Heat Transfer Mechanisms During
Flow Boiling in Microchannels
Satish G. Kandlikar
e-mail: [email protected]
Thermal Analysis and Microfluidics Laboratory,
Department of Mechanical Engineering,
Rochester Institute of Technology,
Rochester, NY 14623
The forces due to surface tension and momentum change during evaporation, in conjunction with the forces due to viscous shear and inertia, govern the two-phase flow patterns
and the heat transfer characteristics during flow boiling in microchannels. These forces
are analyzed in this paper, and two new nondimensional groups, K1 and K2 , relevant to
flow boiling phenomenon are derived. These groups are able to represent some of the key
flow boiling characteristics, including the CHF. In addition, a mechanistic description of
the flow boiling phenomenon is presented. The small hydraulic dimensions of microchannel flow passages present a large frictional pressure drop in single-phase and two-phase
flows. The small hydraulic diameter also leads to low Reynolds numbers, in the range
100–1000, or even lower for smaller diameter channels. Such low Reynolds numbers are
rarely employed during flow boiling in conventional channels. In these low Reynolds
number flows, nucleate boiling systematically emerges as the dominant mode of heat
transfer. The high degree of wall superheat required to initiate nucleation in microchannels leads to rapid evaporation and flow instabilities, often resulting in flow reversal in
multiple parallel channel configuration. Aided by strong evaporation rates, the bubbles
nucleating on the wall grow rapidly and fill the entire channel. The contact line between
the bubble base and the channel wall surface now becomes the entire perimeter at both
ends of the vapor slug. Evaporation occurs at the moving contact line of the expanding
vapor slug as well as over the channel wall covered with a thin evaporating film surrounding the vapor core. The usual nucleate boiling heat transfer mechanisms, including
liquid film evaporation and transient heat conduction in the liquid adjacent to the contact
line region, play an important role. The liquid film under the large vapor slug evaporates
completely at downstream locations thus presenting a dryout condition periodically with
the passage of each large vapor slug. The experimental data and high speed visual
observations confirm some of the key features presented in this paper.
关DOI: 10.1115/1.1643090兴
Keywords: Boiling, Bubble Growth, Heat Transfer, Interface, Microscale
Introduction
It has been well recognized that the flow boiling heat transfer
consists of a nucleate boiling component and a convective boiling
component, e.g., Schrock and Grossman 关1兴. The convective boiling component results from the convective effects, whereas the
nucleate boiling component results from the nucleating bubbles
and their subsequent growth and departure at the heated surface.
The nucleate boiling and the convective boiling mechanisms cannot be distinguished precisely, as they are closely interrelated.
The nucleation, growth and subsequent departure of bubbles
from a heated wall constitute the major stages of a bubble ebullition cycle in pool boiling. The heat transfer mechanisms associated with pool boiling include: transient conduction, film vaporization, microconvection, contact line heat transfer, and to a lesser
degree, the vaporization condensation, and Marangoni convection.
The bubble dynamics under flow boiling conditions are affected in
such a way as to shift toward smaller nucleation cavity sizes and
smaller departure bubble diameters. In this paper, the forces governing the liquid vapor interface in microchannels during flow
boiling are analyzed and two new dimensionless groups are identified. The role of nucleate boiling is re-examined and the heat
transfer mechanisms are discussed. The high-speed flow visualization conducted by the author and his co-workers and the experimental heat transfer data from literature are used in arriving at the
mechanistic description of the flow boiling phenomena in microchannels.
In this paper, the channel classification proposed by Kandlikar
Contributed by the Heat Transfer Division for publication in the JOURNAL OF
HEAT TRANSFER. Manuscript received by the Heat Transfer Division February 20,
2003; revision received September 24, 2003. Associate Editor: M. K. Jensen.
8 Õ Vol. 126, FEBRUARY 2004
and Grande 关2兴 is used. This classification should be used as a
mere guide indicating the size range, rather than rigid demarcations based on specific criteria. In reality, the effects will depend
on fluid properties and their variation with pressure changes. Undoubtedly, the actual flow conditions, such as single phase liquid
or gas flow, or flow boiling or flow condensation, will present
different classification criteria. The classification by Kandlikar
and Grande is based on rarefaction effects for common gases
around 1 atmospheric pressure. At smaller dimensions below
about 10 ␮m, molecular effects begin to be important, again subject to specific operating conditions. Molecular nanochannels are
still very large compared to the molecular dimensions, but the
intermolecular forces begin to play an important role especially in
the near wall region. In two-phase applications, recently Kawaji
and Chung 关3兴 reported significant departure for their 100 ␮m
microchannels from the linear relationship between volumetric
quality versus void fraction proposed by Ali et al. 关4兴 for narrow
channels.
