**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**30121

##### 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:**

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[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.

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[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.

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