Thermodynamics HW Solutions 561

Thermodynamics HW Solutions 561 - (4 Re × = × = υ = −...

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Chapter 7 External Forced Convection 7-31 Air is blown over an aluminum plate mounted on an array of power transistors. The number of transistors that can be placed on this plate 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 Heat transfer from the backside of the plate is negligible. 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 = (65+35)/2 = 50 ° C are (Table A-15) 7228 . 0 Pr /s m 10 798 . 1 C W/m. 02735 . 0 2 5 - = × = ° = υ k Transistors Air V = 4 m/s T = 35 ° C L = 25 cm T s = 65 ° C Note that the atmospheric pressure will only affect the kinematic viscosity. The atmospheric pressure in atm is P == (83. . 4 0823 kPa) 1 atm 101.325 kPa atm The kinematic viscosity at this atmospheric pressure will be /s m 10 184 . 2 823 . 0 / ) /s m 10 798 . 1 ( 2 5 2 5 × = × = υ The Reynolds number is 4 2 5 10 579 . 4 /s m 10 184 . 2 m) m/s)(0.25 (4
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Unformatted text preview: (4 Re × = × = υ = − ∞ L L V which is less than the critical Reynolds number (5 10 5 × ). Thus the flow is laminar. Using the proper relation in laminar flow for Nusselt number, the average heat transfer coefficient and the heat transfer rate are determined to be C . W/m 95 . 13 ) 5 . 127 ( m 25 . C W/m. 02735 . 5 . 127 ) 7228 . ( ) 10 579 . 4 ( 664 . Pr Re 664 . 2 3 / 1 5 . 4 3 / 1 5 . ° = ° = = = × = = = Nu L k h k hL Nu L W 26.2 = C 35)-)(65 m C)(0.0625 . W/m 95 . 13 ( ) ( m 0.0625 = m) m)(0.25 25 . ( 2 2 conv 2 ° ° = − = = = ∞ s s s T T hA Q wL A & Considering that each transistor dissipates 3 W of power, the number of transistors that can be placed on this plate becomes 4 ⎯→ ⎯ = = 4 . 4 W 6 W 2 . 26 n This result is conservative since the transistors will cause the flow to be turbulent, and the rate of heat transfer to be higher. 7-23...
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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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