Liquid oxygen (LOX) for the Space Shuttle can be stored at 90 K prior to launch in a spherical container 4 m in diameter. To reduce the loss of oxygen, the sphere is insulated with superinsulation developed at the U.S. Institute of Standards and Technology’s Cryogenic Division that has an effective thermal conductivity of 0.00012 W/(m K). If the outside temperature is 20°C on the average and the LOX has a heat of vaporization of 213 J/g, calculate the thickness of insulation required to keep the LOX evaporation rate below 200 g/h.

Question

GIVEN



FIND

- The minimum thickness of the insulation (L) to keep evaporation rate below 0.2 kg/h

ASSUMPTIONS

- The thickness is small compared to the sphere diameter so the problem can be considered one

dimensional

- Steady state conditions prevail

- Radiative heat loss is negligible

SKETCH

Answer 1

The maximum permissible rate of heat transfer is the rate that will evaporate 0.2 kg/h of LOX



An upper limit can be put on the rate of heat transfer by assuming that the convective resistance on the

outside of the insulation is negligible and therefore the outer surface temperature is the same as the

ambient air temperature. With this assumption, heat transfer can be calculated

one dimensional steady state conduction



Solving for the thickness of the insulation (L)