ATI (Albany, OR) is the worlds leading producer in titanium alloy metals. The process to produce a titanium alloy ingot (L = 2 m, D = 30 cm) is to melt the metal in a clamshell mold under an inert atmosphere, and then to open the mold and roll the solid ingot (Ti = 1420oC) out onto a horizontal cooling rack (Tair = 27oC) until the center temperature is Tc =200 oC. They can then move the ingot onto the next step in the process. Titanium Alloy (1420oC): k = 12.9 W/m-K, = 4450 kg/m3, Cp = 460 J/kg-K, = 6.3 x 10-6 m2/sec; emissivity () = 0.25, Stefan-Boltzman constant () = 5.676 x 10-8 W/m2-K4 Titanium Alloy Ingot: D= 30.0 cm, L= 2.0 m a) Determine the initial overall convective heat transfer coefficient (htotal) for the cooling process. b) Using the initial overall convective heat transfer coefficient (htotal), determine how long it will take for the center temperature of the ingot to reach Tc =200 oC. c) Would the actual cooling rate to be faster, slower, or the same as your calculation? Explain your answer with a discussion of the cooling mechanisms and some simple calculations.