In a material processing experiment conducted aboardthe

Chapter 5, Problem 5.24

(choose chapter or problem)

In a material processing experiment conducted aboardthe space shuttle, a coated niobium sphere of 10-mmdiameter is removed from a furnace at 900C andcooled to a temperature of 300C. Although propertiesof the niobium vary over this temperature range, con-stant values may be assumed to a reasonable approxi-mation, with ??8600 kg/m3, c?290 J/kg?K, and k?63 W/m?K.(a) If cooling is implemented in a large evacuatedchamber whose walls are at 25C, determine thetime required to reach the final temperature if thecoating is polished and has an emissivity of ??0.1.How long would it take if the coating is oxidizedand ??0.6?(b) To reduce the time required for cooling, considera-tion is given to immersion of the sphere in an inert gas stream for which T??25C and h?200 W/m2?K. Neglecting radiation, what is thetime required for cooling?(c) Considering the effect of both radiation and con- vection, what is the time required for cooling if h?200 W/m2?K and ??0.6? Explore the effecton the cooling time of independently varying hand ?.