A cylindrical power transistor that generates heat at a constant rate is kept cool by a set of 12 rectangular aluminum fins mounted radially as sketched in Fig. P.4.3. The transistor is 1 cm in radius and 5 cm tall. The fins are 1.0 mm thick, 3.0 cm long, and 5.0 cm tall. The ambient temperature is 30°C, and the convective heat transfer coefficient is 50.0 W/m² K. The steady-state temperature at the tip of the fins is measured and is 45°C. Heat transfer from the bare transistor surface can be neglected.

Assuming steady state, calculate:

(a) The transistor surface temperature for these conditions.

(b) The fin efficiency.

(c) The heat generated by the transistor.

(d) The fin efficiency if the fins above are replaced with 12 circular aluminum fins with the same thickness as the rectangular fins above and an outer radius of 4.0 cm.

(e) The transistor surface temperature that would be obtained with 12 circular fins as shown if the thickness is the same.

FIGURE P.4.3:

Transcribed Image Text:

25 2 cm 0 Top view Only one of 12 fins is shown. 8 cm IO Top view