The heat transfer coefficients for the flow of 26.6°C air over a 1.25 cm diameter sphere are measured by observing the temperature-time history of a copper ball of the same dimension. The temperature of the copper ball (c = 376 J/(kg K), ? = 8928 kg/m3) was measured by two thermocouples, one located in the center, and the other near the surface. The two thermocouples registered, within the accuracy of the recording instruments, the same temperature at any given instant. In one test run, the initial temperature of the ball was 66°C and the temperature decreased by 7°C in 1.15 min. Calculate the heat transfer coefficient for this case.
IVEN
• A copper ball with air flowing over it
• Ball diameter (D) = 1.25 cm = 0.0125 m
• Air temperature (T?) = 26.6°C
• Specific heat of ball (c) = 376 J/(kg K)
• Density of the ball (P) = 8928 kg/m3
• Thermocouples in the center and the surface registered the same temperature
• Initial temperature of the ball (To) = 66°C
• Lapse time = 1.15 min = 69 s
• The temperature decrease (To – Tf) = 7°C
FIND
• The heat transfer coefficient ch
ASSUMPTIONS
• The heat transfer coefficient remains constant during the cooling period.
SKETCH
Since the thermocouples register essentially the same temperature, the internal resistance of the ball is small
compared to the external resistance and the ball can be treated with the lumped heat capacity method.
the temperature-time history is
Solving for the heat transfer coefficient
COMMENTS
The value is an average over the cooling period.
The procedure described by this problem can be used to evaluate heat transfer coefficients for odd shaped
object experimentally.
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