Thermodynamics HW Solutions 644

Thermodynamics HW Solutions 644 - W 9 . 276 ) C 150 250 )(...

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Chapter 8 Internal Forced Convection 8-24 Combustion gases passing through a tube are used to vaporize waste water. The tube length and the rate of evaporation of water are to be determined. Assumptions 1 Steady operating conditions exist. 2 The surface temperature of the pipe is constant. 3 The thermal resistance of the pipe is negligible. 4 Air properties are to be used for exhaust gases. Properties The properties of air at the average temperature of (250+150)/2=200 ° C are (Table A-15) kJ/kg.K 287 . 0 C J/kg. 1023 = ° = R C p Also, the heat of vaporization of water at 1 atm or 100 ° C is kJ/kg 2257 = fg h . Analysis The density of air at the inlet and the mass flow rate of exhaust gases are 3 kg/m 7662 . 0 K) 273 250 ( kJ/kg.K) 287 . 0 ( kPa 115 = + = = ρ RT P kg/s 0.002708 = m/s) (5 4 m) (0.03 ) kg/m 7662 . 0 ( 4 2 3 2 π = π ρ = ρ = m m c D A m V V T s =110 ° C L D =3 cm Exh. gases 250 ° C 5 m/s 150 ° C The rate of heat transfer is
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Unformatted text preview: W 9 . 276 ) C 150 250 )( C J/kg. 1023 )( kg/s 002708 . ( ) ( = = = e i p T T C m Q & & The logarithmic mean temperature difference and the surface area are C 82 . 79 250 110 150 110 ln 250 150 ln ln = = = i s e s i e T T T T T T T 2 2 ln ln m 0.02891 ) C 82 . 79 )( C . W/m 120 ( W 9 . 276 = = = = T h Q A T hA Q s s & & Then the tube length becomes cm 30.7 = = = = = m 3067 . m) 03 . ( m 0.02891 2 D A L DL A s s The rate of evaporation of water is determined from kg/h 0.442 = kg/s 0001227 . kJ/kg) 2257 ( kW) 2769 . ( = = = = fg evap fg evap h Q m h m Q & & & & 8-6...
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