Conventional channels: ⬎3 mm
Minichannels: 3 mm⭓Dh⬎200 ␮ m
Microchannels: 200 ␮ m⭓Dh⬎10 ␮ m
Transitional Channels: 10 ␮ m⭓Dh⬎0.1 ␮ m 共100 nanometer, nm, or 1000 Å兲
Transitional Microchannels: 10 ␮ m⭓Dh⬎1 ␮ m
Transitional Nanochannels: 1 ␮ m⭓Dh⬎0.1 ␮ m
Molecular Nanochannels: 0.1 ␮ m⭓Dh
Review of Available Non-Dimensional Groups Related
to Two-Phase Flow and Interfacial Phenomena
Before deriving the relevant new non-dimensional groups in
microchannels, the existing groups commonly applied in the two-
Copyright © 2004 by ASME
Transactions of the ASME
Table 1 Non-dimensional Groups relevant to two-phase flow studies in microchannels
Non-dimensional number
Martinelli parameter, X
dp
dp
X2⫽
dz F
dz F
冉冏 冏 冊 冒 冉冏 冏 冊
L
G
Convection Number, Co
Co⫽ 关 (1⫺x)/x 兴 0.9关 ␳ G / ␳ L 兴 0.5
Boiling number, Bo
q
Bo⫽
G hfg
Bond number, Bo
g共 ␳ L⫺ ␳ G 兲D 2
Bo⫽
␴
Eötvös Number, Eo
g共 ␳ L⫺ ␳ G 兲L 2
Eo⫽
␴
Capillary number, Ca
␮V
Ca⫽
␴
Ohnesorge Number, Z
␮
Z⫽
共␳ L ␴兲1/2
Weber Number, We
L G2
We⫽
␳ ␴
Jakob Number, Ja
␳ L c p,L ⌬T
Ja⫽ ␳
hfg
V
Significance
Relevance to Microchannels
Groups based on Empirical Considerations
Because of its success in predicting pressure drop in
Represents the Ratio of frictional pressure drops with
compact evaporator geometries, it is expected to be a useful
liquid and gas flow. It has been employed successfully
parameter in microchannels as well.
in two-phase pressure drop models in simple as well as
complex geometries
Co is a modified Martinelli parameter, introduced by
Its direct usage beyond flow boiling correlation may be
Shah 关5兴 in correlating flow boiling data
limited.
Since it combines two important flow parameters, q and G,
Heat flux is non-dimensionalized with mass flux and
it will be used in empirical treatment of flow boiling.
latent heat. It is not based on any fundamental
considerations.
Groups based on Fundamental Considerations
Since the effect of gravitational force is expected to be
Bo represents the ratio of buoyancy force to surface
small, Bo is not expected to play an important role in
tension force. Used in droplet atomization and spray
microchannels.
applications.
Eötvös number is similar to the Bond number, except
that the characteristic dimension L could be D h or any
other physically relevant parameter.
Similar to Bo, Eo is not expected to be important in
microchannels except at very low flow velocities and vapor
fractions.
Ca represents the ratio of viscous to surface tension
forces. It is useful in analyzing the bubble removal
process.
Ca is expected to play a critical role as both the surface
tension and the viscous forces are important in
microchannel flows.
Z represents the ratio of the viscous force to the square
root of the product of the inertia and the surface tension
forces. It is used in analyzing liquid droplets and
droplet atomization processes.
We represents the ratio of the inertia to the surface
tension forces. For flow in channels, D h is used in
place of L.
The combination of the three forces into one masks the
individual effects of each force. Although Z may come out
as an important variable, it may not be suitable in the early
stages of microchannel research.
We I useful in studying the relative effects of surface
tension and inertia forces on flow patterns in microchannels.
Ja represents the ratio of the sensible heat for a given
volume of liquid to heat or cool through ⌬T in
reaching its saturation temperature, to the latent heat
required in evaporating the same volume of vapor.
Ja may be used as an important parameter in studying the
effects of liquid superheat prior to initiation of nucleation in
microchannels. It may also be useful in studying the
subcooled boiling conditions.
phase and flow boiling applications are reviewed in this section.
Non-dimensional groups are useful in arriving at key basic relations among system variables that are valid for different fluids
under different operating conditions. Some of these groups have
been derived empirically, often on the basis of experimental data.
Fundamental considerations of the governing forces and their mutual interactions lead to non-dimensional groups that provide important insight into the physical phenomena. A listing of both
types of non-dimensional groups, based on empirical considerations and on theoretical analysis of forces, is given in Table 1. A
brief description of their significance along with their relevance to
flow boiling in microchannels is also included in the table.
The non-dimensional groups based on empirical considerations
have been proposed in literature on the basis of extensive data
analysis. Their extension to other systems requires rigorous validation, often requiring modifications of constants or exponents.
Convection number and boiling number fall under this category.
Although the Martinelli parameter is derived from fundamental
considerations of the gas and the liquid phase friction pressure
gradients, it is used extensively as an empirical group in correlating experimental results on pressure drop, void fraction, and is
some cases, heat transfer as well.
It can be seen from Table 1 that among the groups derived from
fundamental considerations, Capillary number, Ca, and Weber
number, We, are important in microchannel two-phase flows.
They represent the ratios of viscous and surface tension forces,
and inertia and surface tension forces respectively. The ratio of
inertia to viscous forces, represented by Reynolds number, Re, is
extensively used in single phase flows; it is also expected to have
an important role in two-phase flows, as the single-phase heat
transfer and pressure drop characteristics are often found to be
useful in predicting the two-phase flow behavior.
The Bond number represents the ratio of the gravitational to
surface tension forces on a droplet or a bubble. Departure bubble
Journal of Heat Transfer
diameter is sometimes used as the characteristic dimension in the
definition of the Bond number in pool boiling. Since the gravitational forces are expected to be small compared to the surface
tension and viscous forces, usefulness of Bond number in microchannel application is limited.
Additionally, there are a number of non-dimensional groups
used in literature for correlating different boiling phenomena. For
example, Stephan and Abdelsalam 关6兴 utilized eight dimensionless
groups in developing a comprehensive correlation for saturated
pool boiling heat transfer. Similarly, Kutateladze 关7兴 combined the
critical heat flux with other parameters through dimensional
analysis to obtain a non-dimensional group. However, only those
non-dimensional groups that are derived from some basic considerations are reviewed here.
