A spherical shell satellite (3-m-OD, 1.25-cm-thick stainless steel walls) re-enters the atmosphere from outer space. If its original temperature is 38°C, the effective average temperature of the atmosphere is 1093°C, and the effective heat transfer coefficient is 115 W/(m2 °C), estimate the temperature of the shell after reentry, assuming the time of reentry is 10 min and the interior of the shell is evacuated.
GIVEN
• A spherical stainless steel satellite reentering the atmosphere
• Outside diameter (D) = 3 m
• Wall thickness (L) = 1.25 cm = 0.0125 m
• Its original temperature (To) = 38°C
• The effective temperature of the atmosphere (T?) = 1093°C
• The effective heat transfer coefficient ch = 115 W/(m2 °C)
• The time of reentry (tr) = 10 min = 600 s
• The interior of the shell is evacuated
FIND
• The temperature of the shell after reentry (Tf)
ASSUMPTIONS
• Exterior heat transfer is uniform over the shell
• Assume radiation heat transfer is allowed for in the heat transfer coefficient
SKETCH
Since the thickness of the shell is much smaller than the shell radius, the wall can be treated as a plane wall. To
estimate the importance of internal thermal resistance, the Biot number is calculated first
Therefore, the internal resistance is less than 10% of the external resistance and may be neglected. The
temperature-time history of the satellite is given
COMMENTS
The analysis has neglected thermodynamic heating during reentry.
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