An Empirical Modification of Nucleation Theory and Its Application to Boiling Heat Transfer Page: 31 of 38
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11. PHYSICAL INTERPRETATION OF EQ. (zi)
Equation (21) was obtained by dimensional analysis of the equations
of conservation and the necessary boundary conditions, and by the concept
of an eddy thermal diffusivity, which was introduced without looking into the
detailed mechanism of boiling heat transfer. To see how the heat is being
transferred, it is convenient to write Eq. (21) in the following form:
q = C[pcpGs[ H e -in
Quantities inside the first bracket on the right side of this equation can be
considered as proportional to the heat exchange between saturated and
superheated liquid near the heater as propelled by the growing bubbles,
while those inside the second bracket as proportional to the velocity of
this exchange. This confirms, at least in some respect, the "vapor-liquid
exchange" mechanism which was recently proposed by Forster and Grief.(3)
Equation (21) can also be written in the form
where quantities with a bar denote their temporal mean values and the
prime indicates the deviation from the mean value Thus G' is the fluctu-
ating temperature and v' the fluctuating velocity component in the direction
normal to the heating surface. It follows that the boiling heat transfer can
be solved according to Prandtl missing length concept, and an analogy
between momentum and heat transfer in boiling can be established
12. MAXIMUM NUCLEATION
The value of the nucleation function increases at the increase of
superheat, but it has a limit as the exponential function approaches to
unity. This limit should represent the maximum rate of bubble generation
from unit area of the heating surface for a given system. Beyond this
limit, further increase of superheat will cause instability of vapor bubbles,
and the process of heat transfer changes from nucleate boiling to partial
film boiling, as pointed out previously. For example, in the case of boiling
of benzene from a chromium-plated surface in a pool (see Fig. 3) this con-
dition would occur at the superheat of about 80"F under a pressure of one
atmosphere and of about 453F at a pressure of 115 psia. Instead, in the
case of boiling of benzene, from a rough surface (see Fig. 5) this condition
would occur at a considerably larger superbeat, for the value of n is Larger
than that of smooth surface, as can be seen from Table II. In reality, how-
ever, the first critical condition occurs, in general, at a superheat much
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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/m1/31/: accessed May 25, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.