Experimental Thermal and Fluid Science 30 (2006) 441–447
www.elsevier.com/locate/etfs
Nucleation characteristics and stability considerations
during flow boiling in microchannels
Satish G. Kandlikar
*
Rochester Institute of Technology, Rochester, NY 14623, USA
Received 3 May 2005; received in revised form 25 September 2005; accepted 3 October 2005
Abstract
Flow boiling in microchannels and minichannels has received considerable attention in the past decade. The interest stems from the
possibility of achieving the extremely high heat fluxes, over 1 kW/cm2, needed for future generation electronics cooling application. The
attention has been focused on obtaining experimental heat transfer and pressure drop data, but the fundamental aspects of nucleation
have been largely overlooked. In the present paper, the local wall superheat and bulk liquid subcooling prevailing in the channel at the
onset of nucleation are identified as critical in the flow boiling stability. To understand the role of local conditions on nucleation, the
available literature on onset of nucleate boiling is critically reviewed and the relationships between the local bulk subcooling and local
wall superheat as a function of nucleation cavity diameters are presented. The unique flow characteristics in microchannels and minichannels are further analyzed and their influence on flow boiling stability is investigated experimentally using visual images generated
with a high-speed camera.
2005 Elsevier Inc. All rights reserved.
Keywords: Nucleation; Flow boiling; Microchannels; Minichannels; Stabilization
1. Introduction
Microchannels and minichannels are fluid flow channels
with small hydraulic diameters. Following the classification
by Kandlikar and Grande [1], and later modifications suggested by Kandlikar et al. [2], channels with a minimum
cross-sectional dimension between 200 lm and 3 mm are
classified as minichannels and between 1 lm and 200 lm
are classified as microchannels.
Employing smaller diameter channels is desirable
because of two reasons: (i) higher heat transfer coefficient,
and (ii) higher heat transfer surface area per unit flow volume. Combination of these two features makes singlephase heat transfer extremely efficient in minichannels
and microchannels. Although the pressure gradient
increases considerably, providing short flow lengths for
*
Tel.: +1 585 475 6728; fax: +1 585 475 7710.
E-mail address: SGKEME@RIT.EDU
0894-1777/$ - see front matter 2005 Elsevier Inc. All rights reserved.
doi:10.1016/j.expthermflusci.2005.10.001
fluid flow passages can effectively reduce the overall
pressure drop in a microchannel heat exchanger [3].
Flow boiling heat transfer in conventional channels is
associated with the latent heat transfer that can reduce
the mass flow rate required for a given heat dissipation
rate. Combination of microchannels with the flow boiling
process is therefore expected to provide a significant
improvement in the heat dissipation rates.
However, flow boiling in minichannels and microchannels poses a number of difficulties. These issues have been
summarized by Kandlikar [4,5]. The major concerns relate
to (i) increased effects of surface tension forces, (ii) reverse
flow arising from nucleation followed by rapid bubble
growth, and (iii) deterioration in heat transfer and critical
heat flux due to flow instabilities.
This paper focuses on the nucleation characteristics in
microchannels. These characteristics are intimately related
to a number of issues associated with flow boiling in microchannels including stability, heat transfer rates and critical
heat flux.
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S.G. Kandlikar / Experimental Thermal and Fluid Science 30 (2006) 441–447
Nomenclature
D
G
hL
hLV
K1
K2
kL
p
q00
rb
rc,crit
rc,min
rc,max
T
characteristic dimension (bubble departure
diameter in critical heat flux modelling), m
mass flux, kg/m2 s
heat transfer coefficient for single-phase liquid,
W/m2 K
latent heat of vaporization, J/kg
ratio of the evaporation momentum
00 2to inertia
forces, non-dimensional, K1 ¼ Ghq LV qqL
V
ratio of the evaporation momentum to
surface
2
00
tension forces, non-dimensional, K2 ¼ hqLV qDr
V
liquid thermal conductivity, W/m K
pressure, Pa
heat flux, W/m2
bubble radius, m
critical cavity radius at the onset of nucleate
boiling, m
minimum cavity radius allowing for nucleation,
m
maximum cavity radius allowing for nucleation,
m
temperature, K
2. Nucleation criterion
Nucleation criteria for pool boiling and flow boiling in
conventional sized channels were well established following
the work of Hsu [6]. Bubbles are formed over the cavities
that are present on a heater surface. As a bubble covers
the mouth of a cavity, the local temperature field in the surrounding liquid dictates whether the bubble will grow further and nucleate. Since the equilibrium pressure inside a
bubble increases as the bubble diameter reduces, a greater
wall superheat is needed for nucleation over smaller cavities. The analyses presented by Hsu [6] and later researchers provide the necessary nucleation criteria for the onset of
nucleate boiling. A brief summary of these nucleation criteria is presented here.
