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6.4. The Onset of Nucleate Boiling

In a similar fashion to pool boiling heat transfer if the wall temperature rises sufficiently above the local saturation temperature pre-existing vapor in wall sites can nucleate and grow. This temperature, tex2html_wrap_inline5168 , marks the onset of nucleate boiling for this flow boiling situation. From the standpoint of an energy balance this occurs at a particular axial location along the tube length, tex2html_wrap_inline5170 . Once again for a uniform flux condition, Equ (2) becomes

equation2421

We can arrange this energy balance to emphasize the necessary superheat above saturation for the onset of nucleate boiling tex2html_wrap_inline5172

equation2432

Now that we have a relation between tex2html_wrap_inline5174 and tex2html_wrap_inline5176 we must provide a stability model for the onset of nucleate boiling. In a manner similar to the pool boiling situation one can formulate this model based on the metastable condition of the vapor nuclei ready to grow into the world. There are a number of correlation models for this stability line of tex2html_wrap_inline5174 . Using this approach, Bergles and Rohsenow (1964) obtained an equation for the wall superheat required for the onset of subcooled boiling. Their equation is valid for water only, given by

equation2445

where q;SPMquot; is the surface heat flux in tex2html_wrap_inline5182 and p is the system pressure in bar. An alternative expression by Davis and Anderson (1966) valid for all fluids is:

equation2455

where tex2html_wrap_inline4932 is the liquid-vapor surface tension, Equations (10) and (11) are in good agreement with each other for the case of high pressure water flows. Frost and Dzakowic (1967) have extended this treatment to cover other liquids. In their study nucleation was assumed to occur when the liquid temperature, T (y) was matched to the temperature for bubble equilibrium, tex2html_wrap_inline4926 , at a distance tex2html_wrap_inline5192 where tex2html_wrap_inline5194 rather than tex2html_wrap_inline4982 used in past work. Thus Eq. (11) becomes:

equation2472

We would recommend this final general expression to be used with the energy balance to determine tex2html_wrap_inline5174 and tex2html_wrap_inline5176 for a specified uniform heat flux. In the case of a known wall temperature one can find the heat flux at the onset of nucleate boiling as well as its corresponding location.


next up previous contents
Next: Subcooled Boiling Up: FLOW BOILING HEAT TRANSFER Previous: Single-Phase Liquid Heat Transfer


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