Thermodynamics HW Solutions 558

Thermodynamics HW Solutions 558 - T s = 60 C 20 W The...

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Chapter 7 External Forced Convection 7-28 A fan blows air parallel to the passages between the fins of a heat sink attached to a transformer. The minimum free-stream velocity that the fan should provide to avoid overheating is to be determined. Assumptions 1 Steady operating conditions exist. 2 The critical Reynolds number is Re cr = 5 × 10 5 . 3 Radiation effects are negligible. 4 The fins and the base plate are nearly isothermal (fin efficiency is equal to 1) 5 Air is an ideal gas with constant properties. 6 The local atmospheric pressure is 1 atm. Properties The properties of air at 1 atm and the film temperature of (T s + T )/2 = (60+25)/2 = 42.5 ° C are (Table A-15) 7248 . 0 Pr /s m 10 726 . 1 C W/m. 02681 . 0 2 5 - = × = ° = υ k Analysis The total heat transfer surface area for this finned surface is 2 2 2 unfinned s, finned s, total s, 2 unfinned s, 2 finned s, m 0.0118 = m 0.0048 + m 007 . 0 m 0.0048 m) m)(0.1 002 . 0 ( 7 - m) m)(0.062 1 . 0 ( m 0.007 = m) m)(0.005 1 . 0 )( 7 2 ( = + = = × = × = A A A A A Air V T = 25 ° C L = 10 cm
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Unformatted text preview: T s = 60 C 20 W The convection heat transfer coefficient can be determined from Newton's law of cooling relation for a finned surface. C . W/m 43 . 48 C 25)-)(60 m (1)(0.0118 W 20 ) ( ) ( 2 2 = = = = s s s s T T A Q h T T hA Q & & Starting from heat transfer coefficient, Nusselt number, Reynolds number and finally free-stream velocity will be determined. We assume the flow is laminar over the entire finned surface of the transformer. 4 3 / 2 2 2 3 / 2 2 2 3 / 1 5 . 2 10 171 . 9 ) 7248 . ( ) 664 . ( ) 6 . 180 ( Pr 664 . Re Pr Re 664 . 6 . 180 C W/m. 02681 . m) C)(0.1 . W/m 43 . 48 ( = = = = = = = Nu Nu k hL Nu L L m/s 15.83 = = = = m 1 . ) /s m 10 726 . 1 )( 10 171 . 9 ( Re Re 2 5 4 L L L L V V 7-20...
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This note was uploaded on 01/22/2012 for the course PHY 4803 taught by Professor Dr.danielarenas during the Fall '10 term at UNF.

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