A spherical communications satellite 2-m in diameter is placed in orbit around the earth. The satellite generates 1000 W of internal power from a small nuclear generator. If the surface of the satellite has an emittance of 0.3 and is shaded from solar radiation by the earth, estimate the surface temperature. What is the temperature if the satellite with an absorptivity of 0.2 is in an orbit in which it is exposed to solar radiation? Assume the sun is a blackbody and irradiation striking the satellite is 1366 W/m2 and state your assumptions.

Question

GIVEN

• Spherical satellite

• Diameter (D) = 2 m

• Heat generation = 1000 W

• Emittance (?) = 0.3

• Absorptivity of satellite (?)=0.2

• Solar irradiation(G)=1366 W/m2

FIND

• The surface temperature (Ts)

• Surface temperature of satellite

ASSUMPTIONS

• The satellite radiates to space which behaves as a blackbody enclosure at 0 K

• The system is in steady state

SKETCH



PROPERTIES AND CONSTANTS

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

Answer 1

the rate of the heat transfer from a gray body in a blackbody enclosure is



Considering single body radiation T2=0

Solving this for the surface temperature



For steady state the rate of heat transfer must equal the rate of internal generation, therefore the

surface temperature is



The amount of radiation absorbed by the satellite is given by



Total radiation from satellite under steady state is



the rate of the heat transfer from a gray body in a blackbody enclosure is



Considering single body radiation T2=0

Solving this for the surface temperature



For steady state the rate of heat transfer must equal the total amount of energy through generation and

irradiation, therefore the surface temperature is