Calculation of Heat Flux Across the Hot Surface of Continuous Casting Mold Through Two-Dimensional Inverse Heat Conducti
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THE continuous casting problems, such as breakout, the crack of slab, and the deep oscillation marks, are directly related to the heat transfer behavior in the continuous casting mold,[1–3] and the in-mold heat transfer is influenced by multi-factors during the casting process, such as mold flux properties, cooling water flow, pouring temperature, and casting speed. A sudden excessive high heat flux would lead to an irregular shell solidification formation that further causes the shell surface cracks and deep oscillation marks.[4] Conversely, a low heat flux would result in a thinner shell in the mold and thus induce the cracks and even breakout. Therefore, the heat flux could be acted as an indicator that helps make a decision before the continuous casting problems arise. For the interpretation of the mold performance and better controlling of the in-mold heat flux, the value of heat flux should be obtained accurately. The calculation works of the heat flux can be traced back to the emergence of the continuous casting. The main computation methods are summarized as follows: (1) Due to the fact that the heat flux is varying along the length of the mold,[5,6] the mold heat flux q can be assumed as a function of distance from the meniscus
HAIHUI ZHANG, Graduate Student, WANLIN WANG, Shenghua Professor, and LEJUN ZHOU, Lecturer, are with the School of Metallurgy and Environment, Central South University, Changsha 410083, Hunan P.R. China. Contact e-mail: [email protected] Manuscript submitted October 15, 2014. METALLURGICAL AND MATERIALS TRANSACTIONS B
(y) and the shell dwell time in the mold (t). Typical mold heat flux formulas have been developed from the practice, like Schwerdtfeger’s equation q ¼ aecy þ b [7] and Savage equation q ¼ atc þ b.[8–11] Where the parameters of a, b and c could be calibrated with the average heat flux that calculated from the difference of the inlet and outlet cooling water temperatures of the industrial mold.[12,13] (2) Mold is a water-cooled heat exchanger. Once the heat transfer coefficient by convection of the water coolant is given and known, the heat transfer in the mold could be calculated through heat transfer mathematic model. There are two methods to obtain the convection coefficient. One is to employ an empirical correlation to calculate the Nusselt number and hence get the heat transfer coefficient by convection of the water coolant.[14,15] Another one is to adopt thermal boundary layer theory to compute the heat transfer coefficient after calculating the flow field of the mold cooling water.[16] However, the heat transfer coefficient is a time- and space-dependent variable and cannot be calculated accurately due to the complex water flow pattern and the variation of cooling water temperature along the flow direction. (3) Calculation of the heat flux from the measured mold wall temperatures. The method can be classified into two categories according to the algorithm of the heat flux. The first one is the direct calculation of the heat flux based on the temperature gradient (DYm/ Dx) detected from
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