HW1Problem2

HW1Problem2 - The hot channel in a PWR operates under the...

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Boiling Heat Transfer 17 1 The hot channel in a PWR operates under the conditions given below. Compute and compare the outer clad temperature distribution assuming the Jens-Lottes and Thom correlation in the nucleate boiling region and the Bergles and Rosenhow correlation in the mixed boiling region. You may assume an axial heat flux profile of the form + = e H z q z q ) ( sin ) ( 0 λ π Problem Parameters Maximum channel heat flux 474,500 Btu/hr-ft 2 Channel Mass Flux 2.48 x 10 6 lbm/hr-ft 2 Inlet Temperature 552 F Channel Pressure 2250 psia Rod Pitch 0.496 inches Rod Diameter 0.374 inches Rod Height 144 inches Axial Peak to Average Ratio 1.5 SOLUTION Heat Flux The heat flux profile is in terms of two unknown parameters, the extrapolation distance and the amplitude 0 q . The extrapolation distance is determined by the axial peak to average ratio. The amplitude sets the magnitude of the heat flux. Extrapolation Distance The axial peak to average ratio is defined to be q z q F z ) ( max where max z is the position of maximum heat flux in a particular channel, and q is the axially averaged heat flux in the same channel. Note, that since for any given channel ) ( max z q and q both contain the amplitude 0 q , this parameter cancels and the axial peak to average ratio is only a function of shape. The position of maximum heat flux is that location such that 0 max = z q dz d For this heat flux profile, the maximum heat flux occurs at 2 H , such that 500 , 474 ) ( max max 0 = = = q z q q Btu/hr-ft 2 . The axially averaged heat flux is defined to be
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Boiling Heat Transfer 17 2 dz H z q H dz z q H q e H H + = λ π 0 0 0 sin 1 ) ( 1 + = e e e H H H H H q q ) ( cos cos 0 The axial peaking factor is then + = e e e z H H H H H F ) ( cos cos For 2 + H H e , this expression is transcendental in and must be solved iteratively. Iterating on gives feet. 3009 . 0 = Coolant Enthalpy and Temperature Distributions The coolant enthalpy distribution is given by + = z z Dd z q m h z h 0 ) ( 1 ) 0 ( ) ( ± which for the heat flux profile given here yields + + = e e e H z H m D H q h z h ) ( cos cos ) 0 ( ) ( 0 ± and is valid over the entire channel height.
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HW1Problem2 - The hot channel in a PWR operates under the...

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