Forces Acting on a Liquid-Vapor Interface Due to Evaporation Momentum Change, Inertia and Surface Tension. The
non-dimensional groups employed so far in literature for analyzing the flow patterns during flow boiling have been similar to
those employed in the adiabatic two-phase flow applications. The
Jakob number is used in analyzing the bubble growth phenomenon. The Weber number has been recently introduced in flow
pattern maps for microchannels and minichannels. The effect of
heat flux appears only in the Boiling number, which is used in
heat transfer correlations along with the density ratio; the Boiling
number has not been used in flow pattern maps.
Heat flux has a significant effect on the two-phase structure
during flow boiling. A higher heat flux results in a more rapid
bubble growth leading to quickly filling the channel with a vapor
slug. The forces generated due to rapid evaporation become significant for microchannels, as the growing bubbles interact with
the channel walls. Further discussion on this aspect is presented in
the following sections.
As a nucleating bubble grows, the difference in the densities of
FEBRUARY 2004, Vol. 126 Õ 9
Similarly, the force per unit length due to the surface tension force
is given by
F S⬘ ⫽ ␴ cos ␪
(3)
where ␪ is the appropriate contact angle, advancing or receding,
depending on the direction of the motion of the liquid into or
away from the interface respectively.
The net gravitational force 共due to buoyancy兲 may be represented in a similar manner as
F g⬘ ⫽ 共 ␳ L ⫺ ␳ G 兲 gD 2
Fig. 1 Forces acting on a vapor bubble growing on a heater
surface in a liquid pool, only half of a symmetric bubble shown
the two phases causes the vapor phase to leave at a much higher
velocity than the corresponding liquid velocity toward the receding and evaporating interface. The resulting change in momentum
due to evaporation introduces a force on the interface. The magnitude of this force is highest near the heater surface due to a
higher evaporation rate in the contact line region between the
bubble base and the heater surface as illustrated in Fig. 1.
For the case of saturated flow boiling, the heat flux at the wall
results in an evaporation mass flux of q/h f g . The resulting momentum change introduces a force on the liquid interface that can
be expressed as described below per unit characteristic dimension,
either based on the bubble diameter as shown in Fig. 1, or based
on the channel diameter as shown in Fig. 2. This force was first
introduced by Kandlikar 关8兴 in developing a CHF model based on
the force balance at the contact line at the base of a bubble on the
heater surface.
Thus force per unit length due to momentum change caused by
evaporation at the interface is given by
F ⬘M ⫽
冉 冊
q
qD q 1
⫽
h fg h fg ␳G
hfg
2
D
␳G
(1)
where D is the characteristic dimension.
The other forces acting on the interface are due to the inertia of
the flow and the surface tension in the contact line region. The
forces per unit length are given by the respective equations below.
The stress resulting from the inertia forces is given by ␳ V 2 . The
resulting force per unit length due to the inertia is then given by
F I⬘ ⫽ ␳ L V 2 D⫽
G 2D
␳L
(2)
(4)
The gravitational force is generally quite small compared to the
forces due to inertia and the momentum change during flow boiling in microchannels.
The viscous forces are not considered here, although they are
important in determining the flow stability in microchannels.
Their effect is represented through the Capillary number and the
Reynolds number.
New Non-Dimensional Groups Relevant to Flow Boiling in
Microchannels. The relative magnitudes of the forces due to
evaporation momentum, inertia, and surface tension, introduced in
Eqs. 共1–3兲, influence the two-phase structure during flow boiling.
The ratios of these forces, taken two at a time, yield the relevant
non-dimensional groups in flow boiling.
New Non-Dimensional Group K1. This group represents the
ratio of the evaporation momentum force, Eq. 共1兲, and the inertia
force, Eq. 共2兲. It is given by
冉 冊
q 2D
h fg ␳G
q
K1⫽
⫽
G 2D
Gh f g
␳L
冉 冊
2
␳L
␳G
(5)
The non-dimensional group K1 includes the Boiling number and
the liquid to vapor density ratio. The Boiling number alone does
not represent the true effect of the evaporation momentum, and its
coupling with the density ratio is important in representing the
evaporation momentum force.
A higher value of K1 indicates that the evaporation momentum
forces are dominant and are likely to alter the interface movement.
As an example, consider the bubble growth shown in Fig. 3 inside
a 200 ␮m square microchannel, Steinke and Kandlikar, 关9兴. Each
frame in Fig. 3 is 8 ms apart. The bubble grows rapidly aided by
the evaporation at the liquid-vapor interface. The high evaporation
rate causes the interface to move rapidly downstream. The upstream interface also experiences the force due to evaporation
momentum and the increased pressure inside the bubble, causing
it to move against the flow direction in one of the channels as
shown. The flow reversal occurs at high heat fluxes and has been
observed in 1 mm square minichannels as well by Kandlikar et al.
关10兴 and Kandlikar 关11兴. Further discussion on the actual values of
K1 employed in microchannels and minichannels is presented in
later sections.
