Physical and mathematical models of steel flow and heat transfer in a tundish heated by plasma
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I. INTRODUCTION
TEMPERATURE control of liquid steel during continuous casting has become a prime requirement to produce high-quality slabs in an ever more demanding world market. Though continuous casting is already a mature technology, needs are arising to cast products with better structures and lower degrees of segregation at lower operating costs. This leaves an open door for further developments in this field, among them, the optimization of plasma heating of steel in tundishes to maintain its temperature within a narrow and controlled range. Tundish heated by plasma is a justified operation because it is well known that low steel superheats lead to better solidified structures with higher ratios of equiaxed to columnar grains.[1] However, extremely low steel superheats may promote nozzle clogging, surface cracking, and strand freeze-off problems. On the other hand, high superheats exacerbate segregation problems,[2] and in extreme cases, the caster must be slowed down to avoid breakouts, even though this decreases the shop’s throughput. Moreover, each steel grade has a range of acceptable superheat where the trade-off between quality and productivity is optimized. To understand steel flow in tundishes, many researchers have employed water models under isothermal conditions.[3–7] Mathematical models explaining the experimental findings of these physical models have also been reported.[8,9,10] In cases of actual nonplasma-heated and plasma-heated steel in tundishes, nonisothermal and nonadiabatic conditions prevail due to the energy losses through the walls and the free surface of the bath. This situation requires that a physical model should meet thermal similarity requirements of actual operations. Similarly, any physical model should ´ M.A. BARRON-MEZA, Professor, is with the Materials Department, ´ ´ Universidad Autonoma Metropolitana-Azcapotzalco, C.P. 07300, Mexico, ´ D.F. Mexico. J. DE J. BARRETO-SANDOVAL, Professor, is with the ´ Materials Graduate Center, Instituto Tecnologico de Morelia, C.P. 58120, ´ Morelia, Mich. Mexico. R.D. MORALES, Professor, is with the Department ´ ´ of Metallurgy, Instituto Politecnico Nacional, ESIQIE, C.P. 07300, Mexico, ´ D.F. Mexico. Manuscript submitted June 21, 1996. METALLURGICAL AND MATERIALS TRANSACTIONS B
be complemented with a mathematical one so as to be able to complete an analysis of the phenomena involved. There are few reports about physical-mathematical modeling of steel flow and heat transfer under nonisothermal and nonadiabatic conditions. Among these are those of Joo et al.[11,12,13] and Chakraborty and Sahai.[14,15,16] They used a three dimensional (3-D) mathematical model to describe changes in temperature of the incoming stream during a casting heat. There are also the physical and the mathematical models of Barreto-Sandoval et al.[17] using thermal step inputs for the case of nonheated tundishes. Specifically, in plasma-heated tundishes, Barreto-Sandoval et al.[18] have also reported a physical-water model using the same technique of thermal step inpu
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