An electronic circuit contains a power resistor that dissipates 1.5 W. The designer wants to modify the circuitry in such a way that it will be necessary for the resistor to dissipate 2.5 W. The resistor is in the shape of a disk 1 cm in diameter and 0.6-mm-thick. Its surface is aligned with a cooling air flow at 30°C and 10 m/s velocity, i.e., the vertical axis of the disc is in cross-flow with the cooling air. The resistor lifetime becomes unacceptable if its surface temperature exceeds 90°C. Is it necessary to replace the resistor for the new circuit?

Question

GIVEN

• A heat generating resistor disk with its surface 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

• Is it necessary to replace the resistor?

ASSUMPTIONS

• Steady state

• Radiation is negligible

SKETCH

Answer 1

The Reynolds number based on the diameter is



The Nusselt number for the geometry is given by



The rate of heat transfer at the maximum surface temperature of 90°C is



Therefore, the surface temperature must be greater than 90°C to dissipate the required 2.5 Watts. The

resistor must be replaced.