(Solution) - Liquid oxygen at 183 C is stored in a thin -(2025 Original AI-Free Solution)

Paper Details

Liquid oxygen at ? 183°C is stored in a thin walled spherical container with an outside diameter of 2 m. This container is surrounded by another sphere of 2.5 m inside diameter to reduce heat loss. The inner spherical surface has an emissivity of 0.05 and the outer sphere is black. Under normal operation the space between the spheres is evacuated. But due to an accident a leak developed in the outer sphere and the space is filled with air at one atm. If the outer sphere is at 25°C, compare the heat losses before and after the accident.
GIVEN
A sphere filled with liquid oxygen surrounded by a larger sphere
Sphere diameters: Di = 2 m Do = 2.5 m
Emissivity of inner sphere (?) = 0.05
Outer sphere temperature (To) = 25°C = 298 K
Liquid oxygen temperature (Ti) = ?183° = 90 K
Outer sphere is black
ASSUMPTIONS
Steady state
The internal convective resistance and the resistance of the inner sphere wall arenegligible