Thermodynamics HW Solutions 559

Thermodynamics HW Solutions 559 - Chapter 7 External Forced...

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Chapter 7 External Forced Convection 7-29 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 The fins and the base plate are nearly isothermal (fin efficiency is equal to 1) 4 Air is an ideal gas with constant properties. 5 The local atmospheric pressure is 1 atm. Properties The properties of air at 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 We first need to determine radiation heat transfer rate. Note that we will use the base area and we assume the temperature of the surrounding surfaces are at the same temperature with the air ( T surr = ° 25 C ) Air V T = 25 ° C L = 10 cm T s = 60 ° C 20 W W 1.4 ] K) 273 25 ( K) 273 60 )[( C . W/m 10 67 . 5 ( m)] m)(0.062 1 . 0 )[( 90 . 0 ( ) ( 4 4 2 8 4 4 = + + ° × = = surr s s rad T T A Q σε & The heat transfer rate by convection will be 1.4 W less than total rate of heat transfer from the transformer.
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