Evaporation loss from an oxygen tank

(a) Liquefied gases are sometimes stored in well-insulated spherical containers vented to the atmosphere. Develop an expression for the steady-state heat transfer rate through the walls of such a container, with the radii of the inner and outer walls being r₀ and r₁ respectively and the temperatures at the inner and outer walls being T₀ and T₁. The thermal conductivity of the insulation varies linearly with temperature from k0 at T₀ to k₁ at T_1.

(b) Estimate the rate of evaporation of liquid oxygen from a spherical container of 6 ft inside diameter covered with a 1-if-thick annular evacuated jacket filled with particulate insulation. The following information is available:

Temperature at inner surface of insulation................–183°C 

Temperature at outer surface of insulation...............0°C 

Boiling point of 0₂...........................................................–183°C

Heat of vaporization of 0₂ ............................................1636 cal/g-mol 

Thermal conductivity of insulation at 0°C...................9.0 x 10^-4 Btu/hr ∙ ft ∙ F 

Thermal conductivity of insulation at – 183°C............7.2 x 10^–4 Btu/hr ∙ ft ∙ F 

Transcribed Image Text:

-z = 0 -z = L Surface“ at T, Surface at To -12.