An Empirical Modification of Nucleation Theory and Its Application to Boiling Heat Transfer Page: 17 of 38
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Equations (8) to (14) can be written in dimensionless form by select-
ing L, U, and es as the characteristic length, velocity, and temperature,
respectively. From these dimensionless equations and by noting that eddy
heat transfer is independent of x and z, the following parameters are ob-
tained for the determination of c/a near the wall:
PUZL Ap UL g#OL3 v c(e/es) a ThU TZU pcpes tU r*
6 ' pU2' v , 2 ' , (y/L)' L' L' L' PvX ' L' L (15)
If the liquid is subcooled, Eq. (14) would not be valid, but the parame-
ters derived therefrom still hold, except that an additional parameter,
namely, 0 /0s, must be taken into account.
The dimensionless temperature gradient in (15) represents the
Nusselt number and can be written as
L (e/0s)1 _ qL
(y/L) y k s
The time required for a bubble to grow from its critical to final
size depends on the ratio of the final to the critical diameter, D/Zr*. The
period of bubble generation from each site and the bubble spacing (or
number of bubble sites) are related to the rate of nucleation through the
following parameters, which are obtained from Eqs. (5), (6), and (7):
NA Ts 7 \2 G
Hr */U and (Ap KTs
For steady state, i.e., considerations being made for sufficient
length of time, the time parameter tU/L drops from (15). Thus there are
twelve parameters remaining to be considered in the determination of the
eddy thermal diffusivity and hence the heat transfer, namely,
pU2L Ap UL gj3sL3 y pcpes NAKT ( 6 z a D qL r*
a ' ' 2 ', PvX ' Hr*/U' \ yp/ ' TTcS' s' k s'L
The first five parameters are the well-known Weber, Euler, Reynolds,
Grashof, and Prandtl numbers, the sixth represents the effect of bubble
growth, and the seventh and eighth the effect of the nucleation, while the
others are self-explanatory.
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Chang, Y. P. An Empirical Modification of Nucleation Theory and Its Application to Boiling Heat Transfer, report, February 1, 1961; United States. (https://digital.library.unt.edu/ark:/67531/metadc863296/m1/17/: accessed May 26, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.