New Non-Dimensional Group K2. This new group represents
the ratio of the evaporation momentum force, Eq. 共1兲, and the
surface tension force, Eq. 共3兲. It is given by
冉 冊
q 2D
h fg ␳G
q
K2⫽
⫽
␴
hfg
Fig. 2 Forces acting on a liquid-vapor interface that covers
the entire channel cross section
10 Õ Vol. 126, FEBRUARY 2004
冉 冊
2
D
␳ G␴
(6)
The contact angle is not included in the above ratio. The actual
force balance in a given situation may involve more complex
dependence on contact angles and surface orientation. However, it
should be recognized that the contact angles play an important
role in bubble dynamics and contact line movement and need to
be included in a comprehensive analysis. The non-dimensional
group K2 governs the movement of the interface at the contact
Transactions of the ASME
Fig. 4 Variation of K2,CHF with diameter for flow boiling CHF
data of Vandervort et al. †12‡ for different values of G in kgÕm2 s
Fig. 3 Rapid bubble growth causing reversed flow in a parallel
microchannel. Water flow is from left to right, single channel
shown, t Ä„a… 0 ms, „b… 8 ms, „c… 16 ms, „d… 24 ms, „e… 32 ms, „f…
40 ms, „g… 48 ms, and „h… 56 ms, Steinke and Kandlikar †9‡.
line. The high evaporation momentum force causes the interface
to overcome the retaining surface tension force. This group was
effectively used by Kandlikar 关8兴 in developing a model for CHF
in pool boiling. The characteristic dimension D was replaced with
the departure bubble diameter. The resulting expression for the
CHF in pool boiling from a smooth planar surface oriented at an
angle of ␸ with the horizontal was obtained as
1/2
q CHF⫽h f g ␳ G
冉
1⫹cos ␪
16
冊冋
2 ␲
⫹ 共 1⫹cos ␪ 兲 cos ␾
␲ 4
册
1/2
⫻ 关 ␴ g 共 ␳ L ⫺ ␳ G 兲兴 1/4
(7)
Alternatively, the value of K2 at CHF for the case of pool boiling
may be written as
K2,CHF⫽
冉 冊 冉
冋
册
q CHF
hfg
⫻
2
D
1⫹cos ␪
⫽
␳ G␴
16
g共 ␳ L⫺ ␳ G 兲
␴
冊冋
2
2 ␲
⫹ 共 1⫹cos ␪ 兲 cos ␾
␲ 4
册
1/2
D
(8)
The characteristic dimension D is simply half of the critical wavelength, 共alternatively, it may be taken as the departing bubble
diameter兲, given by
D⫽2 ␲
冋
␴
g共 ␳ L⫺ ␳ G 兲
册
冉
1⫹cos ␪
16
冊冋
2
Ranges of Non-Dimensionless Parameters Employed in Microchannel and Minichannel Flow Boiling Experiments in Literature. A large body of experimental data is available for flow
boiling in conventional sized channels. There are only a handful
2 ␲
⫹ 共 1⫹cos ␪ 兲 cos ␾
␲ 4
(9)
册
(10)
In other words, the non-dimensional number K2 has a unique
value for CHF in pool boiling and depends on the contact angle
and the orientation angle of the heater with respect to the horizontal. This group is expected to be important in CHF analysis during
flow boiling in microchannels and minichannels as well.
The experimental CHF data of Vandervort et al. 关12兴 during
flow boiling is plotted with K2,CHF as a function of the hydraulic
Journal of Heat Transfer
Importance of Weber Number and Capillary Number in
Microchannel Flow Boiling. The Weber number, We, and the
Capillary number, Ca, should prove to be useful in determining
the transition boundaries between different flow patterns. We and
Ca are believed to influence the CHF phenomenon as well. These
groups are commonly employed in analyzing the gas-liquid adiabatic flows. They may prove to be useful in refining the mass flux
0.75
and viscous effects on CHF in the K2,CHF K1,CHF
group shown in
Fig. 5. Further work on this can be undertaken after reliable experimental data become available for CHF in microchannels with
a wide variety of fluids.
1/2
Thus, K2,CHF for pool boiling is given by
K2,CHF⫽2 ␲
diameter for three different mass fluxes. The result is shown in
Fig. 4. The value of K2,CHF for each mass flux set is seen to be
quite constant, considering the scatter present in the original data.
This is quite remarkable, and further, as expected, a dependence
of the respective K2,CHF values on the mass flux is seen since
K2,CHF does not include the inertia related forces. Further CHF
modeling needs to include the mass flux effect. Incidentally,
K2,CHF is seen to increase with mass flux as one would expect.
0.75
As a first attempt, applying a mass flux correction factor K1,CHF
to K2,CHF nearly collapses the data of Vandervort et al. 关12兴 for
different mass fluxes on a single horizontal line. Figure 5 shows
the resulting plot. Considering the scatter in the CHF data due to
measurement uncertainties, the agreement is very encouraging.
However, further experimental data need to be included in the
comparison, and additional property effects 共including contact
angles兲 need to be considered while developing a CHF model for
flow boiling in microchannels.
0.75
Fig. 5 Variation of K2,CHF K1,CHF
with diameter for flow boiling
CHF data of Vandervort et al. †12‡ for different values of G in
kgÕm2 s
FEBRUARY 2004, Vol. 126 Õ 11
Fig. 6 Ranges of the new non-dimensional parameter K1 employed in various experimental investigations
of reliable experimental data sets available for minichannels and
microchannels, e.g., 关9兴 and 关13–21兴, although more are emerging
in literature as the interest continues to grow in this field. It is
interesting to look at the ranges of dimensionless parameters employed in these experiments as a function of hydraulic diameter.
