Rectangular fins with k = 250W/mK and thickness t=2 mm and length L = 3cm are on

Question

Rectangular fins with k = 250W/mK and thickness t=2 mm and length L = 3cm are on a 2cm times 2cm chip base. The chip base is 5mm thick, is made of material with k = 2.5 W/mK and puts out 20W total power. Air at 25 degree C flowing around the fins induces a heat transfer coefficient of 150 W/m^2K. There are 5 fins and 5 2mm spacing's (see picture below). You may assume the back and sides of the chip are insulated. Find the base temperature. If the maximum temperature in the chip cannot exceed 90 degree C. will this design work? Prove it.

Explanation / Answer

The answer of following question is as follows.

The base temperature is 56 degree C

Yes the design will work.

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