Thermodynamics HW Solutions 629

Thermodynamics HW Solutions 629 - Chapter 7 External Forced...

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Chapter 7 External Forced Convection 7-99 Wind is blowing over the roof of a house. The rate of heat transfer through the roof and the cost of this heat loss for 14-h period are to be determined. Assumptions 1 Steady operating conditions exist. 2 The critical Reynolds number is Re cr = 5 × 10 5 . 3 Air is an ideal gas with constant properties. 4 The pressure of air is 1 atm. Properties Assuming a film temperature of 10 ° C, the properties of air are (Table A-15) T sky = 100 K Q & 7336 . 0 Pr /s m 10 426 . 1 C W/m. 02439 . 0 2 5 - = × = υ ° = k Analysis The Reynolds number is [] 7 2 5 10 338 . 2 /s m 10 426 . 1 m) (20 m/s ) 3600 / 1000 60 ( Re × = × × = υ = L V L which is greater than the critical Reynolds number. Thus we have combined laminar and turbulent flow. Then the Nusselt number and the heat transfer coefficient are determined to be Air V = 60 km/h T = 10 ° C T in = 20 ° C C . W/m 0 . 31 ) 10 542 . 2 ( m 20 C W/m. 02439 . 0 10 542 . 2 ) 7336 . 0 ]( 871 ) 10 338 . 2 ( 037 . 0 [ Pr ) 871 Re 037 . 0 ( 2 4 4 3 / 1 8 . 0 7 3 / 1 8 . 0 ° = × ° = = × = × = = = Nu L k h k hL Nu L
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