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.
GIVEN
- Spherical LOX tank with superinsulation
- Tank diameter (D) = 4 m
- LOX temperature (TLOX) = 90 K
- Ambient temperature (T?^?) = 20°C = 293 K
- Thermal conductivity of insulation (k) = 0.00012 W/(m K)
- Heat of vaporization of LOX (hfg) = 213 kJ/kg
- Maximum evaporation rate ( mLox ) = 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 isnegligible
