A 45-W power integrated circuit chip mounted on an insulated circuit board is to be kept at its maximum operating temperature of 70°C using five identical straight rectangular aluminum-alloy fins (k = 150 W/m K), 1 mm thick and 4 cm wide, as sketched below. Air at 20°C is circulated through and around the fins by a fan yielding a convective heat transfer coefficient h = 80 W/m² K.

(a) Determine what the transistor temperature would be if no fins were used.

(b) Determine the fin length that is required to keep the transistor at 70°C and estimate the corresponding fin efficiency.

FIGURE P.4.4:

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Chip mounted on insulated circuit board - 2.5 cm - 4.0 cm