Hsu neglected the dynamic effects due to bubble growth
and provided a model based on equilibrium considerations
using the single-phase liquid flow conditions prior to nucleation for determining the temperature profile in the vicinity
of the heater wall. As a bubble attains a certain radius rb
while covering the cavity mouth, the excess pressure inside
the bubble is given by the following equation for static
equilibrium of surface tension and pressure forces
pV pL ¼ 2r=rb
DTSat
DTSub
y
yb
ys
wall superheat, DTSat = TW TSat, K
liquid subcooling, DTSub = TSat Tbulk, K
coordinate axes
distance to the top of a bubble, m
streamline location, m
Greek symbols
dt
thermal boundary layer thickness, m
hr
receding contact angle, degrees
q
density, kg/m3
r
surface tension, N/m
Subscripts
bulk
bulk fluid property
c
cavity
L
in the liquid phase
max
maximum
ONB onset of nucleate boiling
Sat
saturation
V
in the gaseous phase
W
at the wall
ture corresponding to the vapor pressure inside the bubble.
The liquid temperature adjacent to the heater surface is
obtained by considering a linear temperature profile in
the liquid layer. The thickness of the liquid layer dt is
obtained from the following equation:
dt ¼ k L =hL
where dt—thickness of thermal boundary layer, kL—liquid
thermal conductivity, hL—heat transfer coefficient with
liquid flow prior to nucleation.
Fig. 1 shows a nucleating bubble over a cavity and the
temperature profile in the liquid layer adjacent to the heater surface. Equating the temperature at the top of the bubble with the local liquid temperature at y = yb provides the
desired nucleation criterion. Different investigators used
(a)
TB
y = δt
(b)
pL
pV
TL, yb
y = yb
y
rb
ð1Þ
where pV—pressure inside the bubble, pL—pressure of the
liquid surrounding the bubble, r—surface tension, and
rb—bubble radius. Further growth of this bubble depends
on whether the coldest liquid temperature encountered
anywhere at the interface is above the saturation tempera-
ð2Þ
θr
yS
rb
Tw
T
2rc
Fig. 1. Temperature profile (a) and stagnation streamline (b) around a
nucleating bubble.
S.G. Kandlikar / Experimental Thermal and Fluid Science 30 (2006) 441–447
ð3Þ
where qV—vapor density, hr—receding contact angle, T—
temperature, and hLV—latent heat of vaporization. All cavities with radii between rc,min and rc,max will nucleate under
the given wall superheat DTSat and liquid subcooling
DTSub. Assuming cavities of appropriate radii are present
on the heater surface, the wall superheat corresponding
to this condition is obtained by setting the term under
the radical sign in Eq. (3) to zero. The critical cavity radius
rc,crit that will nucleate first under this condition is given by
dt sin hr
DT Sat
rc;crit ¼
ð4Þ
2:2
DT Sat þ DT Sub
where DTSub = TSat Tbulk, DTSat = TW TSat, and
rc,crit—critical cavity radius at the onset of nucleate boiling
(ONB). The local wall superheat at this condition is given by
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ð5Þ
DT Sat;ONB ¼ 8:8rT Sat q00 =ðqV hLV k L Þ
where q00 —heat flux. Note that there was a typographical
error in the constant in Eqs. (3) and (5) as reported in
the original publication by Kandlikar et al. [9]; it should
be 8.8 as shown in these equations.
If the cavity of critical radius is not available, then the
nucleation will occur on the appropriate cavity size that
yields the minimum nucleation wall superheat under a
given set of conditions. The wall superheat required to
nucleate a given size cavity is obtained by Kandlikar
et al. [9] as follows:
DT Sat jONB
at rc
¼
1:1rc q00 2r sin hr T Sat
þ
k L sin hr
rc
qV hLV
ð6Þ
The above criterion was used to compare the experimental data obtained by Kandlikar et al. [9] for water flowing
over a spot heater in a 1 mm · 40 mm minichannel. The
nucleating bubbles were observed using a high-speed camera and the underlying cavity radii were measured using a
16
Bergles & Rohsenow
Hsu
Davis & Anderson
Truncated/Stagnation
Re = 1997
Re = 1664
14
TWALL - TSAT (°C)
different bubble shapes at this condition and obtained different expressions. Hsu [6] used a contact angle of
hr = 53.1, while Bergles and Rohsenow [7] used 90, and
Davis and Anderson [8] retained it as a variable in their
expression for the range of cavity radii that satisfy the
nucleation criterion. Later, Kandlikar et al. [9] numerically
simulated liquid flow around a nucleating bubble in a minichannel and found the location of the streamline, at y = ys
as shown in Fig. 1(b) that sweeps over the bubble. The
location of this streamline was found to be at ys = 1.1rb.
