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?

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


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.

Physics & Space Science

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