zbMATH — the first resource for mathematics

A mathematical model of a slab reheating furnace with radiative heat transfer and non-participating gaseous media. (English) Zbl 1201.80051
Summary: A mathematical model of the reheating process of steel slabs in industrial fuel-fired furnaces is developed. The transient temperature field inside the slabs is computed by means of the Galerkin method. Radiative heat transfer inside the furnace constitutes boundary conditions that couple the dynamic subsystems of the slabs. Constraining the heat fluxes to piecewise linear, discontinuous signals furnishes a discrete-time state-space system. Conditions for an exponential decrease of the open-loop control error are derived. Measurements from an instrumented slab in the real system demonstrate the accuracy of the model. The simple and computationally inexpensive model is suitable for trajectory planning, optimization, and controller design.

80A20 Heat and mass transfer, heat flow (MSC2010)
80M25 Other numerical methods (thermodynamics) (MSC2010)
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
Full Text: DOI
[1] Baehr, H. D.; Stephan, K.: Heat and mass transfer, (2006) · Zbl 1130.80001
[2] Banerjee, S.; Sanyal, D.; Sen, S.; Puri, I. K.: A methodology to control direct-fired furnaces, International journal of heat and mass transfer 47, 5247-5256 (2004) · Zbl 1086.80001 · doi:10.1016/j.ijheatmasstransfer.2004.06.023
[3] Barr, P. V.: The development, verification, and application of a steady-state thermal model for the pusher-type reheat furnace, Metallurgical and materials transactions B 26B, No. August, 851-869 (1995)
[4] Chen, S.; Abraham, S.; Poshard, D.: Modification of reheat furnace practices through comprehensive process modeling, Iron & steel technology 5, No. 8, 66-79 (2008)
[5] G. van Ditzhuijzen, D. Staalman, A. Koorn, Identification and model predictive control of a slab reheating furnace, in: Proceedings of the 2002 IEEE International Conference on Control Applications, Glasgow, UK, pp. 361 – 366, September 2002.
[6] Elliston, D. G.; Gray, W. A.; Hibberd, D. F.; Ho, T. Y.; Williams, A.: The effects of surface emissivity on furnace performance, Journal of the institute of energy 60, 155-167 (1987)
[7] Ezure, H.; Seki, Y.; Yamaguchi, N.; Shinonaga, H.: Development of a simulator to calculate an optimal slab heating pattern for reheat furnaces, Electrical engineering in Japan 120, No. 3, 42-53 (1997)
[8] Fletcher, C.: Computational Galerkin methods, (1984) · Zbl 0533.65069
[9] Fontana, P.; Boggiano, A.; Furinghetti, A.; Cabras, G.; Simoncini, C. A.: An advanced computer control system for reheat furnaces, Iron and steel engineer 60, No. 8, 55-62 (1983)
[10] Franklin, G. F.; Powell, J. D.; Workman, M.: Digital control of dynamic systems, (1997) · Zbl 0697.93002
[11] Golub, G. H.; Van Loan, C. F.: Matrix computations, Johns hopkins series in the mathematical sience (1996) · Zbl 0865.65009
[12] Goyhénèche, J. M.; Sacadura, J. F.: The zone method: A new explicit matrix relation to calculate the total exchange areas in anisotropically scattering medium bounded by anisotropically reflecting walls, Journal of heat transfer 124, No. 4, 696-703 (2002)
[13] Han, S. H.; Baek, S. W.; Kim, M. Y.: Transient radiative heating characteristics of slabs in a walking beam type reheating furnace, International journal of heat and mass transfer 52, 1005-1011 (2009) · Zbl 1156.80327 · doi:10.1016/j.ijheatmasstransfer.2008.07.030
[14] K. Harste, Untersuchung zur Schrumpfung und zur Entstehung von mechanischen Spannungen während der Erstarrung und nachfolgender Abkühlung zylindrischer Blöcke aus Fe-C-Legierungen. Ph.D. thesis, Technische Universität Clausthal, 1989.
[15] Hollander, F.; Zuurbier, S. P. A.: Design, development and performance of online computer control in a 3-zone reheating furnace, Iron and steel engineer 59, No. 1, 44-52 (1982)
[16] Honner, M.; Vesely, Z.; Svantner, M.: Exodus stochastic method application in the continuous reheating furnace control system, Scandinavian journal of metallurgy 33, 328-337 (2004)
[17] Hottel, H. C.; Sarofim, A. F.: Radiative transfer, (1967)
[18] Icev, Z. A.; Zhao, J.; Stankovski, M. J.; Kolemisevska-Gugulovska, T. D.; Dimirovski, G. M.: Supervisory-plus-regulatory control design for efficient operation of industrial furnaces, Journal of electrical & electronics engineering 4, No. 2, 1199-1218 (2004)
[19] Incropera, F. P.; Dewitt, D. P.; Bergman, T. L.; Lavine, A. S.: Fundamentals of heat and mass transfer, (2007)
[20] Jaklič, A.; Vode, F.; Kolenko, T.: Online simulation model of the slab-reheating process in a pusher-type furnace, Applied thermal engineering 27, 1105-1114 (2007)
[21] Khalil, H. K.: Nonlinear systems, (2002) · Zbl 1003.34002
[22] Kim, M. Y.: A heat transfer model for the analysis of transient heating of the slab in a direct-fired walking beam type reheating furnace, International journal of heat and mass transfer 50, 3740-3748 (2007) · Zbl 1125.80310 · doi:10.1016/j.ijheatmasstransfer.2007.02.023
[23] H.S. Ko, J. Kim, T. Yoon, M. Lim, D.R. Yang, I.S. Jun, Modeling and predictive control of a reheating furnace, in: Proceedings of the American Control Conference, Chicago, USA, 4, pp. 2725 – 2729, 2000.
