In a manufacturing process, a long coated plastic rod (p = 2200 kg/m J ∙ c = 800 J/kg ∙ K, k =1 W/m ∙ K) of diameter D = 20 mm is initially at a uniform temperature of 25°C and is suddenly exposed to a cross flow of air at T_∞ = 350°C and V = 50 m/s.

(a) How long will it take for the surface of the rod to reach 175°C, the temperature above which the special coating will cure?

(b) Generate a plot of the time-to-reach 175°C as a function of air velocity for 5 < V < 50 m/s.