Figures 6 –10 show the ranges of non-dimensional parameters
employed in several investigations. The ranges of K1 over the
channel hydraulic diameters employed in literature are shown in
Fig. 6. The 6 and 15-mm diameter data for R-11 by Chawla 关13兴
covers a wide range of K1 . Looking into the experimental data
sets, it is seen that the higher end values of K1 correspond to the
nucleate boiling dominant region, while the lower end values of
K1 indicate the convective boiling dominant region. The large
diameter data sets cover a wide range, whereas it is seen that most
Fig. 7 Ranges of the new non-dimensional parameter K2 employed in various experimental investigations
Fig. 8 Ranges of Weber Number, We, employed in various experimental investigations
Fig. 10 Ranges of Reynolds Number, Re, employed in various
experimental investigations
of the minichannel and microchannel data sets fall toward the
higher end of K1 values. Especially the data set of Yen et al. 关14兴
is seen to fall at the very high end. Higher values of K1 are
indicative of a relatively higher heat flux for a given mass flux
value, and also of the increased importance of the evaporation
momentum force.
Figure 7 shows a similar plot for K2 plotted against D h . The
maximum value of K2 共not shown in the plot as no data are available兲 is indicative of the CHF location. There are very few studies
available on CHF in Minichannels, and practically none for
the microchannels. This is an area where further research is
warranted.
Figure 8 shows the range of We in the data sets analyzed here.
No appreciable differences are noted, and the data sets do not
show any shift in the We range indicative of any change in the
experimental conditions for smaller hydraulic diameter channels.
Although We does not appear to be a significant parameter in this
plot, it may be representative of the inertia effects that are important in modeling the CHF in flow boiling.
The Capillary number is expected to be important in the microchannel flows as both the viscous and the surface tension forces
are expected to be important. Figure 9 shows the variation of Ca
range with hydraulic diameter for representative data sets. It can
be seen that there is a systematic shift toward higher values of Ca
for smaller channel diameters. This indicates that the viscous
forces become more important than the surface tension forces under flow boiling conditions in microchannels. This is somewhat of
an unexpected result, as one would believe the dominance of the
surface tension forces at smaller channel dimensions.
Finally, Fig. 10 shows the range of all liquid flow Reynolds
numbers employed in the data sets. As the channel diameter is
decreased, a clear shift toward lower Reynolds number is seen.
This points to the increased importance of the viscous forces in
microchannels. Combining this observation with the discussion on
the Capillary number in the above paragraph, it can be concluded
that the viscous forces are extremely important in microchannel
flows. The effect of lower Re on flow boiling heat transfer modeling will be discussed in the section on heat transfer coefficient
prediction.
Influence of Channel Hydraulic Diameter on Flow Boiling Heat Transfer Mechanisms
Flow Patterns. Flow boiling in a channel is studied from the
subcooled liquid entry at the inlet to a liquid-vapor mixture flow
at the channel outlet. As the liquid flows through a microchannel,
nucleation occurs over cavities that fall within a certain size range
under a given set of flow conditions. Assuming that cavities of all
sizes are present on the heater surface, the wall superheat necessary for nucleation may be expressed from the equations developed by Hsu and Graham 关22兴 and Sato and Matsumura 关23兴:
Fig. 9 Ranges of Capillary Number, Ca, employed in various
experimental investigations
12 Õ Vol. 126, FEBRUARY 2004
⌬T sat,ONB⫽
冋 冑
4 ␴ T satv f g h
1⫹
kh f g
1⫹
kh f g ⌬T sub
2 ␴ T satv f g h
册
(11)
Transactions of the ASME
Fig. 11 Wall superheat required to initiate nucleation in
a channel with hydraulic diameter D h for saturated liquid conditions
For a conservative estimate, ⌬T sub⫽0 is taken in estimating the
local superheat at the onset of nucleate boiling. Since the single
phase liquid flow is in the laminar region, the Nusselt number is
given by
Nu⫽
hD h
⫽C
k
(12)
where C is a constant dependent on the channel geometry and the
wall thermal boundary condition. Combining Eqs. 共11兲 and 共12兲
with zero subcooling, we get,
⌬T sat,ONB⫽
8 ␴ T satv f g C
D hh f g
(13)
Taking the case of a constant wall temperature boundary condition, representative of microchannels in a large copper block, the
variation of ⌬T sat with D h is plotted in Fig. 11 for water at a
saturation temperature of 100°C and for R-134a at 30°C. For
channels larger than 1 mm, the wall superheat is quite small, but
as the channel size becomes smaller, larger superheat values are
required to initiate nucleation. For water in a 200 ␮m channel, a
wall superheat of 2°C is required before nucleation can begin.
The actual nucleation wall superheat may increase due to the absence of cavities of all sizes, while it may reduce due to 共a兲 the
presence of dissolved gases in the liquid, Kandlikar et al., 关24兴,
共b兲 corners in the channel cross section, and 共c兲 pressure fluctuations.
From the above discussion, for channels smaller than 50 ␮m,
the wall superheat may become quite large, in excess of 10°C
with water, and above 2 – 3°C for refrigerants. Flow boiling in
channels smaller than 10 ␮m will pose significant challenges. The
buildup of wall superheat presents another issue that is discussed
in the following paragraph.
