HEFAT2002
1 ST international Conference on Heat Transfer, Fluid Dynamics and Thermodynamics
8-10 April 2002, Kruger National Park, South Africa
KS1
INSIGHT INTO MECHANICSMS AND REVIEW OF AVAILABLE MODELS FOR
CRITICAL HEAT FLUX (CHF) IN POOL BOILING
Satish G. KANDLIKAR
Department of Mechanical Engineering
Rochester Institute of Technology
Rochester, NY 14623
[email protected]
ABSTRACT
Greek Symbols
Critical Heat Flux (CHF) has been a subject of interest for
boiling equipment designers from design as well safety as
viewpoints. Although considerable data exists in literature, a
fundamental knowledge of the mechanisms responsible for the
CHF phenomenon is needed to develop better predictive
methods and efficient enhancement strategies. A critical
assessment of the CHF models available in the literature is
presented here, highlighting the needs for future research in this
area.
φ - angle of inclination of the tube with horizontal
ψm - cavity mouth angle, degrees
µL – liquid viscosity, Ns/m2
θ - contact angle, degrees
ρ L , ρ G - liquid and vapor density, kg/m3
σ - surface tension, N/m
1. INTRODUCTION
NOMENCLATURE
Dc – cavity mouth diameter, m
g – acceleration due to gravity, m2/s
h – heat transfer coefficient, W/m2K
h L – single phase heat transfer coefficient with liquid phase,
W/m2K
iLG – latent heat of vaporization, J/kg
k – thermal conductivity, W/mK
K – contstant in eq. (4)
Na – number of active cavities, number/cm2
Nas – number of available cavities, number/cm2
q – heat flux, W/m2
q C – critical heat flux, W/m2
Tsat – saturation temperature, K
∆Tsat - wall superheat, K
∆Tsat,ONB - wall superheat at ONB, K
u- flow velocity, m/s
v LG – specific volume difference between vapor and liquid,
m3/kg
Critical Heat Flux, or CHF, represents the maximum heat
flux that can be dissipated by nucleate boiling. Any further
increase in the wall superheat leads into transition boiling mode
with deterioration in the accompanying heat transfer rate. In
heat flux controlled systems, CHF represents the point of
discontinuity where an increase in the heat flux causes a rapid
temperature excursion in the wall temperature, terminating
nucleate boiling and leading into film boiling mode of heat
transfer.
As early as in 1888, Lang [1] recognized through his
experiments with high pressure water that as the wall
temperature increased beyond a certain point, it resulted in a
reduction in the heat transfer rate in a nucleate boiling system.
However, it was Nukiyama [2] who realized that the “maximum
heat transmission rate” might occur at relatively modest
temperature differences. Drew and Mueller [3] present an
excellent summary of the historical development in this area. A
recent survey of the critical heat flux literature is presented by
Kandlikar [4].
2.
THERMAL AND HYDRODYNAMIC CONDITIONS
PRIOR TO CHF
required for the bubble to grow beyond the cavity opening,
(same as ∆Tsat ,ONB ), was obtained as
The models proposed in the literature are generally based on
the physical phenomena that are supported by experimental
evidence. A brief overview of the thermal and hydrodynamic
conditions existing on the heater surface prior to reaching CHF
is presented in this section.
2.1 Nucleation and Bubble Dynamics
Bubble Characteristics over the Nucleate Boiling Range:
The bubble characteristics during nucleate boiling was
investigated with a high-speed motion camera by Gaertner [5].
He identified different regions based on these characteristics as
illustrated in Fig. 1. In the initial phase of nucleate boiling,
discrete bubbles are formed over isolated cavities. As the heat
flux increases, the bubbles depart in rapid succession forming
vapor columns as shown in Fig. 1(b). Subsequently, the
neighboring vapor columns merge into a large bubble. This
large bubble is referred to as a vapor patch by Zuber [6], and as
a hovering bubble by Haramura and Katto [7]. The thin liquid
film existing under the large bubble is referred to as the
macrolayer. Existence of such macrolayer has been confirmed
by Kirby and Westwater [8] and Yu and Mesler [9]. Further
increase in the heat flux results in a broader coverage of the
heater surface with the large bubbles as shown in Fig. 1(c).
