Heat Chap10-021 - Chapter 10 Boiling and Condensation 10-21...

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Chapter 10 Boiling and Condensation 10-21 Water is boiled at 1 atm pressure and thus at a saturation (or boiling) temperature of T sat = 100 ° C by a horizontal nickel plated copper heating element. The maximum (critical) heat flux and the temperature jump of the wire when the operating point jumps from nucleate boiling to film boiling regime are to be determined. Assumptions 1 Steady operating conditions exist. 2 Heat losses from the boiler are negligible. Properties The properties of water at the saturation temperature of 100 ° C are (Tables 10-1 and A-9) ρ σ l v l = = = = 957 9 0 60 0 0589 175 . . . . kg / m kg / m N / m Pr 3 3 h fg l pl = × = × = ⋅° - 2257 10 0 282 10 4217 3 3 J / kg kg m / s C J / kg C μ . Also, C sf = 0.0060 and n = 1.0 for the boiling of water on a nickel plated surface (Table 10-3 ). Note that we expressed the properties in units specified under Eqs. 10-2 and 10-3 in connection with their definitions in order to avoid unit manipulations. The vapor properties at the anticipated film temperature of T f = ( T s +T sat )/2 of 1000 ° C (will be checked) (Table A-16) s kg/m 10 762 . 4 C W/m 1362 . 0 C J/kg 2471 kg/m 1725 . 0 5 3 × = ° = ° = = - v v pv v k C Analysis ( a ) For a horizontal heating element, the coefficient C cr is determined from Table 10-4 to be 136 . 0 ) 60 . 0 ( 12 . 0 * 12 . 0 1.2 < 60 . 0 0589 . 0 60 . 0 9 . 957 ( 8 . 9 ) 0015 . 0 ( ) ( * 25 . 0 25 . 0 2 / 1 2 / 1 = = = = - = - = - - L C g L L cr v l Then the maximum or critical heat flux is determined from [ ( )] . ( )[ . . ( . ) ( . . )] max / / q C h g cr fg v l v = - = × × × - = σρ 2 1 4 3 2 1 4 0136 2257 10 0 0589 9 8 0 6 957 9 0 60 1,153,000 W / m 2 The Rohsenow relation which gives the nucleate boiling heat flux for a specified surface temperature can also be used to determine the surface temperature when the heat flux is given. Substituting the maximum heat flux into the Rohsenow relation together with other properties gives 3 sat , 2 / 1 nucleate Pr ) ( ) ( - - = n l fg sf s l p v l fg l h C T T C g h q 3 3 1/2 3 3 75 . 1 ) 10 2257 ( 0130 . 0 ) 100 ( 4217 0060 . 0 0.60) - 9.8(957.9 ) 10 )(2257 10 282 . 0 ( 000 , 153 , 1 × - × × = - s T It gives C 109.3 ° = s T ( b ) Heat transfer in the film boiling region can be expressed as 10-14 P = 1 atm q max T s Water, 100 ° C Heating element
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Chapter 10 Boiling and Condensation ) ( 4 3 ) ( ) ( )] ( 4 . 0 )[ ( 62 . 0 4 3 4 sat 4 sat 4 / 1 sat 3 rad film total T T T T T T D T T C h gk q q q s s s v sat s pv fg v l v v - + - - - + - = + = εσ μ ρ Substituting, [ ] 4 4 4 2 8 4 / 1 5 3 3 ) 273 100 ( ) 273 ( ) K W/m 10 67 . 5 )( 5 . 0 ( ) 100 ( ) 100 )( 003 . 0 )( 10 762 . 4 ( )] 100 ( 2471 4 . 0 10 2257 )[ 1725 . 0 9 . 957 )( 1723 . 0 ( ) 1362 . 0 ( 81 . 9 62 . 0 000 , 153 , 1 + - + × + - × - × - × + × - = - - s s s s T T T T Solving for the surface temperature gives T s = 1871 ° C. Therefore, the temperature jump of the wire when the operating point jumps from nucleate boiling to film boiling is Temperature jump: C 1762 ° = - = - = 109 1871 crit , film s, s T T T Note that the film temperature is (1871+100)/2=985 ° C, which is close enough to the assumed value of 1000 ° C for the evaluation of vapor paroperties.
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This homework help was uploaded on 03/19/2008 for the course ME 410 taught by Professor Benard during the Spring '08 term at Michigan State University.

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Heat Chap10-021 - Chapter 10 Boiling and Condensation 10-21...

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