Once the nucleation begins, the large wall superheat causes a
sudden release of energy into the vapor bubble, which grows rapidly and occupies the entire channel. A number of investigators
have considered this vapor slug as an elongated bubble. The rapid
bubble growth pushes the liquid-vapor interface on both caps of
the vapor slug at the upstream and the downstream ends, and leads
to a reversed flow in the parallel channel case as the liquid on the
upstream side is pushed back, and the other parallel channels
carry the resulting excess flow. Kandlikar et al. 关10兴 observed this
reversed flow in 1-mm square parallel channels, while Steinke and
Kandlikar 关9兴 report a rapid flow reversal inside individual channels in a set of six parallel microchannels, D h ⫽200 ␮ m. Reversed flow was also observed by Peles et al. 关26兴. Kandlikar and
Balasubramanian 关25兴 observed only a small reverse displacement
of the interface in a 197 ␮m x 1054 ␮m single microchannel. Due
to the relatively high inlet ‘‘stiffness’’ of the water supply loop,
the single microchannel does not show as dramatic reversed flow
behavior as the parallel microchannels. 共In case of parallel channels, the other channels act as the upstream sections for any given
channel兲. Figure 3 by Steinke and Kandlikar 关9兴 shows a sequence
of bubble formation and reversed flow 共from right to left兲 in a
channel. The images are 8 ms apart and show a bubble from its
nucleation stage, as it occupies the entire channel, and eventually
Journal of Heat Transfer
Fig. 12 High speed flow visualization of water boiling in
a 197 ␮ mÃ1054 ␮ m channel showing rapid dryout and
wetting phenomena with periodic passage of liquid and vapor
slugs, each successive frame is 5ms apart, Kandlikar and
Balasubramanian †25‡
becomes a vapor slug that expands in both directions. The flow
patterns are seen as periodic, with small nucleating bubbles growing into large bubbles that completely fill the tube and lead to
rapid movement of the liquid-vapor interface along the channel.
Figure 12 shows the periodic dryout and rewetting through an
image sequence obtained with a flow of water in a single channel,
197 ␮ m⫻1054 ␮ m in cross-section, by Kandlikar and Balasubramanian 关25兴. Here the bubble growth is extremely rapid, and the
moving interface could not be precisely imaged. However, the
flow goes from all liquid flow in frames 共a兲 and 共b兲 to a thin film
in frames 共c兲-共d兲-共e兲. In frames 共f兲-共l兲, the liquid film has been
completely evaporated, and the channel walls are under a dryout
condition. The liquid front is seen to pass through the channel in
frame 共m兲, followed by all liquid flow in the last frame. The
periodic wetting and rewetting phenomena were also observed by
Hetsroni et al. 关27兴 for parallel microchannels of 103–129 ␮m
hydraulic diameters.
Other flow patterns reported by Steinke and Kandlikar 关9兴 include slug flow, annular flow, churn flow and dryout condition. A
number of investigators, including Hetsroni et al. 关27兴 and Zhang
et al. 关28兴 have also reported these flow patterns. The long vapor
bubble occurring in a microchannel is similar to annular flow with
intermittent slugs of liquid between two long vapor trains.
The periodic phenomena described above is seen to be very
similar to the nucleate boiling phenomena, with the exception that
the entire channel acts like the area beneath a growing bubble,
going through periodic drying and rewetting phases. The transient
heat conduction under the approaching rewetting film and the heat
transfer in the evaporating meniscus region of the liquid-vapor
interfaces in the contact line region exhibit the same characteristics as the nucleate boiling phenomena.
Dynamic Advancing and Receding Contact Angles. The
contact angles are believed to play an important role during dryout
and rewetting phenomena during flow boiling in a microchannel.
These angles are important in the events leading to the CHF as
FEBRUARY 2004, Vol. 126 Õ 13
Fig. 14 Comparison of the Kandlikar †1,2,35‡ correlation and
Eqs. „15… and „16… for the Nucleate Boiling Dominant Region
with Yen et al. †14‡ data in the laminar region, plotted with heat
transfer coefficient as a function of local vapor quality x ,
R-134a,
D h Ä190 ␮ m,
ReLOÄ73,
GÄ171 kgÕm2 s,
q
2
Ä6.91 kWÕm
Fig. 13 Changes in contact angle at the liquid front during
flow reversal sequence, water flowing in a parallel microchannel with D h Ä200 ␮ m, Steinke and Kandlikar †9‡
well. The pool boiling CHF model by Kandlikar 关8兴 incorporates
these angles as seen from Eq. 共7兲. During normal bubble growth,
the dynamic receding contact angle comes into play. During the
rewetting process, the liquid front is advancing with its dynamic
advancing contact angle. As the CHF is approached, or as the flow
reversal takes place due to flow instabilities, the liquid front
changes its shape from the dynamic advancing angle to the dynamic receding angle. This event was captured by Steinke and
Kandlikar 关9兴 using high-speed imaging techniques and is displayed in Fig. 13 for the flow of water in a set of six parallel
microchannels, each with a 200 ␮m square cross section.
The events in Fig. 13 show the changes in the contact angles.
The liquid front is moving forward from left to right in frames
共a兲-共d兲. In frame 共d兲, it stops moving forward. Note the dynamic
advancing contact angle in this frame, which is greater than
90 deg. During frames 共d兲-共i兲, it experiences rapid evaporation at
the right side of the front interface and changes to the receding
contact angle value, which is less than 90 deg. The liquid slug
subsequently becomes smaller, making way to the vapor core with
its residual liquid film in frames 共i兲-共m兲. Eventually, the liquid
film dries out completely as seen in frames 共n兲-共p兲. Additional
studies on the contact angle changes at evaporating interfaces are
reported by Kandlikar 关29兴. More detailed experiments are needed
to further understand the precise effect of contact angles on CHF.
As the channel size becomes smaller, the Reynolds number also
becomes smaller for a given mass velocity, and the flow patterns
exhibit characteristics similar to a bubble ebullition cycle as discussed in the previous sections. It is therefore expected that the
flow boiling correlation for the nucleate boiling dominant region
should work well here.
Consider the flow boiling correlation by Kandlikar 关30,31兴.