Kandlikar et al. [9] then derived the nucleation criterion
by comparing the liquid temperature at ys with the equilibrium pressure corresponding to the radius of the bubble
over the cavity mouth and maintaining the receding
contact angle as a variable as shown in Fig. 1
dt sin hr
DT Sat
frc;min ; rc;max g ¼
2:2
DT Sat þ DT Sub
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi#
"
8:8rT Sat ðDT Sat þ DT Sub Þ
1 1
qV hLV dt DT 2Sat
443
12
10
o
8
TBULK = 80 C
6
4
2
0
0
2
4
6
8
10
12
14
16
rc (µm)
Fig. 2. Nucleation data for water in a 1 mm · 40 mm rectangular channel
compared with four nucleation criteria, Hsu [6], Bergles and Rohsenow
[7], Davis and Anderson [8], and the truncated/stagnation model by
Kandlikar et al. [9].
microscope. Fig. 2 shows the comparison of different nucleation criteria with the experimental data. It should be
noted that the nucleation data points should fall above
the line representing a criterion. The lines represent the
minimum superheat needed to nucleate a cavity of a given
radius. The cavity will continue to nucleate at higher wall
superheats (as seen for most of the data points). A data
point falling below a line indicates that the particular
nucleation criterion is predicting a higher wall superheat
than the experimental data. The nucleation criterion of
Hsu [6] is seen to be most restrictive while the Bergles
and Rohsenow [7] criterion is seen to predict the lowest
wall superheat values. All data points fall above or very
close to the line representing the truncated/stagnation
model of Kandlikar et al. [9].
Such a study on bubble nucleation characteristics is not
available for microchannels. However, the model described
above should be applicable to microchannels as well.
Experiments showing nucleation in microchannels are
reported in this paper in a later section.
3. Bubble growth following nucleation in microchannels
Bubble growth following nucleation plays a critical role
in the flow boiling stability in microchannels and minichannels. The resulting flow boiling instabilities were observed
by a number of investigators:
Hetsroni et al. [10] observed periodic annular flow in
microchannels of 103–129 lm hydraulic diameters with
water flow; Kennedy et al. [11] studied the onset of instability as a function of flow rate and exit quality in circular
minichannels of 1.17 and 1.45 mm diameter; Kandlikar
et al. [12] observed flow instabilities leading to flow reversal
with water in 1 mm square minichannels; Peles [13] studied
local pressure fluctuations and flow reversals in 50–200 lm
triangular microchannels; Balasubramanian and Kandlikar
[14] obtained clear high-speed images of the flow phenomenon simultaneously in a set of six 1054 · 197 lm
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S.G. Kandlikar / Experimental Thermal and Fluid Science 30 (2006) 441–447
Fig. 3. High-speed image sequence (a) at 1 ms time intervals in a channel showing bubble growth and reverse flow (overall flow is up) and (b) simultaneous
movement of liquid–vapor interfaces in opposite directions in a set of six parallel microchannels (overall flow left to right), Kandlikar and
Balasubramanian [15].
00
DT Sub;ONB ¼ q =hL DT Sat;ONB
ð7Þ
where DTSub = TSat Tbulk. The wall superheat at the
ONB condition can be calculated from Eqs. (5) or (6)
depending on the available cavity sizes.
Analyzing Eq. (7) further, it is observed that the high
heat transfer coefficient in the microchannels may lead to
a low subcooling at the nucleation site. In some cases,
the liquid may become superheated (negative subcooling).
Under these conditions, the nucleating bubble experiences
a superheated environment as it grows from the nucleation
site on the wall into the bulk liquid. This causes an extremely rapid bubble growth, which pushes the liquid in both
the upstream and downstream directions as seen in Fig. 3.
