7-32 A transformer that is 10 CM long, 6. 2 CM wide, and 5 CM high is to be cooled by attaching a 10-CM by 6. 2-CM wide polished aluminum heat sink (emissive = 0. 03) to its top surface. The heat sink has seven fins, which are 5 mm high , 2 mm thick, and 10 CM long.
A fan blows air at ICC parallel to the passages between the fins. The heat sink is to dissipate 12 W of heat and the base temperature of the heat sink is not to exceed ICC. Assuming the fins and the base plate to be nearly isothermal and the radiation heat transfer to be negligible, determine the minimum free-stream velocity he fan needs to supply to avoid overheating.With the simplifying assumptions given in this problem, we really have a problem of 7 flat plates with heat transfer from two sides. The spaces at the base of the fins also form flat plates.
So we find the heat transfer from one flat plate with a total area of all the fins plus the unified surface at the base of the fins. We have to work this problem in reverse. We are essentially given the required heat transfer - the IOW that the transformer has to dissipate - ND data on the fin area, and the temperature difference.We can therefore compute the heat transfer coefficient and work backwards to find the air velocity. The flat plates in this case have a length of 10 CM and a width of 0.
5 CM. The total area from one side of one fin is (0. 005 m)(O. 1 m) = 0. 0005 mm. There are 14 such sides giving an area of 0.
007 mm. In addition, the total area at the top of the transformer is (0. 1 m) (0. 062 m) = 0. 0062 mm. The bases of the seven fins take up an area.