再
h T P,NBD
h T P,CBD
(14)
h T P,NBD⫽0.6683Co ⫺0.2共 1⫺x 兲 0.8 f 2 共 FrLO 兲 h LO
⫹1058.0Bo 0.7共 1⫺x 兲 0.8F Fl h LO
(15)
h T P,CBD⫽1.136Co ⫺0.9共 1⫺x 兲 0.8 f 2 共 FrLO 兲 h LO
⫹667.2Bo 0.7共 1⫺x 兲 0.8F Fl h LO
where FrLO is the Froude number with all flow as liquid. Since the
effect of Froude number is expected to be small in microchannels,
14 Õ Vol. 126, FEBRUARY 2004
NuLO ⫽
h LO D h
⫽C,
kL
(16)
where the constant C is dependent on the channel geometry and
the wall thermal boundary condition.
Kandlikar and Steinke 关34兴 showed that the use of Eq. 共16兲 for
h LO is appropriate in Eq. 共15兲 when the all-liquid flow is in the
laminar region. The use of turbulent flow correlation by Gnieliski
was found to be appropriate for Re⬎3000, while for Re⬍1600,
the use of laminar flow correlation yielded good agreement. In the
transition region, a linear interpolation was recommended between the limiting ReLO values of 1600 and 3000.
With further reduction in the Reynolds number, Re⬍300,
Kandlikar and Balasubramanian 关35兴 showed that the flow boiling
mechanism is nucleate boiling dominant and the use of only the
nucleate boiling dominant expression in Eq. 共15兲 for h T P,NBD is
appropriate in the entire range of vapor quality. Thus, Kandlikar
and Balasubramanian 关35兴 recommend the following scheme:
h T P ⫽h T P,NBD
Heat Transfer Coefficients during Flow Boiling
in Microchannels
h T P ⫽larger of
the function f 2 (FrLO ) is taken as 1.0. The single-phase, all-liquid
flow heat transfer coefficient h LO is given by appropriate correlations given by Petukhov and Popov 关32兴, and Gnielinski 关33兴,
depending on the Reynolds number in the turbulent liquid flow.
The values of the fluid-dependent parameter F Fl can be found in
关34兴 or 关35兴.
For microchannels with the all-liquid flow in the laminar region, the corresponding all-liquid flow Nusselt number is given by
for ReLO ⬍300
(17)
Using the above scheme, a recent data set published by Yen
et al. 关14兴 was tested. Figure 15 shows a comparison between the
experimental data and the above correlation scheme. Here ReLO
⫽73, and only the nucleate boiling dominant part of the correlation in Eq. 共15兲 is used. At such low Reynolds numbers, the convective boiling does not become the dominant mechanism in the
entire vapor quality range. In this plot, the first few points show a
very high heat transfer coefficient. This is due to the sudden release of the high liquid superheat following nucleation that causes
rapid bubble growth in this region as seen in Fig. 14 as well.
Steinke and Kandlikar 关36兴 observed a similar behavior with their
water data as shown in Fig. 15.
The flow boiling mechanism is quite complex in microchannels
as seen from the experimental data and flow visualization studies.
Although simple models available in literature, e.g., 关37兴, present
a good analysis under certain idealized conditions, phenomena
such as rapid bubble growth, flow reversal, and periodic dryout
introduce significantly greater complexities. Effect of parallel
channels on heat transfer is another area where little experimental
work is published.
Transactions of the ASME
Conclusions
Flow boiling in microchannels is addressed from the perspective of interfacial phenomena. The following major conclusions
are derived from this study:
Fig. 15 Comparison of the Kandlikar †1,2,35‡ correlation and
Eqs. „15… and „16… for the Nucleate Boiling Dominant Region
with Steinke and Kandlikar 36 data in the laminar region, plotted with heat transfer coefficient as a function of local vapor
quality x , water, D h Ä207 ␮ m, ReLOÄ291, GÄ157 kgÕm2 s, q
Ä473 kWÕm2
Heat Transfer Mechanism during Flow Boiling in Microchannels
Based on the above discussion, the heat transfer mechanisms
can be summarized as follows:
1. When the wall superheat exceeds the temperature required
to nucleate cavities present on the channel walls, nucleate boiling
is initiated in a microchannel. Absence of nucleation sites of appropriate sizes may delay nucleation. Other factors such as sharp
corners, fluid oscillations, and dissolved gases affect the nucleation behavior. The necessary wall superheat is estimated to be
2 – 10°C for channels smaller than 50–100 ␮m hydraulic diameter
with R-134a and water respectively at atmospheric pressure conditions.
2. Immediately following nucleation, a sudden increase in heat
transfer coefficient is experienced due to release of the accumulated superheat in the liquid prior to nucleation. This leads to rapid
evaporation, sometimes accompanied by flow reversal in parallel
channels.
3. The role of the convective boiling mechanism is diminished
in microchannels. The nucleate boiling plays a major role as the
periodic flow of liquid and vapor slugs in rapid succession continues. The wall dryout may occur during the vapor passage. The
wetting and rewetting phenomena have marked similarities with
the nucleate boiling ebullition cycle. The dryout period becomes
longer at higher qualities and/or at higher heat fluxes. The nucleate boiling heat transfer suffers further as the liquid film completely evaporates 共dryout兲 during extended periods of vapor passage.
4. As the heat flux increases, the dry patches become larger and
stay longer, eventually reaching the CHF condition.
