Discuss the below in detail:
Q: In a material processing experiment conducted aboard the space shuttle, a coated niobium sphere of l0-mm diameter is removed from a furnace at 900°C and cooled to a temperature of 300°C. Although properties of the niobium vary over this temperature range, constant values may be assumed to a reasonable approximation, with p = 8600 kg/m3, c = 290 J/kg · K, and k = 63 W/m · K.
(a) If cooling is implemented in a large evacuated chamber whose walls are at 25°C, determine the time required to reach the final temperature if the coating is polished and has an emissivity of e = 0.1. How long would it take if the coating is oxidized and e = 0.67
(b) To reduce the time required for cooling, consideration is given to immersion of the sphere in an inert gas stream for which T8 = 25°C and h = 200 W/m2 · K. Neglecting radiation, what is the time required for cooling?
(c) Considering the effect of both radiation and convection, what is the time required for cooling if h = 200 W/m2 · K and e = 0.6? Explore the effect on the cooling time of independently varying h and e.