Suppose the resistor is rotated so that its axis is aligned with the flow. What is the maximum permissible power dissipation?
GIVEN
• A heat generating resistor disk with its axis aligned with a cooling airflow
• Heat generation rate ( Q
G) = 2.5 W
• Disk diameter (D) = 1 cm = 0.01 m
• Disk thickness (t) = 0.6 mm = 0.0006 m
• Air temperature (T?) = 30°C
• Air velocity (U?) = 10 m/s
• Maximum surface temperature (Ts) = 90°C FIND
• The maximum permissible power dissipation ( Q G)
ASSUMPTIONS
• Heat transfer from the edges is negligible
• The heat flux is equal from both faces
SKETCH
The Reynolds number based on the film temperature is unchanged from Problem 6.33 ReDf = 5155
The Reynolds number based on the free stream conditions is ReDfs = 5988
The Nusselt number for the upstream face of the disk is given by using the free stream
properties
The Nusselt number for the downstream face can be estimated (using the
properties at film temperature) because the flow behind the disk will be separated and the separated
region behind a normal flat plate will be similar
The maximum power dissipation for the whole chip is
COMMENTS
The circuit designer cannot solve the problem by reorienting the resistor. The upstream face of the disk
has about the same heat transfer coefficient as the surface of the disk aligned with the flow. However,
the downstream face has significantly lower heat transfer coefficient because it is in a separated flow
regime.
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