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Thermodynamics HW Solutions 729

Thermodynamics HW Solutions 729 - m(60 0603 C W/m 823 7 42...

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Chapter 9 Natural Convection 9-36 A steam pipe extended from one end of a plant to the other with no insulation on it. The rate of heat loss from the steam pipe and the annual cost of those heat losses are 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. Properties The properties of air at 1 atm and the film temperature of ( T s + T )/2 = (170+20)/2 = 95 ° C are (Table A-15) Steam L = 60 m D =6.03 cm T s = 170 ° C ε = 0.7 Air T = 20 ° C 1 - 2 5 K 002717 . 0 K ) 273 95 ( 1 1 7121 . 0 Pr /s m 10 252 . 2 C W/m. 0306 . 0 = + = = = × = ° = f T k β υ Analysis The characteristic length in this case is the outer diameter of the pipe, m 0.0603 = = D L c . Then, 6 2 2 5 3 -1 2 2 3 10 231 . 1 ) 7121 . 0 ( ) /s m 10 252 . 2 ( ) m 0603 . 0 )( K 20 170 )( K 002717 . 0 )( m/s 81 . 9 ( Pr ) ( × = × = = D T T g Ra s () [] () [] 42 . 15 7121 . 0 / 559 . 0 1 ) 10 231 . 1 ( 387 . 0 6 . 0 Pr / 559 . 0 1 387 . 0 6 . 0 2 27 / 8 16 / 9 6 / 1 6 2 27 / 8 16 / 9 6 / 1 = + × + = + + = Ra Nu 2 2 m 37 . 11 m)
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Unformatted text preview: m)(60 0603 . ( C . W/m 823 . 7 ) 42 . 15 ( m 0603 . C W/m. 0306 . = = = ° = ° = = ππ DL A Nu D k h s Then the total rate of heat transfer by natural convection and radiation becomes kW 27.4 = = + − + × + ° − ° = − + − = − ∞ W T T A T T hA Q surr s s s s 27,388 ] ) K 273 20 ( ) K 273 170 )[( .K W/m 10 67 . 5 )( m 37 . 11 )( 7 . ( C ) 20 170 )( m 37 . 11 )( C . W/m 823 . 7 ( ) ( ) ( 4 4 4 2 8 2 2 2 4 4 σε & The total amount of gas consumption and its cost during a one-year period is therms/yr 496 , 10 s/h) 3600 h/yr 8760 ( kJ 105,500 therm 1 78 . kJ/s 388 . 27 = × ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = η Δ = t Q Q gas & \$5647/yr = = therm) / 538 . )(\$ therms/yr 496 , 10 ( Cost 9-30...
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