Mathematical Modeling of Heat Transfer in Mold Copper Coupled with Cooling Water During the Slab Continuous Casting Proc
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e steel continuous casting process, the mold copper is very important. Water in slots of copper transfers the heat of mold absorbed from liquid steel continuously, which makes the molten steel in mold from a solidification shell[1] avoid the breakout. In addition, the surface defects of slab are mostly formed at the early solidification stage, and these defects are significantly influenced by the heat transfer in the mold.[2–4] Many studies have been performed on this stage in order to get more understanding about the heat transfer mechanisms. The mostly extensively studies are the analysis of heat transfer with flow patterns in mold.[5–7] In contrast, the amount of research on the heat transfer in copper has been limited. Basically, the methods of researching heat transfer in mold copper are about direct measurement by thermocouple and mathematical simulation. The first method drills holes and installs the thermocouples in mold, and this method has limited thermocouples that could not show the whole temperature field of the mold.[8,9] The second method assumes that the temperature of water slots keeps constant[10] or provides linear variation based on the temperature rise of cooling water at the inlet and the outlet.[8] And the heat transfer coefficients
XIN XIE, Ph.D Student, DENGFU CHEN, Professor, HAIJUN LONG and KUI LV, Master Students, and MUJUN LONG, Lecturer, are with the Laboratory of Metallurgy and Materials, College of Materials Science and Engineering, Chongqing University, Chongqing 400030, P.R. China. Contact e-mail: [email protected] Manuscript submitted December 18, 2013. Article published online August 12, 2014. 2442—VOLUME 45B, DECEMBER 2014
on the slots wall calculated by the most common equations (Dittus–Boelter model[8] or Sleicher–Rouse model[11,12]) are used to simulate the effect of different shapes of water slots on the heat transfer of copper. This conventional method ignores the huge number of meshes in water slots and makes modeling and calculation easier. However, the temperature of the hot face from the bottom to the top of the mold changes nonuniformly,[11,13] which makes the temperature of a water slot variation.[12] In addition, the temperatures at the different positions of the water slot on the cross section of mold are different.[14] Thus, the inaccurate water temperature boundary condition would get imperfect results. The temperature variation of cooling water in mold could be simulated by the coupled heat transfer method. This method includes the heat transfer in copper, the flow behavior and heat transfer of cooling water, and the heat transfer between copper and water. KyungWoo Yi and coworkers[15] studied the effect of the heat transfer of copper with cooling water on different hot face temperatures, cooling water velocity, copper thickness, and water slots space. However, this research did not give the details of the heat transfer model between water and copper, and it assumed the temperature on the hot face was uniform. In addition, the temperature field in the water slot was not discusse
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