Subsequently, the critical heat flux is reached, beyond which
point, the degradation caused by the large vapor coverage
offsets the increase in the heat transfer due to rapid bubble
growth and efficient heat transfer in the macrolayer.
The focus of the present discussion is on the exact
mechanism that causes the transition from the region depicted
in Fig. 1(c) to the CHF condition.
Nucleation Site Density:
The key elements of pool boiling are bubble nucleation and
bubble growth followed by coalescence with neighboring
bubbles, and collapse or departure from the heater surface. For
a given wall superheat, the range of active cavity sizes is
determined by the cavity size distribution on the heater surface.
At high heat fluxes, a large number of small diameter cavities are
activated.
The size and shape of a cavity governs its nucleation
characteristics. Griffith and Wallis [10] postulated that as a
bubble grows in a cavity, it comes at the mouth of the cavity
and assumes a hemispherical shape. This state also represents
the point where the radius of curvature of the interface is a
minimum. The cavity is assumed to be active when a bubble
grows past this condition. Employing the Clasius-Clapeyron
equation for the pressure difference between the vapor inside
the bubble and the surrounding liquid, the wall superheat
Figure 1. Bubble characteristics in different regions of
nucleate boiling, Gaertner, [5].
∆Tsat,ONB =
4σ Tsat
ρV i LG Dc
(1)
where Dc is the cavity mouth diameter, m. It is seen that the wall
superheat to activate a cavity varies inversely with the cavity
diameter.
Smaller cavities are activated at higher wall
superheats.
Subsequently, Hsu [11] and Sato and Matsumura [12]
considered the temperature profile in the liquid and suggested
that the hemispherical bubble on a cavity will grow if the liquid
temperature at the tip of the bubble was above the saturation
temperature corresponding to the vapor pressure inside the
bubble. Assuming that cavities of all sizes are available, the
following expression for the wall superheat at the onset of
nucleate boiling, ONB, was obtained.
∆Tsat,ONB
4σ Tsat v LG h L
=
k L i LG

k L i LG ∆Tsub
1 + 1 +
2σ Tsat v LG h L


 (2)

Hsu, and Sato and Matsumura also obtained an expression for
the range of active cavity radii.
In deriving the above equation, the liquid temperature at the
bubble tip was calculated from the single-phase convection heat
transfer coefficient in the liquid phase. As boiling progresses,
the actual heat transfer coefficient increases progressively. It is
therefore expected that nucleation will progress toward smaller
cavity sizes more rapidly with an increase in the wall superheat.
Indeed, the nucleation site density increases rapidly with an
increase in the wall superheat. Nucleation is also facilitated by
the availability of vapor from neighboring sites. Following a
mechanistic approach, Wang and Dhir [13, 14] derived the
following relationship between the nucleation site density and
the wall superheat.
N s ( sites / cm2 ) = 5.8 ×10 −5 Dc
−5. 4
(3)
value of wall superheat. The conditions near the wall are
therefore very crowded with nucleating bubbles.
3. CHF MODELS
CONSIDERATIONS
•
•
•
•
•
•
Since the wall superheat is inversely proportional to the
cavity diameter, it follows that the nucleation site density varies
5 .4
∆Tsat
. Dhir [15] presented a plot showing this relationship
for different values of contact angle (θ ) and cavity mouth
opening angle (ψ m ). Figure 2 shows such a plot for a contact
as
angle of 18° and cavity mouth angles below 90°. It can be seen
that the number of active cavities increases quite dramatically
for smaller cavity diameters (on the order of a few micrometers).
