A 2.5-cm-OD, 2-cm-ID copper pipe carries 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
nsulated 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
FIND
Thickness of insulation (L) needed to prevent condensation
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
SKETCH
The thermal circuit for the pipe is shown below
The rate of heat transfer from the pipe is
The rate of heat transfer by convection and radiation from the outer surface of the pipe is
Equating these two expressions
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