Thermodynamics HW Solutions 781

Thermodynamics HW Solutions 781 - + + = Nu 2 2 m 5 . 1 ) m...

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Chapter 9 Natural Convection 9-108 A hot part of the vertical front section of a natural gas furnace in a plant is considered. The rate of heat loss from this section and the annual cost of this heat loss 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. 4 Any heat transfer from other surfaces of the tank is disregarded. Properties The properties of air at 1 atm and the film temperature of ( T s + T )/2 = (110+25)/2 = 67.5 ° C are (Table A-15) 1 - 2 5 K 002937 . 0 K ) 273 5 . 67 ( 1 1 7184 . 0 Pr /s m 10 97 . 1 C W/m. 02863 . 0 = + = = = × = ° = f T k β υ Analysis The characteristic length in this case is the height of that section of furnace, L c = L = 15 m. Then, ε = 0.7 T s = 110 ° C Room 25 ° C Plate on furnace 1.5 m × 1.5 m 10 2 2 5 3 -1 2 2 3 10 530 . 1 ) 7184 . 0 ( ) /s m 10 97 . 1 ( ) m 5 . 1 )( K 25 110 )( K 002937 . 0 )( m/s 81 . 9 ( Pr ) ( × = × = = L T T g Ra s 1 . 289 7184 . 0 492 . 0 1 ) 10 530 . 1 ( 387 . 0 825 . 0 Pr 492 . 0 1 Ra 387 . 0 825 . 0 2 27 / 8 16 / 9 6 / 1 10 2 27 / 8 16 / 9 6 / 1 = + × + =
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Unformatted text preview: + + = Nu 2 2 m 5 . 1 ) m 5 . 1 )( m 1 ( C . W/m 518 . 5 ) 1 . 289 ( m 5 . 1 C W/m. 02863 . = = = = = s A Nu L k h and W 5 . 703 C ) 25 110 )( m 5 . 1 )( C . W/m 518 . 5 ( ) ( 2 2 = = = T T hA Q s s & The radiation heat loss is W 812 ] ) K 273 25 ( ) K 273 110 )[( .K W/m 10 67 . 5 )( m 5 . 1 )( 7 . ( ) ( 4 4 4 2 8 2 4 4 = + + = = s surr s rad T T A Q & W 1515 = + = 812 5 . 703 total Q & The amount and cost of natural gas used to overcome this heat loss per year is kJ 10 14 . 2 s/hr) 3600 hr/day 10 days/yr 310 ( 0.79 kJ/s) 5151 . 1 ( 79 . 7 = = = = t Q t Q Q total gas gas & & $152.2 = = .75/therm) therm)($0 500 , 105 / 10 14 . 2 ( Cost 7 9-105...
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This note was uploaded on 01/24/2012 for the course PHY 4803 taught by Professor Dr.danielarenas during the Fall '10 term at UNF.

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