Relating the active site density information to the critical
heat flux condition, it becomes clear that a large number of
cavities, with very small diameters, are activated at the high
ON
HYDRODYNAMIC
As the heat flux is increased to the critical heat flux value,
vapor generation rate increases and presents an increasing
resistance to the liquid flowing toward the heating surface. The
hydrodynamic models of CHF are based on the instability
encountered at the liquid-vapor interface. The exact location of
the interface where the instability sets in is somewhat different
in different models presented in literature:
•
Figure 2 Active nucleation site density variation with cavity
mouth diameter, Dc , for a contact angle θ =18° and cavity
mouth angle ψ m<90° , Nas – number of available cavities, Na –
number of active cavities, Liaw and Dhir [26].
BASED
Kutateladze [16, 17] – destruction of stability of twophase flow near the heater surface
Borishanskii [18] – liquid flowing coaxially in a
countercurrent manner
Zuber [19] – instability of a vapor patch over the heater
surface, CHF modeling from the transition boiling side
Chang [20] – considers a force balance on a bubble
attached to a vertical surface, relative velocity between
the rising bubble and the liquid reaches a critical value
at CHF
Moissis and Berenson [21] – instability in the vertical
vapor columns surrounded by the counterflow of
liquid flowing toward the heater surface
Katto and Yokoya [22] and Haramura and Katto [7] –
instability of vapor columns formed in the macrolayer,
dryout of the macrolayer
Sefiane et al. [23] – instability at the interface of an
evaporating meniscus at the base of a bubble
Perhaps not so surprisingly, all the above formulations,
with the exception of Sefiane et al.’s model (which presents a set
of equations), lead to a similar expression for the critical heat
flux as originally obtained by Kutateladze [17]. This shows that
all the instability models, irrespective of their physical model,
utilize the same functional groups in representing the instability
criterion for the liquid-vapor interface. A brief description of
these models is given below.
Kutateladze [16, 17] proposed that the meaning of bubble
generation and departure was lost near the critical heat flux
condition, which is essentially a hydrodynamic phenomenon
with the destruction of the stability of the two-phase flow
existing close to the heating surface. Critical condition is
reached when the velocity in the vapor phase reaches a critical
value. Following a dimensional analysis, he proposed the
following correlation.
qC′′
i LG ρ G
0. 5
[σ g ( ρ L − ρ G )]1 / 4
=K
(4)
The value of K was found to be 0.16 from the experimental data.
Borishanskii [18] modeled the problem by considering the
two-phase boundary in which liquid stream flowing coaxially
with gas experiences instability. His work lead to the following
equation for K in the Kutateladze’s equation, Eq. (4)


ρL σ 3/ 2
K = 0.13 + 4 2
1/2 
 µ [g (ρ L − ρ G )] 
−0. 4
(5)
Although viscosity appears in eq. (5), its overall effect is quite
small on CHF.
to 0.138. Simplifying the analysis further, Zuber proposed a
value of K=0.131.
Chang [20] performed a force balance on a single bubble,
close to its departure condition on a vertical surface. He
obtained the vapor rise velocity from an expression developed
for gas bubbles in a pool of liquid. The resulting departure
bubble radius and relative velocity between the two phases
were employed in defining the Weber number.
Chang
postulated that this Weber number reached a critical value at the
CHF condition. This resulted in the same expression as eq. (4),
with K=0.098. The CHF for vertical surfaces was taken to be 75
percent of the value predicted for a horizontal surface.
Moissis and Berenson [24] developed a model based on the
interaction of the continuous vapor columns with each other.
The maximum heat flux is then determined by introducing
Taylor-Helmholtz instability for the counterflow of vapor flow in
columns and liquid flow between them as shown in Fig. 4.
L
V
L
V
V
Figure 4
Moissis and Berenson’s [24] model with
countercurrent flow of liquid (L) between vapor columns (V)
adjacent to the heated wall.
Figure 3 Instability of a liquid-vapor interface over a heated
surface leading to vapor jets, Zuber [19].
Zuber [19] also postulated that vapor patches form and
collapse on the heater surface as CHF is approached.
