Solve the below:
Q: A 2.5-cm-OD, 2-cm-ID copper pipe carriers liquid oxygen to the storage site of a space shuttle at -183°C and 0.04 m3/min. The ambient air is at 21°C and has a dew point of 10°C. How much insulation with a thermal conductivity of 0.02 W/(m K) is needed to prevent condensation on the exterior of the insulation if hc + hr = 17 W/(m2 K) on the outside?
GIVEN
Insulated copper pipe carrying liquid oxygen
Inside diameter (Di) = 2 cm = 0.02 m
Outside diameter (Do) = 2.5 cm = 0.025 m
LOX temperature (Tox) = - 183°C
LOX flow rate (mox) = 0.04 m3/min
Thermal conductivity of insulation (ki) = 0.02 W/(m K)
Exterior heat transfer coefficients (ho = hc + hr) = 17 W/(m2 K)
Ambient air temperature (T) = 21°C
Ambient air dew point (Tdp) = 10°C
ASSUMPTIONS
Steady-state conditions have been reached
The thermal conductivity of the insulation does not vary appreciably with temperature
Radial conduction only
The thermal resistance between the inner surface of the pipe and the liquid oxygen is negligible, therefore Twi =Tox
