Thermodynamics HW Solutions 702

Thermodynamics HW Solutions 702 - [ ] 15 . 13 7245 . / 559...

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Chapter 9 Natural Convection 9-16 A horizontal hot water pipe passes through a large room. The rate of heat loss from the pipe by natural convection and radiation 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 The temperature of the outer surface of the pipe is constant. Properties The properties of air at 1 atm and the film temperature of ( T s + T )/2 = (65+22)/2 = 43.5 ° C are (Table A-15) Air T = 22 ° C Pipe T s = 65 ° C ε = 0.8 L =10 m D = 6 cm 1 - 2 5 K 00316 . 0 K ) 273 5 . 43 ( 1 1 7245 . 0 Pr /s m 10 735 . 1 C W/m. 02688 . 0 = + = = = × = ° = f T k β υ Analysis ( a ) The characteristic length in this case is the outer diameter of the pipe, Then, m. 06 . 0 = = D L c 805 , 692 ) 7245 . 0 ( ) /s m 10 735 . 1 ( ) m 06 . 0 )( K 22 65 )( K 00316 . 0 )( m/s 81 . 9 ( Pr ) ( 2 2 5 3 -1 2 2 3 = × = = D T T g Ra s () [] ()
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Unformatted text preview: [ ] 15 . 13 7245 . / 559 . 1 ) 805 , 692 ( 387 . 6 . Pr / 559 . 1 387 . 6 . 2 27 / 8 16 / 9 6 / 1 2 27 / 8 16 / 9 6 / 1 = + + = + + = Ra Nu 2 2 m 885 . 1 ) m 10 )( m 06 . ( C . W/m 893 . 5 ) 15 . 13 ( m 06 . C W/m. 02688 . = = = = = = DL A Nu D k h s W 477.6 = = = C ) 22 65 )( m 885 . 1 )( C . W/m 893 . 5 ( ) ( 2 2 T T hA Q s s & ( b ) The radiation heat loss from the pipe is [ ] W 468.4 = + + = = 4 4 4 2 8 2 4 4 ) K 273 22 ( ) K 273 65 ( ) .K W/m 10 67 . 5 )( m 885 . 1 )( 8 . ( ) ( surr s s rad T T A Q & 9-3...
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