Fig. 4 shows a plot of local wall superheat and liquid
subcooling as a function of nucleating cavity radius for
water in a microchannel corresponding to the operating
conditions studied in [15]. The wall superheat decreases
with cavity radius, reaching a minimum at the ONB location corresponding to the critical cavity radius, and then
ΔTsat, ONB
ΔTsub, ONB
60
40
20
Δ TONB (oC)
rectangular channels. These studies indicated that the nucleation of a bubble followed by its rapid growth into a vapor
slug resulted in reverse flow leading to flow instability.
Fig. 3 shows a high-speed video image sequence
obtained by Kandlikar and Balasubramanian [15]. The
rapid bubble growth filling the entire channel causes backflow in the channel. This backflow coupled with the inlet
manifold interactions between the parallel channels causes
the unstable operation. The instabilities occurring in
conventional evaporators due to a negative slope in the
pressure drop demand curve are also present in microchannels [16].
The bubble growth rate following nucleation depends on
the wall superheat and the local liquid conditions surrounding a bubble. The local liquid subcooling at the onset
of nucleate boiling (ONB) can be obtained from the following single-phase heat transfer equation:
0
0.1
1
10
100
-20
-40
-60
rc (μm)
Fig. 4. Local wall superheat and liquid subcooling at the ONB location as
a function of cavity radius, water in a 1054 · 197 lm microchannel at
340 kW/m2.
increases again for higher cavity radii. The local subcooling
is calculated from Eq. (7). It can be seen that the liquid subcooling is negative in the entire region, indicating the bulk
liquid to be in the superheated state. The cavity radius at
the ONB is around 6 lm. The corresponding value of wall
superheat is 8 C, while the liquid subcooling is 4 C,
indicating a liquid superheat of 4 C. If the cavities of radii
in the vicinity of the critical cavity radius condition are not
available, then the wall superheat and the corresponding
liquid superheat are higher as seen from Fig. 4.
Fig. 4 is generated with a wall heat flux of 340 kW/m2.
Similar plots can be generated for any other operating conditions. It is also noted that the liquid subcooling condition
represented in Fig. 4 corresponds to the bulk liquid condition, and the liquid closer to the wall may be superheated
even further.
S.G. Kandlikar / Experimental Thermal and Fluid Science 30 (2006) 441–447
445
ΔTsat, ONB
ΔTsub, ONB
50
40
ΔTONB (oC)
30
20
10
0
0.1
10
1
100
-10
-20
Fig. 6. Schematic representation of pressure variation following nucleation during flow boiling in a microchannel under stable operation.
-30
rc (μm)
Fig. 5. Local wall superheat and liquid subcooling at the ONB location as
a function of cavity radius, water in a 1054 · 197 lm microchannel at
1 MW/m2.
As the heat flux increases, the local subcooling and wall
superheat at the nucleation location, and the nucleation
characteristics also change. Fig. 5 shows the local wall
superheat and liquid subcooling plot for a heat flux of
1 MW/m2 for the same channel depicted in Fig. 4. The wall
superheat and the local subcooling are affected and both
increase as seen from Eq. (7). The bulk liquid subcooling
increases with heat flux and the region between the cavity
radii 1.5–7 lm becomes subcooled. The increased wall
superheat will lead to a very rapid bubble growth, while
the increased liquid subcooling will present a colder liquid
at the interface. However, the rapid expansion from the
increased wall superheat is expected to dominate with a
resultant increase in the backflow intensity.
4. Stabilization of flow boiling following nucleation
The high heat transfer coefficient in microchannels
causes the liquid surrounding a nucleating bubble to be
close to its saturation state, or even in the superheated state
as shown in Fig. 4. The flow boiling characteristics in
microchannels therefore differs from that in the conventional sized channels because of this additional factor
affecting the flow boiling stability.
Consider a microchannel under flow boiling conditions.
Assuming equilibrium and stable operating conditions, the
pressure varies qualitatively as shown in Fig. 6. The singlephase pressure gradient is relatively small. The gradient
increases in the two-phase region following the onset of
nucleation.
As a bubble grows over a cavity, the maximum pressure
that can be sustained inside the bubble is dictated by the
saturation pressure corresponding to the heater surface
temperature. This condition assumes that the entire bubble
interface is in contact with superheated liquid at the same
temperature as the heater surface, and neglects the excess
pressure required to sustain the dynamic growth of the
bubble, Mikic et al. [17].
The onset of nucleate boiling thus introduces a pressure
spike at the nucleation location as shown in Fig. 6. The
maximum pressure that can be theoretically attained, as a
limiting case, inside the nucleating bubble is governed by
the saturation pressure corresponding to the wall temperature at the nucleation location as discussed above
pV;max ¼ pSat jT W;ONB
ð8Þ
where pV,max—maximum pressure inside a nucleating bubble, and pSat jT W;ONB —saturation pressure corresponding to
the wall temperature at ONB.
