TECHNICAL REPORT NO.
CORRELATION OF MAXIMUM HEAT FLUX DATA
FOR BOILING OF SATURATED LIQUIDS
BY
WARREN M. ROHSENOW and PETER GRIFFITH
FOR
THE OFFICE OF NAVAL RESEARCH
CONTRACT N5ori-07827
NR-035-267
D.I.C. PROJECT NUMBER 6627
MARCH 1, 1955
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CORRELATION OF MAXILW
IEAT FLUX DATA
FOR BOILING OF SATURATED LIQUIDS
by
arren M. Rohsenow * and Peter Griffith
Characteristic data for the boiling of single oamponent liquids
show in the region of transition fran nucleate boil ing to vapor film
boiling the existence of a maximum heat flux as the wall temperature,
henoe heat flux, is raised.
and
If electric heating is employed, the maximum
heat flux point usually coincides with a burnout point since the metal
surface temperature usually rises wiell above the melting point in attempt.ing to transfer this maximum heat flux after nucleate boiling changes to
vapor film type boiling.
These two terms - maximum heat flux and burnout
-- will be used interchangeably.
A correlation has been attempted by Addams(l)(2)
in which a
plot is made of
(q/A)max
V
v
h a g 1/5vs.
i
The quantity (q/A)mai'/ yhfg is an average velocity of vapor leaving the
heating surface and the quantity (a g)
was introduced merely to produce
a dimensionless group, which follows logically from dimensional analysis
if a and g are included as significant quantities.
Since it was observed(3) that bubbles "shoot" away frem a
surface perpendicularly fran vertical surfaces it appears that gravity
should perhaps not have a significant effect on the peak heat flux values.
Associate Professor of Mechanical Engineering, Massachusetts Institute of
Technology, Cambridge, Massachusetts.
Instructor of Mechanical Engineering, Massachusetts Institute of Teohnology,
Cambridge., Massachusetts.
The correYation methrl proposad here is
based on reasoning similar to that
used in developing the boilin, heat transfer correlation tmploying the
concept of a bubble Reynolds number(4)O.
Proposed Correlation
At present, no satisfactory peak heat flux correlation exists
which gives insight into the mechanism of vapor bindingo
However, it
is
possible to eliminate some variables and predict a qualitative effect for
the others o
The mechanism of transition to vapor binding may be visualized,
in qualitative terms, as follows.
bubbles form on certain spots
At the onset of nucleate boiling,
Under certain oonditiqns these bubbles
.e.ave due to the action of gravity and, under other conditions, to the
inertia of the surrounding liquid.
nearly independent of q/Ao
The size and frequency, however, are
As one goes to high q/A, the number of spots
at which bubbles form increases in direo't proportion to the q/A (5)a
At
some point the spacing of the bubbles becomes so small that neighboring
bubbles join and the surface becomes partially covered with vapor, thus
suddenly decreasing q/A at that point if the wall temperature is held
constant.
The maximum heat flux exists just before the transition fran
nucleate to film boiling occurs,,
With this physical picture in mind, it becomes possible to
postulate a "burnout" criterion.
Imagine an idealized condition on the
surface such that the vapor bubbles touch each other as sketched in Fig. 1
.Considering this to be the vapor binding conditions, the number, "n",
places on the surface at which bubbles form is equal to
/Db per unit
of
length or 1/%2 per unit area. We can say then that the criterion for
q/A)
or burnout is
n=
Cvb
b
Db2
(1)
where Cyb is -unity for the condition of touching bubbles shown in Fig. I
but is probably les than unity when burnout actually occurs.
The heat
transfer to the bubbles was shown(4) to be proportional to q/A)ttgo
4
a q hf
where "f" is the frequency.
n
Db3 f
Then
(2)
Jakob(6) found that the time interval during
which a bubble grows on a surface and becomes detached approximately equals
the time interval required to form a new bubble at the particular point
on the surface.
