Example Problem with Complete Solution

4B-3 Surface Temperature of a Spacecraft
4 pts
The outer surface of a spacecraft has an emissivity of 0.8 and an absorptivity of 0.3 for solar radiation. If solar radiation is incident on the spacecraft at a rate of 1000 W/m2, determine the temperature of the surface of the spacecraft when the radiation emitted equals the solar energy absorbed. 
Read : The key to solving this problem is to recognize that solar radiation is incident on the spacecraft and the spacecraft radiates heat to deep space, which is at an average temperature of 3 K.
Figure 1.
 
 
Given : Qsun
1000
W/m2
α
0.3
ε
0.8
Tspace
3
K  
σ
5.67E-08
W/m2-K4  
 
Find : Tsurface
???
oC  
 
Assumptions :
- Incident solar radiation on the spacecraft is uniform.
- The spacecraft radiates thermal energy to its surroundings which are at an average temperature of 3 K.
Solution : The spacecraft absorbs 30% of the incident radiation from the sun, because:
Equation. Eqn 1 Qin
300
W/m2
The space craft radiates to deep space and deep space radiates to the spacecraft as well.
Equation. Eqn 2
When the temperature on the surface of the spacecraft reaches a steady-state value, there will be no net amount of heat transfer to or from the surface :
Equation. Eqn 3
Next, we can combine Eqns 2 & 3 and solve for the surface temperature of the spacecraft.
Equation. Eqn 4 Tsurface
285.18
K
Tsurface
12.0
oC
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