In a thin-slab, continuous 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 en 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 200-mm-thick solid slab of steel (p = 7800 kg/m3, c = 700 J/kg ∙ K. k = 30 W/m ∙ K), initially at a uniform temperature of Ti = 1400°C. The slab is cooled at its top and bottom surfaces by water jets (T∞ = 50°C), which maintain an approximately uniform convection coefficient of h = 5000 W/m2 ∙ K at both surfaces. Using a finite-difference solution with a space increment of ∆x = I mm, determine the time required to cool the surface of the slab to 200°C. What is the corresponding temperature at the mid plane of the slab? If the slab moves at a speed of V = 15 mm1s, what is the required length of the cooling section?

21- 200 mm Solid (T, = 1400C)- Tundish Mold Liquid Solid Water jet