Journal of Materials Processing Technology 178 (2006) 379–387 A mathematical and computational model of furnaces for continuous steel strip processing S.R. Carvalho, T.H. Ong, G. Guimar˜ aes ∗ Federal University of Uberlˆ andia, School of Mechanical Engineering, Campus Santa Mˆ onica, Bloco M, 38400-902, Av. Jo ˜ ao Naves de ´ Avila, 2121, Uberl ˆ andia, MG, Brazil Received 23 December 2004; received in revised form 23 December 2004; accepted 4 April 2006 Abstract This study presents the development of a mathematical and computational model for simulating and controlling of an annealing process of a silicon steel strip that occurs in an industrial combustion furnace. Both the combustion process and the strip heating are simulated by using energy and mass balances inside the industrial furnace. These balances are performed considering important variables, such as composition, temperature and pressure of gas components, adiabatic flame and environmental temperature. Besides the balances, an optimization technique is implemented in order to estimate the temperature distribution of the strip at any time. The optimization technique used is the Golden section algorithm that minimizes a least square function based on difference of the experimental and theoretical temperature in two different locations of the strip. All steps of the software development are presented here: the combustion and annealing process, the energy and mass balance and the fundamentals of the optimization process. The efficiency of the software is then demonstrated through an analysis and application of data acquired from operational conditions in continuous annealing lines of a steel company. This study is concluded presenting a discussion about the uncertainty and error sources the can be present in the results. The software SIMCO—RB2 seems to be a very powerful tool in the simulation of metal annealing processes. © 2006 Elsevier B.V. All rights reserved. Keywords: GTAW process; Phase change; Welding; Temperature; Optimization; Identification 1. Introduction Actually, the steel industry is developing silicon steel with less carbon content, which increases the magnetic properties and reduces the processing time of the final product. Hence, increasing performance and reducing costs. The importance of silicon steel in electrical equipments explains the need for qual- ity. Silicon steel is used in rotors and stators of electrical motors and compressors for refrigeration and in the form of sheets for transformers. The quality and the productivity depend very much on the processing conditions in the furnace. Control of the operat- ing conditions, such as strip speed and the combustion process and the materials and geometry of the furnace are crucial to obtain the final product desired. The development of a model able to do part of this control is one of the objectives of this paper. ∗ Corresponding author. Tel.: +55 34 32394415; fax: +55 34 32394206. E-mail address: gguima@mecanica.ufu.br (G. Guimar˜ aes). This study proposes a new methodology to simulate the annealing of silicon steel in a tunnel furnace, predicting the com- position and flowrate of the gases using measured, temperature and composition of the fuels. The formulation of the pre-heat, heating and soaking zones as well as the annealing process of the silicon steel strip due to the combustion process are described. 2. Theory The furnace studied is a tunnel furnace compost of one pre- heat zone, three heating zones and three soaking zones. Each zone has a determined number of gas burners, which generate the heat in the furnace. A strip of silicon steel is inserted in the pre-heat zone and conveyed by a belt to the others zones. Two pyrometers in the furnace measure the strip temperature in two different positions. The blast furnace is shown in Fig. 1 and with the heat exchanger in Fig. 14. For the combustion process, the following fuels were used: blast furnace gas (GAF) in various composition, liquefied petroleum gas (GLP), mixed gas (M = GLP + GAF) and diesel fuel. The combustion process was simulated with both lack of 0924-0136/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2006.04.083