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Thermodynamics HW Solutions 782

# Thermodynamics HW Solutions 782 - Chapter 9 Natural...

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Unformatted text preview: Chapter 9 Natural Convection 9-109 A group of 25 transistors are cooled by attaching them to a square aluminum plate and mounting the plate on the wall of a room. The required size of the plate to limit the surface temperature to 50 ° C is to be determined. Assumptions 1 Steady operating conditions exist. 2 Air is an ideal gas with constant properties. 3 The local atmospheric pressure is 1 atm. 4 Any heat transfer from the back side of the plate is negligible. Properties The properties of air at 1 atm and the film temperature of ( T s + T ∞ )/2 = (50+30)/2 = 40 ° C are (Table A-15) Transistors, 25 × 1.5 W ε = 0.9 T s = 50 ° C Room 30 ° C Plate L × L 1- 2 5 K 003195 . K ) 273 40 ( 1 1 7255 . Pr /s m 10 702 . 1 C W/m. 02662 . = + = = = × = ° = − f T k β υ Analysis The Rayleigh number can be determined in terms of the characteristic length (length of the plate) to be 3 9 2 2 5 3-1 2 2 3 10 571 . 1 ) 7255 . ( ) /s m 10 702 . 1 ( ) )( K 30 50 )( K 003195 . )( m/s 81 . 9 ( Pr )...
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