A 10 ft (3.05 m) long 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/(hr 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).(b) The outlet temperature of the exhaust gas.Show your assumptions and approximations.GIVENExhaust gases flowing through an insulated long vertical cylindrical ductExhaust gases have the physical properties of dry airDuct length (L) = 3.05 mDuct inside diameter (D) = 15.2 cm = 0.152 mEntering exhaust temperature (Tb,in)Rock wool insulation thickness (s) = 10.2 cm = 0.102 mThermal conductivity of insulation (k) = 0.025 + 0.0005 T (k in Btu/(h ft2 ?F), T in ?F)Exhaust velocity (V) = 0.61 m/sGas inlet temperature (Tb,in) = 316?CASSUMPTIONSSteady stateThermal resistance of the duct wall is negligibleHeat transfer by radiation is negligibleNatural convection on the inside of the duct can be approximated by natural convection from a vertical plateThe interior heat transfer coefficient can be accurately estimated using uniform surface temperature correlationsThe ambient air isstill

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L- 3,05 m T.- 15.6°C D,- 15.2 cm Insulation, Thickness (s) = 10.2 cm Exhaust Tain - 316°C V-0.61 m/s