A small gray sphere having an emissivity of 0.5 and a surface temperature of 1000°F is located in a blackbody enclosure having a temperature of 100°F. Calculate for this system:

(a) The net rate of heat transfer by radiation per unit of surface area of the sphere,

(b) The radiative thermal conductance in Btu/(h °F) if the surface area of the sphere is 0.1 ft2,

(c) The thermal resistance for radiation between the sphere and its surroundings,

(d) The ratio of thermal resistance for radiation to thermal resistance for convection if the convective heat transfer coefficient between the sphere and its surroundings is 2.0 Btu/(h ft2 °F), (e) The total rate of heat transfer from the sphere to the surroundings, and

(f) The combined heat transfer coefficient for the sphere.

GIVEN

Small gray sphere in a blackbody enclosure

Sphere emissivity (εs) = 0.5

Sphere surface temperature (T1) = 1000°F = 1460 R

Enclosure temperature (T2) = 100°F = 560 R

The surface area of the sphere (A) is 0.1 ft2

The convective transfer coefficient ( hc ) = 2.0 Btu/(h ft2 °F)

ASSUMPTIONS

Steady state prevails

The temperature of the fluid in the enclosure is equal to the enclosuretemperature

Transcribed Image Text:

Enclosure: TE = 1460 R EE" 1.0 Gray sphere: T,- 560 R E= 0.5