The pressure spike in the flow at the nucleation site
introduces a disruption in the flow. Depending on the local
conditions, the excess pressure inside the bubble may overcome the inertia of the incoming liquid and the pressure in
the inlet manifold, and cause a reverse flow of varying
intensity depending on the local conditions.
There are two ways to reduce the flow instabilities:
(i) reduce the local liquid superheating at the ONB, and
(ii) introduce a pressure drop element at the entrance of
each channel
The local liquid superheat at ONB can be reduced by
making cavities of the right radii (minimum wall superheat
as seen in Fig. 4) available on the heated surface. The
reversed flow can be reduced by introducing pressure drop
elements at the entrance of each channel and operating the
system with an inlet manifold pressure higher than the
maximum pressure given by Eq. (8).
pInlet manifold > pSat jT W;ONB
ð9Þ
Flow stabilization was experimentally investigated by
Kandlikar et al. [2]. They introduced pressure drop elements of various area constriction ratios at the inlet of
1054 · 197 lm rectangular channels and incorporated artificial nucleation sites of 5–30 lm radii in the heated wall.
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S.G. Kandlikar / Experimental Thermal and Fluid Science 30 (2006) 441–447
The flow was completely stabilized with inlet pressure drop
elements providing only a 4% free flow area. The average
heater surface temperature was 111.5 C for a heat flux
of 340 kW/m2, which corresponds to a cavity radius range
of 2–11 lm range as seen from Fig. 4. Artificial nucleation
sites (radius range 5–30 lm) cover part of this active range.
The inlet pressure in the manifold was 139.5 kPa, which is
slightly less than the saturation pressure of 150 kPa corresponding to the average heater surface temperature of
111.5 C. Fig. 7 shows a high-speed image sequence under
stabilized conditions in one of the channels. Slight movement of the bubble interface in the reverse flow direction
is due to liquid film flow between the wall and the bubble.
The location of the ONB point plays an important role
in the stability of the flow boiling process. When the nucleation occurs toward the exit end, see Fig. 8, the flow resistance in the backflow direction is higher than that in the
flow direction due to a longer distance from the inlet
manifold. On the other hand, if the nucleation occurs near
the inlet end, the flow resistance to backflow is lower, and
vapor may flow back into the inlet manifold. Mukherjee
and Kandlikar [18] studied the problem numerically and
confirm that introducing the pressure drop elements and
operating the inlet manifold at a higher pressure leads to
a reduction in the backflow intensity.
Flow boiling characteristics are intimately linked to the
local nucleation characteristics in the microchannels. In
addition, the increasing importance of the surface tension
force and the diminishing effect of the gravitational force
have been recognized by many investigators. Scaling these
forces, two new non-dimensional groups were proposed by
Kandlikar [19]. The group K1 represents the ratio of the
evaporation momentum to inertia forces, and K2 represents
the ratio of the evaporation momentum to surface tension
forces
00 2
q
qL
K1 ¼
ð10Þ
GhLV qV
00 2
q
D
K2 ¼
ð11Þ
hLV qV r
where G—mass flux, D—characteristic dimension (bubble
departure diameter in critical heat flux modelling), and
r—surface tension. The group K1 replaces the boiling number q00 /(GhLV) by incorporating the density ratio effect, and
the group K2 was seen to be useful in modelling the critical
heat flux in pool boiling conditions, Kandlikar [20].
5. Conclusions
Nucleation during flow boiling in microchannels is studied and expressions for local wall superheat and liquid
subcooling at the nucleation location are obtained. The
high heat transfer coefficient in microchannels leads to a
superheated liquid environment surrounding a nucleating
bubble. The rapid increase in the pressure inside a bubble
introduces a pressure spike, which is governed by the saturation pressure corresponding to the local temperature of
the heater wall. Introducing a pressure drop element, in
addition to the artificial nucleation sites, and operating
the system with an inlet pressure above the pressure spike
stabilizes the flow. The results have been confirmed by
conducting experiments with flow boiling of water.
Fig. 7. Stabilized flow with an inlet pressure drop element with a 4% free
flow area and artificial nucleation cavities of 5–30 lm radii during flow
boiling in 1054 · 197 lm rectangular microchannels, Kandlikar et al. [2].
Fig. 8. Effect of nucleation location on flow boiling characteristics.
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