You are an engineer working in a company that plans to manufacture 100-mm by 50-mm thin rectangular electronic devices.

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You are an engineer working in a company that plans to
manufacture 100-mm by 50-mm thin rectangular electronic devices.
The top surface of the electronic device is to be made of aluminum
and attached with an array of aluminum pin fins. The electronic
device generates 50 W of heat that has to be dissipated through the
fins. To prevent the electronic device from overheating the top
surface temperature should be kept below 85 o C in an ambient
surrounding of 30 oC with film heat transfer coefficients of 15
W/m2 oC. Assuming a square array, determine suitable combinations
of number of fins, fin spacing and fin dimension (diameter and
length) to accomplish this cooling at minimum weight/cost of
aluminum.