**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**31108

##### Inverse Heat Transfer Analysis of a Melting Furnace Using Levenberg-Marquardt Method

**Authors:**
Mohamed Hafid,
Marcel Lacroix

**Abstract:**

**Keywords:**
melting furnace,
inverse heat transfer,
enthalpy method,
levenberg–marquardt method

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1125529

**References:**

[1] 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.

[2] 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.

[3] 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.

[4] 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.

[5] 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.

[6] 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.

[7] 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.

[8] 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.

[9] 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.

[10] 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.

[11] Y. Zhang, R. Deshpande, D. F. Huang, P. Chaubal, and C. Q. Zhou, Numerical analysis of blast furnace hearth inner profile by using CFD and heat transfer model for different time periods, Int. J. of Heat and Mass Transfer, vol. 51, nos. 1–2, pp. 186–197, 2008.

[12] C.M. Chang, W.T. Cheng, C.E. Huang and S.W. Du, Numerical prediction on the erosion in the hearth of a blast furnace during tapping process, Int. J. of Heat and Mass Transfer, vol. 36, no. 5, pp. 480–490, 2009.

[13] 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.

[14] M. N. Ozisik and H. R. B. Orlande, Inverse Heat Transfer: Fundamentals and Applications, Taylor and Francis, New York, 2000.

[15] V. R. Voller, Development and application of a heat balance integral method for analysis of metallurgical solidification, Applied Mathematical Modelling, pp. 3-11, 1989.

[16] V. R. Voller and C. R. Swaminathan, General Source-Based Method for Solidification Phase Change, Numer. Heat Transfer, vol. 19, pp. 175–189, 1991.

[17] A.M. Guzmán, D.I. Martínez and R. González, Corrosion–erosion wear of refractory bricks in glass furnaces, Engineering Failure Analysis, Vol. 46, pp. 188–195, 2014.

[18] M. Kaur, H. Singh, and S. Prakash, Surface engineering analysis of detonation-gun sprayed Cr3C2–NiCr coating under high-temperature oxidation and oxidation–erosion environments, Surface and Coatings Technology, vol. 206, no. 2–3,pp. 530–541, 2011.

[19] 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.

[20] C. G. Broyden, A class of methods for solving nonlinear simultaneous equations, Mathematics of computation, pp. 577-593, 1965.

[21] B. Sawaf, and M. N. Özisik, Determining the constant thermal conductivities of orthotropic materials by inverse analysis, Int. communications in heat and mass transfer, vol. 22, no. 2, pp. 201-211, 1995.

[22] 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.

[23] 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.

[24] M. Hafid and M. Lacroix, Prediction of the Thermal Parameters of a High-Temperature Metallurgical Reactor Using Inverse Heat Transfer, Int. J. of Mechanical, Aerospace, Industrial, Mechatronic and Manufacturing Engineering, vol. 10, no 6, pp. 907-913, 2016.