There's a fin array made of 2024 T-6 aluminum. Each fin is 12mm long, 2mm thick, and they are spaced 5mm apart (actual distance between two fins, not centerline to centerline). Assume the entire array is 5cm tall. The array is surrounded by air at 20°C, which is blown over the array by a fan producing an average heat transfer coefficient of 25W/m^2-C.
a) This array is attached to an electronic component in a control box for a huge kettle in which beer is being brewed. The device operates at 40°C, and the fin array dissipates heat. How much heat does this array dissipate under these conditions? (Ignore contact resistance in this problem and assume the array base is 40°C)
b) Now suppose the fan fails and h drops to 10W/m^2-C. The component still produces the same power that must be dissipated. How hot does the component become?