Closing Remarks. Although it is desirable to have a good
mathematical description of the heat transfer mechanism during
flow boiling in microchannels, the rapid changes of flow patterns,
complex nature of the liquid film evaporation, transient conduction, and nucleation make it quite challenging to develop a comprehensive analytical model. Further, the conduction in the substrate, parallel channel instability issues, header-channel
interactions, and flow maldistribution in parallel channels pose
additional challenges. The usage of the new non-dimensional
groups K1 and K2 in conjunction with the Weber number and the
Capillary number is expected to provide a better tool for analyzing
the experimental data and developing more representative models.
The scale change in hydraulic diameter introduces a whole new
set of issues in microchannels that need to be understood first
from a phenomenological standpoint.
Journal of Heat Transfer
1. After reviewing the non-dimensional groups employed in
the two-phase applications, the forces acting on the liquid-vapor
interface during flow boiling are investigated, and two new nondimensional groups K1 and K2 are derived. These groups represent the surface tension forces around the contact line region, the
momentum change forces due to evaporation at the interface, and
the inertia forces.
2. In a simple first-cut approach, the combination of the nondimensional groups, K2K0.75
is seen to be promising in represent1
ing the flow boiling CHF data by Vandervort et al. 关12兴. Further
analysis and testing with a larger experimental data bank with a
wide variety of fluids is recommended in developing a more comprehensive model for CHF. In additon, the influence of We, and
Ca on the CHF needs to be studied further.
3. The nucleation criterion in flow boiling indicates that the
wall superheat required for nucleation in microchannels becomes
significantly large (⬎2 – 10°C) as the channel hydraulic diameter
becomes smaller, about 50–100 ␮m depending on the fluid. The
presence of dissolved gases in the liquid, sharp corners in the
cross section geometry, and flow oscillations will reduce the required wall superheat, while the absence of cavities of appropriate
sizes may increase the nucleation wall superheat.
4. Considerable similarities are observed between the flow
boiling in microchannels and the nucleate boiling phenomena with
the bubbles nucleating and occupying the entire channel. The process is seen to be very similar to the bubble ebullition cyle in pool
boiling.
5. Heat transfer during flow boiling in microchannels is seen to
be nucleate boiling dominant.
6. A description of the heat transfer mechanisms during flow
boiling in microchannels is provided based on the above observations. Some of the key features, such s rapid bubble growth, flow
reversal, nucleate boiling dominant heat transfer have been confirmed with high speed video pictures and experimental data.
7. Further experimental research is needed to generate more
data for developing more accurate models and predictive techniques for flow boiling heat transfer and CHF in microchannels.
Nomenclature
A
Bo
Bo
C
Ca
Co
cp
d
d P/dz
Dh
Eo
F Fl
⫽
⫽
⫽
⫽
⫽
⫽
⫽
⫽
⫽
⫽
⫽
⫽
Fr
F⬘
f
G
g
h
hfg
Ja
K1
K2
k
⫽
⫽
⫽
⫽
⫽
⫽
⫽
⫽
⫽
⫽
⫽
area, (m2 )
Bond number, Table 1
Boiling number, Table 1
a constant
capillary number, Table 1
convection number, ( ␳ G / ␳ L ) 0.5((1⫺x)/x) 0.8
specific heat, 共J/kg K兲
diameter, 共m兲
pressure gradient, N/m3
hydraulic diameter, 共m兲
Eötvös number, Table 1
Fluid dependent parameter in Kandlikar 关1,2兴 correlation, ⫽1 for water, ⫽1.60 for R-134a
Froude number, ⫽G2 /( ␳ L2gD)
force per unit length, 共N/m兲
friction factor
mass flux, (kg/m2 s)
gravitational acceleration, (m/s2 )
heat transfer coefficient, (W/m2 K)
latent heat of vaporization, 共J/kg兲
Jakob number, Table 1
new non-dimensional constant, eq. 共5兲
new non-dimensional constant, eq. 共6兲
thermal conductivity, 共W/m K兲
FEBRUARY 2004, Vol. 126 Õ 15
L,l
ṁ
Nu
P
q
Re
T
⌬T
V
v
We
w
X
x
Z
⫽
⫽
⫽
⫽
⫽
⫽
⫽
⫽
⫽
⫽
⫽
⫽
⫽
⫽
⫽
length 共m兲
mass flow rate 共kg/s兲
Nusselt number (⫽hDh /k)
pressure 共Pa兲
heat flux (W/m2 )
Reynolds number (⫽GDh / ␮ )
temperature (°C)
temperature difference 共K兲
velocity 共m/s兲
specific volume (m3 /kg)
Weber number, Table 1
channel width 共m兲
Martinelli parameter, Table 1
vapor mass fraction
Ohnesorge number, Table 1
Greek
␾ ⫽ orientation with respect to horizontal (°)
␮ ⫽ dynamic viscosity (Ns/m2 )
␪ ⫽ contact angle (°)
␳ ⫽ density (kg/m3 )
␴ ⫽ surface tension 共N/m兲
Subscripts
CHF ⫽ critical heat flux
F ⫽ friction
CBD ⫽ convection dominated region
G ⫽ gas or vapor
g ⫽ due to gravity
I ⫽ inertia
L ⫽ liquid
LO ⫽ all flow as liquid
f g ⫽ latent quantity, difference between vapor and liquid
properties
M ⫽ due to momentum change
NBD ⫽ nucleate boiling dominant region
ONB ⫽ onset of nucleate boiling
S ⫽ surface tension
sat ⫽ saturation
sub ⫽ subcooled
T P ⫽ two-phase
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Transactions of the ASME