A 10-ft-long (3.05 m) vertical cylindrical exhaust duct from a commercial laundry has an ID of 6.0 in. (15.2 cm). Exhaust gases having physical properties approximating those of dry air enter at 600°F (316°C). The duct is insulated with 4 in. (10.2 cm) of rock wool having a thermal conductivity of k = 0.25 + 0.005 T (where T is in °F and k in Btu/h ft °F). If the gases enter at a velocity of 2 ft/s (0.61 m/s), calculate
(a) the rate of heat transfer to quiescent ambient air at 60°F (15.6°C) and
(b) the outlet temperature of the exhaust gas. Show your assumptions and approximations.