[24] Leden, B.: A control system for fuel optimization of reheating furnaces, Scandinavian journal of metallurgy 15, 16-24 (1986)
[25] Li, Z.; Barr, P. V.; Brimacombe, J. K.: Computer simulation of the slab reheating furnace, Canadian metallurgical quarterly 27, No. 3, 187-196 (1988)
[26] Marino, P.; Pignotti, A.; Solis, D.: Numerical model of steel slab reheating in pusher furnaces, Latin amercian applied research 32, No. 3, 257-261 (2002)
[27] Modest, M. F.: Radiative heat transfer, (2003)
[28] Noble, J. J.: The zone method: explicit matrix relations for total exchange areas, International journal for heat and mass transfer 18, 261-269 (1975)
[29] L.M. Pedersen, B. Wittenmark, On the reheat furnace control problem, in: Proceedings of the American Control Conference, pp. 3811 – 3815, June 1998.
[30] Reddy, B. D.: Introductory functional analysis, Texts in applied mathematics (1997)
[31] Rhine, J. M.; Tucker, R. J.: Modelling of gas-fired furnaces and boilers and other industrial heating processes, (1991)
[32] Roth, J. L.; Sierpinski, H.; Chabanier, J.; Germe, J. M.: Computer control of slab furnaces based on physical models, Iron and steel engineer 63, No. 8, 41-47 (1986)
[33] Samyudia, Y.; Sibarani, H.: Identification of reheat furnace temperature models from closed-loop data – an industrial case study, Asia-Pacific journal of chemical engineering 1, 70-81 (2006)
[34] Schurko, R. J.; Weinstein, C.; Hanne, M. K.; Pellecchia, D. J.: Computer control of reheat furnaces: A comparison of strategies and applications, Iron and steel engineer 64, No. 5, 37-42 (1987)
[35] J.L.V.A. Sousa, J. Ward, R.A. Wallis, D.A. Lawson, Simulation and measurement of the transient performance of a gas-fired heat treatment furnace, in: Proceedings of the Second European Thermal-Sciences and 14th UIT National Heat Transfer Conference, May 1996.
[36] Staalman, D. F. J.; Kusters, A.: On-line slab temperature calculation and control, Manufacturing science and engineering 4, 307-314 (1996)
[37] A. Steinboeck, D. Wild, T. Kiefer, A. Kugi, A flexible time integration method for the 1D heat conduction problem, in: Proceedings of the 6th Vienna Conference on Mathematical Modelling, Vienna, Austria, ARGESIM Report no. 35, pp. 1204 – 1214, February 2009.
[38] Trivic, D. N.; Amon, C. H.: Modeling the 3D radiation of anisotropically scattering media by two different numerical methods, International journal of heat and mass transfer 51, 2711-2732 (2008) · Zbl 1143.80329 · doi:10.1016/j.ijheatmasstransfer.2007.10.015
[39] Vidyasagar, M.: Nonlinear systems analysis, Number 42 in classics in applied mathematics (1992) · Zbl 0759.93001
[40] Wild, D.; Meurer, T.; Kugi, A.: Modelling and experimental model validation for a pusher-type reheating furnace, Mathematical and computer modelling of dynamical systems 15, No. 3, 209-232 (2009) · Zbl 1169.93308 · doi:10.1080/13873950902927683
[41] D. Wild, T. Meurer, A. Kugi, O. Fichet, K. Eberwein, Nonlinear observer design for pusher-type reheating furnaces, in: Proceedings of the Third International Steel Conference on New Developments in Metallurgical Process Technologies, Düsseldorf, Germany, pp. 790 – 797, June 2007.
[42] N. Yoshitani, T. Ueyama, M. Usui, Optimal slab heating control with temperature trajectory optimization, in: Proceedings of the 20th International Conference on Industrial Electronics, Control and Instrumentation, IECON’94, 3, pp. 1567 – 1572, September 1994.
[43] B. Zhang, Z. Chen, L. Xu, J. Wang, J. Zhang, H. Shao. The modeling and control of a reheating furnace, in: Proceedings of the American Control Conference, Anchorage, Alaska, USA, pp. 3823 – 3828, May 2002.
[44] Zienkiewicz, O. C.; Morgan, K.: Finite elements and approximation, (1983) · Zbl 0582.65068
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.