in Inhomogeneous Cylindrical Media with Anisotropic Scattering, J. Quantitative Spectroscopy Radiative Transfer, 109 (2008), 3, pp. 494-513
  11. Grissa, H., et al., Prediction of Radiative Heat Transfer in 3D Complex Geometries Using the Unstructured Control Volume Finite Element Method, J. Quantitative Spectroscopy Radiative Transfer, 111 (2010), 2, pp. 144-154
  12. Lazard, M., et al., Radiative and Conductive Heat Transfer: A Coupled Model for Parameter Estimation, High Temperatures-High Pressures, 32 (2000), 1, pp. 9-17
  13. Kim, K. W., Baek, S. W., Inverse Radiation-Conduction Design Problem in a Participating Concentric Cylindrical Medium, Int. J. Heat Mass Transfer, 50 (2007), 13, pp. 2828-2837
  14. Zhao, S. W., Zhang, B. M., Du, S. Y., An Inverse Analysis to Determine Conductive and Radiative Properties of a Fibrous Medium, J. Quantitative Spectroscopy Radiative Transfer, 110 (2009), 13, pp. 1111-1123
  15. Marquardt, D.W., An algorithme for Least Squares Estimation of Nonlinear Parameters, J. Social Industrial Applied Mathematics, 11 (1963), 2, pp.431-441
  16. Fiveland, W. A., Three Dimensional Radiative Heat Transfer Solutions by Discrete Ordinates Method, J. Thermophysics Heat Transfer, 2 (1988), 4, pp. 309-316
  17. Coelho, P. J., A Hybrid Finite Volume/Finite Element Discretization Method for the Solution of the Radiative Heat Transfer Equation, J. Quantitative Spectroscopy Radiative Transfer, 93 (2005), 1, pp. 89-101

© 2022 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence