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.
You might also like to view...
Which of these is a transverse wave?
A) a Slinky shaken to and fro. B) a radio wave C) a sound wave D) all of the above E) none of the above
As the temperature of a radiation emitting blackbody becomes lower, what happens to the peak wavelength of the radiation?
a. remains constant b. increases c. decreases d. is directly proportional to temperature
A normal lapse rate of 3.5 °F/1000 ft is equivalent to
a. 3.5 °C/m. b. 1.9 °C/1000 ft. c. 3.5 °C/1000 ft. d. 6.5 °C/1000 ft.
To find an image by ray tracing requires
A) four rays. B) two rays. C) eight rays. D) three rays. E) only one ray.