According to Zuber, “In collapsing, ... [as] the vapor-liquid
interface of a patch approaches the heated surface, large rates
of evaporation occur and the interface is pushed violently
back.” Zuber considered the dynamic effects of vapor jets to be
important and proposed that the Taylor and Helmholtz
instabilities are responsible for the CHF condition. Figure 3
shows a heater surface covered with vapor after it has reached
the critical heat flux value. The progression from (a) through (f)
shows how the smooth interface experiences instability and
creates vapor jets and mushrooms. In Fig. 3(c), the liquid
fingers extend to the wall and are pushed back resulting in
vapor jets as shown in Fig. 3(f). Using the stability criterion of a
vapor sheet, Zuber obtained an equation similar to that of
Kutatelazde [17], but the value of constant K ranged from 0.157
Figure 5 Macrolayer evaporation model with vapor jet
instability within the macrolayer, Haramura and Katto [7].
Haramura and Katto [7] refined an earlier model proposed by
Katto and Yokoya [22] and proposed that the heat transfer is
related to formation and evaporation of a macrolayer under a
hovering vapor bubble as shown in Fig. 5. An expression for
the hovering period was obtained using the force balance
between the buoyancy and inertia forces.
Complete
evaporation of liquid in the macrolayer within the hovering time
leads to the critical heat flux condition. However, the thickness
of the macrolayer is unknown in this formulation. Haramura and
Katto considered the merger of the adjacent vapor stems to
result in pushing the bulk liquid away from the hovering bubble.
Combining with Zuber’s model for the critical heat flux,
Haramura and Katto obtained an expression for the thickness of
the macrolayer. This approach combines the hydrodynamic and
thermal aspects in a single model.
Sefiane et al. [23] considered the recoil forces in their
analysis of the liquid-vapor interface instability in the contact
line region. The rapid evaporation in this region generates a
recoil force due to the unbalanced momentum caused by the
velocity difference between the liquid and vapor phases at the
interface. This recoil force was assumed to create an instability
condition at the interface as shown in Fig. 6. A set of equations
was developed for predicting the interface motion and the
accompanying heat flux.
Vapor
Liquid
Stable
evaporating
interface
Perturbed
evaporating
interface
θ
Figure 6 A liquid-vapor interface near the contact line region
perturbed by the recoil forces, Sefiane et al. [23].
The models presented in this section are derived mainly on
the basis of hydrodynamic considerations. One of the major
drawbacks of these models is that the contact angle is not
considered to be a relevant parameter. However, it is well known
that the contact angle has a major influence on the CHF.
Gaertner’s [25] experiments clearly showed that the CHF value
was dramatically reduced for a surface coated with a nonwetting plastic (very high contact angle). The bubbles
coalesced and formed a vapor film underneath the liquid. Liaw
and Dhir [26] observed a similar trend over a contact angle
range of 0 to 108° for water boiling on a vertical plate. Although
Sefine et al.’s [23] analysis considers the contact angle effect,
the instability of the interface alone does not seem to be a
sufficient condition for CHF condition. Drying and rewetting
with considerable instability are constantly occurring during the
boiling process. A review of CHF models based on thermal
considerations is presented in the next section.
4.
CHF
MODELS
CONSIDERATIONS
BASED
ON
THERMAL
The CHF models based on hydrodynamic considerations
presented in Section 3 consider the instability of the liquidvapor interface that somehow prevents the liquid from reaching
the heater surface. In Zuber’s model, he considers the CHF from
the transition boiling side. A vapor film covers the heated
surface, and the instability of the interface causes liquid
wavelets to approach the heater surface. The rapid evaporation
of these wavelets causes the vapor to get violently pushed back
in the form of uniformly spaced jets. Although this describes
the transition boiling phenomenon, the initiation of the critical
heat flux condition is not entirely clear. Haramura and Katto
provide an explanation of how this condition is arrived at by
proposing the macrolayer evaporation theory. They postulate
that the CHF is reached when the macrolayer evaporates
completely. Using the Zuber’s correlation, they derived an
expression for the initial macrolayer thickness. The hovering
bubble in Haramura and Katto’s model represents the vapor
patch in the Zuber’s model. Haramura and Katto’s model thus
provides an explanation for the formation of the macrolayer (and
vapor patch in Zuber’s model), but it does not provide an
answer to the mechanism leading to the CHF condition.
