Problema 30 Capitulo 1 - [SOLUCAO] FUNDAMENTOS DE TRANSFERENCIA DE CALOR E DE MASSA 7ed

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PROBLEM 1.30 
 
KNOWN: Diameter and emissivity of spherical interplanetary probe. Power dissipation 
within probe. 
 
FIND: Probe surface temperature. 
 
SCHEMATIC: 
 
 
ASSUMPTIONS: (1) Steady-state conditions, (2) Negligible radiation incident on the probe. 
 
ANALYSIS: Conservation of energy dictates a balance between energy generation within 
the probe and radiation emission from the probe surface. Hence, at any instant 
 
 -E + E = 0out g& & 
 
 ε σA T Es s4 g= & 
 
 
E
T
D
1/ 4
g
s 2επ σ
⎛ ⎞= ⎜ ⎟⎜ ⎟⎝ ⎠
&
 
 
 ( )
150WT
2 40.8 0.5 m 5.67 10
1/ 4
s 2 8 W/m K π
⎛ ⎞⎜ ⎟= ⎜ ⎟×⎝ ⎠− ⋅
 
 
 T K.s = 254 7. < 
 
COMMENTS: Incident radiation, as, for example, from the sun, would increase the surface 
temperature.