assume that the surface of the storage vessel has an absorptance (equal to the emittance) of 0.1. Then determine the rate of evaporation of the liquid oxygen in kilograms per second and pounds per hour, assuming that convection can be neglected. The heat of vaporization of oxygen at –183°C is 213.3 kJ/kg.

Question

GIVEN

• A spherical vessel of liquid oxygen in a large black room

• Emittance of vessel surface (?) = 0.1

• Liquid oxygen temperature (To) = –183°C = 90 K

• Sphere diameter (D) = 0.3 m

• Room wall temperature (Tw) = 27°C = 300 K

• Heat of vaporization of oxygen (hfg) = 213.3 kJ/kg

FIND

(a) The rate of radiative heat transfer (qr) to the liquid oxygen in W (b) The rate of evaporation of oxygen (mo) in kg/s

ASSUMPTIONS

• Steady state prevails

• The temperature of the vessel wall is equal to the temperature of the oxygen

• Convective heat transfer is negligible

SKETCH



PROPERTIES AND CONSTANTS

The Stefan-Boltzmann constant (?) = 5.67 ? 10–8 W/(m2 K4)

Answer 1

(a) The net radiative heat transfer from a gray body in a black enclosure,



(b) The rate of evaporation of oxygen is given by