The questions not addressed in the hydrodynamic models
are the liquid supply to the wall and the expansion of the
hovering vapor bubble. Further, the effect of contact angle on
CHF is not included. As seen from Gaertner’s [25] photographic
study and Liaw and Dhir’s [26] experimental investigation, CHF
reduces significantly as the contact angle increases. This leads
us to believe that the CHF is more intimately linked to the liquidvapor-solid interactions at the wall, where thermal effects are
important and need to be included in the modeling of CHF.
Sefiane et al. [23] present a model that addresses the contact
line region and the effect of contact angle to some extent. This
model includes the recoil forces that arise due to the momentum
change as liquid at the interface in the contact line region
evaporates into vapor. The higher vapor velocity results in an
unbalanced momentum, which provides a recoil force at the
interface. However, the instability of this interface initiated by
the recoil forces is assumed to lead to CHF. The exact sequence
of events that lead to the CHF condition following the
instability condition still remains unanswered.
5.
A NEW MODEL BASED ON CONTACT LINE
MOVEMENT CRITERION
Critical heat flux phenomenon occurs at the heater surface.
It occurs at speeds that are in the microseconds range as we see
the bubble growth and collapse information generated through
studies on the inkejet printers. With this is mind, although the
hydrodynamic conditions occurring at the interface of the
hovering bubble provide answers to the occasional contacts of
liquid with the heater surface, they are not able to describe the
mechanism responsible for the critical heat flux condition. The
motion of the interface at the contact line holds the key to
whether the vapor will push the liquid away, or the liquid front
will rewet the heater and release the bubble that is covering the
heater surface. A new model presented in the following sections
to include the effects of contact angle and the recoil forces in
determining the movement of the interface at the contact line.
5.1 Macrolayer Evaporation
The agglomeration of vapor in the vicinity of the wall
restricts the flow of liquid toward the heater surface. The
macrolayer under the bubble continues to evaporate. As seen
from Fig. 2, the number of active sites is very large at high wall
temperatures encountered near CHF. These sites are present in
the thin film as well. Presence of a thin film above nucleating
cavities would cause the bubbles to open up at the interface
thereby increasing the bubble frequency. Heat conduction
through the macrolayer is also quite efficient as the interface of
the film is at saturation temperature due to evaporation of liquid.
However, the limited availability of the liquid in the macrolayer
leads to its eventual dryout.
Figure 7 shows a high speed photograph of a liquid droplet
boiling on a glass plate. The picture is taken with a high speed
video camera looking from the underside of the glass plate. The
initial glass temperature is 170°C. A bubble is formed in the
liquid as identified by the four bright spots in Fig. 7(a). In the
next frame, 1 ms later, a dryout front appears in the center of the
bubble. The dryout front continues to expand in frame 7(c)
where it almost reaches the left edge of the bubble base. In
subsequent frames, the dryout front stops expanding and is
seen to recede causing the rewetting of the base. This happens
because the glass temperature has dropped considerably from
its initial high temperature. In this case, the dryout front could
not push the liquid-vapor interface further under the liquid
because of the lower surface temperature.
5.2 Model Description
Kandlikar [4] presented a model that incorporates the effects
of contact angle and recoil forces. Figure 8 shows a force
balance on a vapor bubble growing on a horizontal heated
surface. The interface is considered to be cylindrical in shape
with a unit length. A force balance is performed on the left half
of the cylinder. The surface tension forces act at the top of the
bubble, parallel to the heated wall, Fs,2, and at the heater surface,
along the interface in the contact line region, at an angle equal
to the contact angle θ. Fs,1 represents the component of the
surface tension force along the heater surface. The hydrostatic
pressure difference between the top and the bottom of the
bubble introduces a force due to gravity. The inertia forces are
neglected. A n additional force, FM, due to recoil is introduced to
represent the recoil force due to change in momentum as liquid
evaporates into vapor with a higher velocity.
