Use MATLAB code for part C and D

In a material processing experiment conducted aboard the space shuttle, a coated niobium sphere of 10-mm diameter is removed from a furnace at 900 C and cooled to a temperature of 300C. Although properties of 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 evacuated chamber whose walls are at 25C, determine the time required to reach the final temperature if the coating is polished and has an emissivity of ? = 0.1 . How long would it take if the coating is oxidized and ? = 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 the time 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 effect on the cooling time of independently varying h and ?. (d) Make plots of the temperature variation in three cases