He also observed that the distance of the center of
gravity of the bubble above the heater strip increased almost linearly
with time.
The total time interval elapsed is 1/f and the distance
traversed is Db; hence the bubble velocity at detaohment is
Db
~
tb
Yb
Thus, ve oan put Equation (1) into Equation (2)
q/A).,
I
I
(f
D)
(4C
where f Db a the bubble velocity.
The diameter of the bubble at departure is dependent on the
mechanism of departure.
Since our knowledge of this mechanism is quite
inognplete, we are unable to ocmplete this correlation.
Jakob(6) found
M
4
-
that f Db was nearly the same for boiling CC1
mately to 920
ft/hro
sa
20 and equal approxi-
If this is universally true, a burnout criterion
might be
(q/A)
-
vf~g (Db
where (
vs0
is a bouyancy term which varies inversely with pressure
and hence is essentially a pressure effect.
Actually, since f Db is taken
as a constant, it is omitted in the plot shown in Fig0 2 which includes
data of Cichelli and Bonilla(7), Addcs(4), and Braunlich(8).
abscissa as plotted has units of ft/hr.
like the dimensionless quantity.
Then the
Nevertheless, the quantity behaves
It could actually have been made dimen-
sionless by dividing the plotted nunber by 920 ft/hr. 'This seemed like
an unnecessary stepl thus it was not taken.
The deviation of the data from the suggested correlation line
in Fig. 2 is only slightly less than in Addams' correlation.
This is due
to the fact that (aJg)l/3 for the range of data considered varied only by
a factor of approximately 2.
It should be noted that in both the present correlation and the
Addoms correlation (q/A)a varies by a factor of about 30 hf
(f-
) by about 3 end 3 V by about 1500a
Since
by about 4,
'V is by far the strong-
est variable and it appears in both abscissa and ordinate, the data tend
toward a slope of unity.
(q/A)
Further. since the quantity of interest is
which appears only in the ordinate, the percentage deviation fram
the correlation curve represents the degree of correlation of (q/A)
A pl ot of
max
4
-
5
(q/A)
shows the same deviation as the plot in Fig0 2,
The equation of the straight line drawn through the data points
on Fig 4 2 is
(q/A) ma-x
0,6
? 143 ()
ft/hr
()
with an approximation deviation range of about + 11%.
NGaENCLATURE
a
- thermal diffusivity of liquid, k/jo
o
- specific heat
f
- frequency with which bubbles form and depart at a point on the
heating surface
- acceleration of gravity
h
- latent enthalpy change during evaporation
k
- thermal conductivity
n
- muber of places on surface at which bubbles form per unit area
g/A-
heat transfer rate per unit area
0q
coefficient in Equation (2)
Cvb
Db
coefficient in Equation (1)
bubble diameter at deparbure fran surface
density of vapor
v
-
density of liquid
REFEMSUCES
1.
Addans J. N., SeD thesis, Chemioal Engineering Departent, Llass.
Inst. of Tech., 1948.
2.
*Heat Tranuaission," by W. H. MoAdamso UoOrawHIll, 1954, Ord
Edition, Fig. 1448
B. "Study of MNohni of Boiling Beat Transfer," by W. U. RohsenOw
and J. A. Clark, ASME Trans., vol. 73, 1961, pp. 609*620.
4.
"A Method of Correlating Heat Transfer Data for Surfam Boiling of
Liquids," by W. M. Rohsenow, ASI Trans., vol. 74, No. 8, Aug.
1962.
5.
"Reet Transfer," by M. Jakob,
6.
"Heat Transfer," by M. Jakob, %,107,
7.
Ciohelli, M. T., and C. F. Bonilla, Trans. AIMhE, 1946, vol. 41, p. 766.
8.
Branlich, R. H., Thesis, Chenical Engineering Department, Mass.
Inst. of Teoh., 1941.
eliey, 1049, p. 627.
Fs1I
1049, p. 6838.
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