FG
FS,2
Db
FM
Hb
θ
(a)
Figure 7 Development of a dryout front in the macrolayer
under a bubble inside an impinging droplet, viewed from the
bottom of a heated glass surface, successive frames 1 ms apart,
(a) a vapor bubble identified by four bright reflections, (b)
formation of a dryout front, (c) dryout front reaches the edge of
the bubble, (d)-(f) liquid rewets the dry spot.
Heater
surface
A
FS,1
Figure 8 Force balance on a bubble experiencing a high
evaporation rate in the vicinity of contact line region,
Kandlikar [4].
The heat transfer from the bubble is considered to cover an
area of twice the bubble diameter over the heater surface.
Critical heat flux condition is reached when the recoil force
overcomes the combined surface tension and hydrostatic forces
along the heater surface. The final expression for the critical
heat flux is given by:
CHF, W/m2
1,000,000
Figure 9 shows a comparison of the above model with the
experimental data from Lienhard and Dhir [27]. Kutateladze [27]
correlation is also shown in Fig. 9 for comparison. A contact
angle value of 45° is used. It can be seen that the Kandlikar
model given by eq. (6) predicts the data quite well over the
entire range of pressure.
The effect of contact angle on CHF was studied by Liaw and
Dhir for water on a vertical plate. Figure 10 shows a comparison
of the Kandlikar model and Kutateladze model with their data.
The Kutateladze correlation does not account for the contact
angle variation. The Kandlikar model is able to correctly predict
the CHF trend seen in the experimental data.
Lienhard and Dhir (1973)
Experimental data
Kutateladze (1951)
Distilled Water
Present model
Horizontal Plate
Liquid-Vapor
Interface
100,000
10
20
30
40
50
Vapor
Liquid
Pressure, kPa
Figure 9 Variaton of CHF with pressure for distilled water
boiling on a horizontal plate; comparison of present model,
Kandlikar [4], (using contact angle of 45 degrees) and
Kutateladze correlation with Lienhard and Dhir [27] data.
Motion of the
interface
A
(a)
10,000,000
Water
Vertical Plate
CHF, W/m2
Evaporating
Vapor
Liquid-Vapor
Interface
1,000,000
Liquid
Liaw and Dhir (1986)
Experimental data
Kutateladze (1951)
Vapor
Evaporating vapor
pushing the
interface in the
contact line region
Present model
A
100,000
0
20
40
60
80
100
120
Contact Angle, Degrees
(b)
Figure 10 Effect of contact angle on CHF for water boiling on a
vertical plate; comparison of present model and Kutateladze
correlation with Liaw and Dhir [26] data.
 1 + cos θ
q′C′ = iLG ρ G1/ 2 
 16
 2 π

 + (1 + cosθ ) cosφ 
 π 4

1/ 2
[σ g( ρ L − ρ G )]1/ 4
(6)
This model includes the contact angle, θ, and the orientation
angle of the heater with horizontal, φ.
Figure 11 A schematic representation of the changes in the
interface profile due to recoil forces, Kandlikar and Steinke
[28].
The interface geometry in the contact line region determines
the contact angle of the receding interface. The shape of the
interface in this region has been investigated by Kandlikar and
Steinke [28]. They obtained high-speed videos of the side
views of impinging liquid droplets on a heated surface. The
liquid drop spreads and recoils following the impact. The
dynamic advancing and receding contact angles were measured
during the spread and the recoil phases respectively. Figure 11
shows the contact angle variations with the heater surface
temperature. It is seen that the dynamic receding contact angle
undergoes a step change at a surface temperature around 135150°C and attains the same value as the dynamic advancing
contact angle. The change in the dynamic receding contact
angle is believed to be due to recoil forces resulting from high
evaporation rates in the contact line region. A schematic
representation of this behavior is illustrated in Fig. 12. The
contact angle increases due to recoil forces as the interface
recedes into the liquid, thereby allowing the vapor to cut under
the bulk of the liquid. This phenomenon has been termed as the
vapor cutback phenomenon by Kandlikar and Steinke [28].
