Heat Chap10-072 - Chapter 10 Boiling and Condensation...

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Chapter 10 Boiling and Condensation Review Problems 10-72 Steam at a saturation temperature of T sat = 40 ° C condenses on the outside of a thin horizontal tube. Heat is transferred to the cooling water that enters the tube at 25 ° C and exits at 35 ° C. The rate of condensation of steam, the average overall heat transfer coefficient, and the tube length are to be determined. Assumptions 1 Steady operating conditions exist. 2 The tube can be taken to be isothermal at the bulk mean fluid temperature in the evaluation of the condensation heat transfer coefficient. 3 Liquid flow through the tube is fully developed. 4 The thickness and the thermal resistance of the tube is negligible. Properties The properties of water at the saturation temperature of 40 ° C are h fg = 2407 × 10 3 J/kg and ρ v = 0.05 kg/m 3 . The properties of liquid water at the film temperature of T T T f s = + = ( ) / sat 2 (50 + 20)/2 = 35 ° C and at the bulk fluid temperature of T T T b = + = ( ) / in out 2 (25 + 35)/2 = 30 ° C are (Table A-9), At 35 C: ° = = × = ⋅° = ⋅° - ρ μ l l pl l k 994 0 0 720 10 4178 0 623 3 3 . . . kg / m kg / m s C J / kg C W / m C At 30 C: ° = = = × = ⋅° = ⋅° - ν l l l l pl l k 996 0 0801 10 4178 0 615 3 6 . / . . kg / m m / s C J / kg C W / m C Pr = 5.42 2 Analysis The mass flow rate of water and the rate of heat transfer to the water are ( ( . / ] . ( ) ( . m A Q mC T T c p out in water 3 2 kg / m )(2 m / s)[ m) kg / s kg / s)(4178 J / kg C)(35 25) C = = = = = - = ⋅° - ° π V 996 0 03 4 1408 1408 58,820 W The modified latent heat of vaporization is h h C T T fg fg pl s * . ( ) = + - = × × ⋅° - ° × 0 68 2407 10 30) 10 3 3 sat J / kg + 0.68 4178 J / kg C(40 C = 2435 J / kg The heat transfer coefficient for condensation on a single horizontal tube is C W/m 9292 m) C(0.03 ) 30 40 ( s) kg/m 10 720 . 0 ( ) C W/m 623 . 0 )( J/kg 10 2435 )( kg/m 05 . 0 994 )( kg/m 994 )( m/s 8 . 9 ( 729 . 0 ) ( ) ( 729 . 0 2 4 / 1 3 3 3 3 3 2 4 / 1 sat 3 * horizontal ° = ° - × ° × - = - - = = - D T T k h g h h s l l fg v l l o The average heat transfer coefficient for flow inside the tube is determined as follows: Re ( , . Re Pr . ( , ) ( . ) ( . . . . . = = × = = = = = = ⋅° × = ⋅° V D h k D m i 2 74 906 0 023 0 023 74 906 542 359 0 615 7357 0 8 0 4 0 8 0 4 m / s)(0.03 m) 0.801 10 Nu Nu W / m C) 359 0.03 m W / m C -6 2 Noting that the thermal resistance of the tube is negligible, the overall heat transfer coefficient becomes U h h i o = + = + = ° 1 1 1 1 1 7357 1 9292 / / / / 4106 W / m . C 2 The logarithmic mean temperature difference is: T T T T T i e i o ln ln( / ) ln( / ) . = - = - = ° 15 5 15 5 910 C The tube length is determined from 10-60 Steam 40 ° C Condensate 25 ° C Cooling water 35 ° C
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Chapter 10 Boiling and Condensation m 16.7 = ° ° = = = C) 10 . 9 )( m 03 . 0 ( ) C W/m 4106 ( W 820 , 58 ) ( 2 ln ln π T D h Q L T hA Q s Note that the flow is turbulent, and thus the entry length in this case is 10D = 0.3 m is much shorter than the total tube length. This verifies our assumption of fully developed flow. 10-61
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Chapter 10 Boiling and Condensation 10-73 Saturated ammonia at a saturation temperature of T sat = 25 ° C condenses on the outer surface of vertical tube which is maintained at 15 ° C by circulating cooling water. The rate of heat transfer to the coolant and the rate of condensation of ammonia are to be determined.
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Heat Chap10-072 - Chapter 10 Boiling and Condensation...

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