Suppose the resistor is rotated so that its axis is aligned with the flow. What is the maximum permissible power dissipation?

Question

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

Answer 1

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.