In a thin-slab, continous casting process, molten steel leaves a mold with a thi

Question

In a thin-slab, continous casting process, molten steel leaves a mold with a thin solid shell, and the molten material solidifies as the slab is quenched by water jets in route to a section of rollers. Once fully solidified, the slab continues to cool as it is brought to an acceptable handling temperature. It is this portion of the process that is of interest.

Consider a 200mm thick solid slab of steel(p=7800 kg/m^3, c=700 J/kg*K, k=30 W/m*K), initially at a uniform temperature of Ti=1400 Celcius. The Slab is cooled at its top and bottom surfaces by water jets (Too=50 Celcius ), which maintain a approximadely uniform convection coefficient of h=5000 W/m^2*K at both surfaces. Using a finite-diference solution with a space increment of Dx =I mm determine the time required to cool the surface of the slab to 200 Celcius . What is the corresponding temperature at the mid plane of the slab? If the Slab moves at a speed of V=15 mm/s, What is the required legth of the cooling section?

Explanation / Answer

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web2.clarkson.edu/projects/fluidflow/kam/courses/2005/.../hw_ch05_2.pdf

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