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.

Question

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

Answer 1

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.