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 C in an ambient surrounding of 30 C with film heat transfer coefficients of 15 W/m C. 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. Assume uniform value of h for both the fin and wall surface.