7-28 A transformer that is 10-cm long, 6.2-cm wide, and 5-cm high is to be cooled by attaching a 10-cm x 6.2-cm-wide polished aluminum heat sink (emissivity = 0.03) to its top surface. The heat sink hasseven fins, which are 5-mm high, 2-mm thick, and 10-cm long. A fan blows air at 25°C parallel to the passages between the fins. The heat sinkheat sink is not to exceed 60°C. 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 the fan needs tosupply to avoid overheating. Assume the flow is laminar over the entire finned surface of the transformer.to dissipate 12 W of heat, and the base temperature of theFIGURE P7-28Air25°C60°C-Fins0.5 cm10 cmTransformer5 cm12 W+6.2 cm -

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Asked Dec 11, 2019
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7-28 A transformer that is 10-cm long, 6.2-cm wide, and 5-cm high is to be cooled by attaching a 10-cm x 6.2-cm-wide polished aluminum heat sink (emissivity = 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 25°C parallel to the passages between the fins. The heat sink
heat sink is not to exceed 60°C. 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 the fan needs to
supply to avoid overheating. Assume the flow is laminar over the entire finned surface of the transformer.
to dissipate 12 W of heat, and the base temperature of the
FIGURE P7-28
Air
25°C
60°C
-Fins
0.5 cm
10 cm
Transformer
5 cm
12 W
+6.2 cm -
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7-28 A transformer that is 10-cm long, 6.2-cm wide, and 5-cm high is to be cooled by attaching a 10-cm x 6.2-cm-wide polished aluminum heat sink (emissivity = 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 25°C parallel to the passages between the fins. The heat sink heat sink is not to exceed 60°C. 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 the fan needs to supply to avoid overheating. Assume the flow is laminar over the entire finned surface of the transformer. to dissipate 12 W of heat, and the base temperature of the FIGURE P7-28 Air 25°C 60°C -Fins 0.5 cm 10 cm Transformer 5 cm 12 W +6.2 cm -

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Since the fins atie at the same tempenature as that of the base. Heat transfor rate from the finned swrface can be weitten as follows. Radiation is h As [Ts- To] neg ligi ble Qp finned surface

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As = Total surface area aualable for heat transfor. As = Asf t Asef Ast = Surface axeaof fins Asuf = Unfinned surface area . %3D %3D

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+ x2x (0-5 x10) + +x(2 x10x10) area of fins, Agf = +x2x(05 x10) + +x(2 x1o'ew) Sutare avea Asf = 84 Cm? Ast : 84 x1ó m Untinned surtace area (Asf) (10x6:2) – (+x 10 x 012) %3| = 48cm? (Ant) = 48 xió* m²

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