A 3.05 m vertical cylindrical exhaust duct from a commercial laundry has an ID of 15.2 cm. Exhaust gases having physical properties approximating those
of dry air enter at 316°C. The duct is insulated with 10.2 cm of rock wool having a thermal conductivity of k = 0.7 + 0.016 T (where T is in °C and k in W/m K). If the gases enter at a velocity of 0.61 m/s, calculate 

(a) The rate of heat transfer to quiescent ambient air at 15.6°C  

(b) The outlet temperature of the exhaust gas. Show your assumptions and approximations.