Prediction of the Thermal Parameters of a High-Temperature Metallurgical Reactor Using Inverse Heat Transfer

Authors: Mohamed Hafid, Marcel Lacroix

Abstract:

This study presents an inverse analysis for predicting the thermal conductivities and the heat flux of a high-temperature metallurgical reactor simultaneously. Once these thermal parameters are predicted, the time-varying thickness of the protective phase-change bank that covers the inside surface of the brick walls of a metallurgical reactor can be calculated. The enthalpy method is used to solve the melting/solidification process of the protective bank. The inverse model rests on the Levenberg-Marquardt Method (LMM) combined with the Broyden method (BM). A statistical analysis for the thermal parameter estimation is carried out. The effect of the position of the temperature sensors, total number of measurements and measurement noise on the accuracy of inverse predictions is investigated. Recommendations are made concerning the location of temperature sensors.

Keywords: Inverse heat transfer, phase change, metallurgical reactor, Levenberg–Marquardt method, Broyden method, bank thickness.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1124507

References:

[1] O. Tadrari and M. Lacroix, Prediction of Protective Banks in High-Temperature Smelting Furnaces by Inverse Heat Transfer, Int. J. of Heat and Mass Transfer, vol. 49, no. 13–14, pp. 2180–2189, 2006.
[2] M. A. Marois, M. Désilets, and M. Lacroix, Prediction of a 2-D Solidification Front in High-Temperature Furnaces by an Inverse Analysis, Numer. Heat Transfer A, vol. 59, no. 3, pp. 151–166, 2011.
[3] M. A. Marois, M. Désilets, and M. Lacroix, Prediction of the Bank Formation in High Temperature Furnaces by a Sequential Inverse Analysis with Overlaps, Numer. Heat Transfer A, vol. 60, pp. 561–579, 2011.
[4] M. A. Marois, M. Désilets, and M. Lacroix, What is the Most Suitable Fixed Grid Solidification Method for Handling Time-Varying Inverse Stefan Problems in High Temperature Industrial Furnaces? Int. J. of Heat and Mass Transfer, vol. 55, pp. 5471–5478, 2012.
[5] C. Bertrand, M. A. Marois, M. Désilets, G. Soucy, and M. Lacroix, A combined 2D inverse predictions and experimental analysis for the bank formation internal a metallurgical reactor, Int. J. of Heat and Mass Transfer, vol. 59, pp. 58-65, 2013.
[6] M. LeBreux, M. Désilets, and M. Lacroix, Fast Inverse Prediction of Phase Change Banks in High-Temperature Furnaces with a Kalman Filter Coupled with a Recursive Least-Square Estimator, Int. J. of Heat and Mass Transfer, vol. 53, no. 23–24, pp. 5250–5260, 2010.
[7] M. LeBreux, M. Désilets, and M. Lacroix, An unscented Kalman filter inverse heat transfer method for the prediction of the ledge thickness internal high-temperature metallurgical reactors, Int. J. of Heat and Mass Transfer, vol. 57, no. 1, pp. 265-273, 2013.
[8] M. LeBreux, M. Désilets, and M. Lacroix, Control of the Ledge Thickness in High-Temperature Metallurgical Reactor using a Virtual Sensor, Inverse Problems in Sci. and Eng., vol. 20, no. 8, pp. 1215–1238, 2012.
[9] M. LeBreux, M. Désilets, and M. Lacroix, Prediction of the Time-Varying Ledge Profile internal a High-Temperature Metallurgical Reactor with an Unscented Kalman Filter-Based Virtual Sensor, Numer. Heat Transfer A, vol. 64, pp. 551-576, 2013.
[10] M. LeBreux, M. Désilets, and M. Lacroix, Is the performance of a virtual sensor employed for the prediction of the ledge thickness internal a metallurgical reactor affected by the thermal contact resistance? WIT Transactions on Eng. Sci. , Vol. 83, pp. 517-526, 2014.
[11] V. Guillaume, L. Gosselin, and M. Lacroix, an enhanced thermal conduction model for the prediction of convection dominated solid–liquid phase change, Int. J. of Heat and Mass Transfer, vol. 52, no. 7-8, pp. 1753-1760, 2009.
[12] V. R. Voller and C. R. Swaminathan, General Source-Based Method for Solidification Phase Change, Numer. Heat Transfer, vol. 19, pp. 175–189, 1991.
[13] S. V. Patankar, Numerical Heat Transfer and Fluid Flow, McGraw-Hill, New York, 1980.
[14] V. R. Voller, Development and application of a heat balance integral method for analysis of metallurgical solidification, Applied Mathematical Modelling, pp. 3-11, 1989.
[15] D. W. Marquardt, An algorithm for least-squares estimation of nonlinear parameters, J. of the Society for Industrial and Applied Mathematics, pp. 431-441, 1963.
[16] M. N. OZISIK and H. R. B. Orlande, Inverse Heat Transfer: Fundamentals and Applications, Taylor and Francis, New York, 2000.
[17] C. G. Broyden, A class of methods for solving nonlinear simultaneous equations, Mathematics of computation, pp. 577-593, 1965.
[18] B. Moghadassian, and F. Kowsary, Inverse boundary design problem of natural convection–radiation in a square enclosure, Int. J. of Thermal Sci. vol. 75, pp. 116-126, 2014.
[19] K. W. Kim, and S. W. Baek, Inverse radiation–conduction design problem in a participating concentric cylindrical medium, Int. J. of Heat and Mass Transfer, vol. 50, no. 13-14, pp. 2828-2837, 2007.