Heat Chap07-099 - Chapter 7 External Forced Convection 7-99...

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Q T sky = 100 K 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) 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 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 In steady operation, heat transfer from the room to the roof (by convection and radiation) must be equal to the heat transfer from the roof to the surroundings (by convection and radiation), which must be equal to the heat transfer through the roof by conduction. That is, Q Q Q Q = = = room to roof, conv+rad roof, cond roof to surroundings, conv+rad Taking the inner and outer surface temperatures of the roof to be T s,in and T s,out , respectively, the quantities above can be expressed as [ ] 4 , 4 4 2 8 2 , 2 2 4 , 4 , rad + conv roof, to room K) 273 ( K) 273 20 ( ) .K W/m 10 67 . 5 )( m 300 )( 9 . 0 ( C ) )(20 m C)(300 . W/m 5 ( ) ( ) ( + - + × + ° - ° = - + - = - in s in s in s room s in s room s i T T T T A T T A h Q σ ε m 15 . 0 ) m 300 )( C W/m. 2 ( , , 2 , , cond roof, out s in s out s in s s T T L T T kA Q - ° = - = [ ] 4 4 , 4 2 8 2 , 2 2 4 4 , , rad + conv surr, to roof K) 100 ( K) 273 ( ) .K W/m 10 67 . 5 )( m 300 )( 9 . 0 ( C ) 10 )( m C)(300 . W/m 0 . 31 ( ) ( ) ( - + × + ° - ° = - + - = - out s out s surr out s s surr out s s o T T T T A T T A h Q Solving the equations above simultaneously gives C 5 . 3 and C, 6 . 10 , W 025 , 28 , , ° = ° = = = out s in s T T Q kW 28.03 The total amount of natural gas consumption during a 14-hour period is therms 75 . 15 kJ 105,500 therm 1 85 . 0 ) s 3600 14 )( kJ/s 03 . 28 ( 85 . 0 85 . 0 = × = = = t Q Q Q total gas Finally, the money lost through the roof during that period is $9.45 = = ) therm / 60 . 0 $ therms)( 75 . 15 ( lost Money 7-84 Air V = 60 km/h T = 10 ° C T in = 20 ° C
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Chapter 7 External Forced Convection 7-100 Steam is flowing in a stainless steel pipe while air is flowing across the pipe. The rate of heat loss from the steam per unit length of the pipe is to be determined. Assumptions
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This homework help was uploaded on 03/19/2008 for the course ME 410 taught by Professor Benard during the Spring '08 term at Michigan State University.

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Heat Chap07-099 - Chapter 7 External Forced Convection 7-99...

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