2.
3.
4.
5.
6. CONCLUDING REMARKS
6.
The hydrodynamic models of the CHF phenomenon are
based on the instability of the interface as originally proposed
by Kutateladze [17], and then refined by Zuber [19] and Moissis
and Berenson.[21]. The formation of the macrolayer and the
vapor patch implicit in the Zuber’s model was explained by the
macrolayer dryout model by Haramura and Katto [7]. The major
concerns in the hydrodynamic models are: (a) the contact angle
effect on CHF is not considered, (b) the actual mechanisms of
CHF and transition boiling are not clearly explained.
As the heater surface temperature increases, many small
diameter (a few micrometers) cavities are activated. As a result,
the macrolayer under a vapor bubble evaporates rapidly and
provides a high heat transfer coefficient. The dryout spot under
a bubble has been observed by Kandlikar and Steinke [28]
through the underside of a heated glass plate. The dryout front
reached the edge of the bubble, but did not cause further
expansion of the bubble as the heater surface temperature was
not high enough. The vapor recoil forces and the associated
receding contact angle at the edge of the bubble (in the contact
line region) have been identified to play an important role in the
motion of the interface near CHF. The contact angle is seen to
change at temperatures near CHF condition. The theoretical
model developed by Kandlikar [4] based on thermal
considerations is able to correctly predict the effect of contact
angle and orientation on CHF.
Future research is needed to obtain additional data on the
effect of contact angle on the CHF. Another area of interest is
the measurement of the dynamic contact angles for different
fluids as the system approaches the CHF condition.
7.
8.
9.
10.
11.
12.
13.
14.
7. REFERENCES
1.
Lang, C., 1888, Transactions of Institute of Engineers and
Shipbuilders, Scotland, Vol. 32, pp. 279-295.
15.
Nukiyama, S., 1934, “Maximum and Minimum Values of Heat
Transmitted from a Metal to Boiling Water under
Atmospheric Pressure,” Japanese Society of Mechanical
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Drew, T.B., and Mueller, A.C., 1937, “Boiling,” Transactions
of AIChE, Vol. 33, pp. 449-471.
Kandlikar, S.G., 2000, “A Theoretical Model To Predict Pool
Boiling Chf Incorporating Effects Of Contact Angle And
Orientation,” Paper accepted for presentation in the
session on Fundamentals of Critical Heat Flux in Pool
and Flow Boiling, at the ASME National Heat Transfer
Conference, Pittsburgh, August 2000. Also accepted for
publication in the Journal of Heat Transfer.
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Boiling on a Horizontal Surface,” Journal of Heat Transfer,
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Transfer,” Ph.D. thesis, Research Laboratory, Los Angeles
and Ramo -Wooldridge Corporation, University of
California, Los Angeles.
Haramura, Y., and Katto, Y., 1983, “New Hydrodynamic
Model of Critical Heat Flux Applicable Widely to both Pool
and Forced Convection Boiling on Submerged Bodies in
Saturated Liquids, International Journal of Heat and
Mass Transfer, Vol. 26, pp. 379-399.
Kirby, D.B., and Westwater, J.W., 1965, “Bubble and Vapor
Behavior on a Heated Horizontal Plate During Pool Boiling
Near Burnout,” Chemical Engineering Progress
Symposium Series, Vol. 61, No. 57, pp. 238-248.
Yu, C.L., and Mesler, R.B., 1977, “Study of Nucleate Boiling
Near the Peak Heat Flux Through Measurement of
Transient Surface Temperature,” International Journal of
Heat and Mass Transfer, Vol. 20, pp. 827-840.
Griffith, P. and Wallis, J.D., 1960, “The Role of Surface
Conditions in Nucleate Boiling,” Chemical Engineering
Progress Symposium, Ser. 56, 30:49-63.
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