Paper No 7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Application of Liquid Film Characteristics to Predicting Annular Flow Boiling Heat
Transfer Coefficients in Mini and Microchannels
K.H. Bang, S.K. Lee, H.T. Kim and H.S. Jeong
Department of Mechanical Engineering, Korea Maritime University
1 DongsamDong, YeongdoGu, Busan, 606791, Korea
klIbaiuII' hIu Iu c kr
Keywords: Flow boiling, Microchannel, Minichannel, Twophase flow, Electronic cooling
Abstract
An experimental study on flow boiling of water in a minichannel of 1.73 mm innerdiameter round tube and in a microchannel
of 0.31 mm diameter round tube has been conducted and the measured flow boiling heat transfer coefficients were compared
with available correlations. The comparison shows that there are yet a large discrepancy between the data and the correlation
predictions. Liquid film is generally very thin in minichannel and microchannel flow and it envisages that liquid film
characteristics plays a major role in constructing a model for flow boiling heat transfer coefficient. Two approaches were
carried out: an empirical correlation of liquid film thickness for slug flow and a relation between void fraction and twophase
frictional multiplier for annular flow. Combining the slug flow model and the annular flow model over the appropriate range of
vapor quality gives a good agreement with the experimental data.
Introduction
For the last several decades compact heat exchangers
have shown growing interest and demand in many industrial
applications such as automobile radiators, HVAC and
refrigeration systems, and recently electronic equipment
cooling such as computer CPUs and highluminance LED
lighting packages. The hydraulic diameters of the tubes and
channels for these miniature heat exchange devices are
continuously getting smaller and now sizes of even down to
tens of micrometers are considered for microprocessor chip
cooling.
Classifying a tube or channel size as large or small seems
rather vague since the heat transfer and fluid flow
characteristics can be different even over the ranges of
millimeter to submillimeter size. Recently the term
"minichannel" has become a common word for tubes and
channels whose hydraulic diameters are in the range of 0.3
mm to 3 mm. The channel sizes over 3 mm are called
conventional channel, and the channel sizes smaller than 0.3
mm are called microchannel (Kandlikar, 2004).
The main motivation of such channel size classification
has come from the question that the existing knowledge of
heat transfer and fluid flow, which has been documented
from the data collected largely from the conventional larger
size channels, can be valid for smaller channels;
minichannels and microchannels. For twophase flow
boiling, the recent articles have reported different
characteristics depending upon flow conditions and fluid
type. The past work has shown different trends of the
influence of mass flux, vapor quality and heat flux on the
flow boiling heat transfer coefficients. Also the influence of
the channel size in flow boiling is associated with the length
scales involved; bubble size or liquid film thickness and the
twophase flow patterns such as bubbly, slug and annular
flow.
Since early 1990s a number of experimental studies on
the flow boiling heat transfer in minichannels have been
reported. These include the experiments of Wambsganss et
al. (1993) and their coworkers Tran et al. (1996) using small
round and rectangular tubes of 2.42.9 mm inner diameter
and R12/R113 fluids. They reported that in small tubes the
evaporation heat transfer coefficients are greatly affected by
the heat flux and it does not seem to be a function of vapor
quality at higher heat fluxes. Bang and Choo (2i 4) with
1.6 mm round tubes and R22 also reported a similar trend
to Wambsganss et al. (1993) results such that the heat
transfer coefficients are independent of vapor quality and
mass flux. However, Yan and Lin (1998) conducted
experiments using small round tube of 2.0 mm inner
diameter and R134a refrigerant and found a trend similar to
the Kandlikar (1990) correlation such that the evaporation
heat transfer coefficient decreases as the vapor quality
increases. Some selected experimental works on the flow
boiling in minichannels are summarized in Table 1.
The major tend of flow boiling heat transfer in
minichannels is that the local heat transfer coefficients are
largely independent of mass flux or vapor quality, but only a
function of wall heat flux. These experimental observations
may indicate that the flow boiling in minichannels is of
socalled nucleate boiling dominant regime. One notes,
however, that most of the experimental work mentioned
here used Freon type fluids. The work by Steinke &
Kandlikar (2003) and Qu & Mudawar (2003) have a
Paper No
Nomenclature
Bo boiling number, q"/Ghfg
Bo bond number, pad2/ o
Ca capillary number, gV/ o
Co convection number, ((1x)/x) 8(p/ p)0 5
d hydraulic diameter
G mass flux
h heat transfer coefficient
k thermal conductivity
L channel length
Nu Nusselt number, hd/k
P pressure
A P pressure drop
Pr Prandtl number
q heat transfer rate
q" heat flux
r radius
Re Reynolds number, Gd/ p
T temperature
V velocity
x vapor quality
Greek letters
a void fraction
6 liquid film thickness
f twophase multiplier
p viscosity
p density
a surface tension
Subsripts
g vapor
h hydraulic
i inner
1 liquid
o outer
sat saturation
w wall
LO liquid only
NBD nucleate boiling dominant
CBD convective boiling dominant
common in working fluid of water and in general showed a
contradicting trend of heat transfer coefficient v.s. mass flux
and heat flux to Freon cases. Convection dominant heat
transfer in water system may be related to high latent heat of
vaporization of water compared to hydrocarbons.
The microchannels having a hydraulic diameter smaller
than 300 gm are the practical ones for the heat sinks of
computer chip cooling and the shape of the parallel channels
is normally rectangular due to the nature of fabrication.
Some selected experimental works on the flow boiling in
microchannels are summarized in Table 1.
Yen et al. (2003) used three different circular
microchannels of 0.19, 0.30 and 0.51 mm of inner diameter
for flow boiling of HCFC123. Their data show a sharp
decrease in flow boiling heat transfer coefficients as the
vapor quality increases from 0.0 to 0.3. Also the heat
transfer coefficient tends to be independent of heat flux
when the heat flux is greater than 10 kW/m2.
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Steinke & Kandlikar (2003) used a copper substrate of six
parallel microchannels; 214 pm wide, 200 pm deep and 64
mm in length. They reported that flow boiling heat transfer
coefficients decreased as the vapor quality increased, but
little affected by the heat flux. Qu & Mudawar (2003)
reported their experimental data for 21 parallel rectangular
microchannels of 231 pm wide, 712 pm deep and 44.8 mm
in length. But in this report, flow boiling heat transfer
coefficients increased as the mass flux increased for the
same quality and it decreased as the quality increased for the
same mass flux. They proposed also that the flow boiling
heat transfer coefficients in microchannels were greatly
affected by mass flux, but little by heat flux.
These two reports of Steinke & Kandlikar and Qu &
Mudawar have a common in working fluid of water and in
general showed a contradicting trend of heat transfer
coefficient v.s. mass flux and also v.s. heat flux to the
experimental data using hydrocarbons. Convection
dominant heat transfer in water system may be related to
high latent heat of vaporization of water compared to
hydrocarbons. Considering relatively high pressure drop in
microchannels, a slight subcooling may lead to pure
convection without actual bubble formation and twophase
boiling.
The experimental work of flow boiling in parallel
microchannels fabricated on a substrate is generally a
difficult task in terms of accurate measurement of wall
temperature and local pressure as well as possible flow
oscillation in parallel channels. The flow pattern in these
rectangular channels may differ from that in a circular
channel, in particular, in annular flow the liquid film flow
can be confined in the corners of the rectangle, causing most
of the wall dried out. Also, the test setup usually has a large
mass compared to the channel fluid volume and not only the
channel surface area but also a large extra surface area of
the test setup may contribute on the balance of physical
parameters between the inlet and outlet plenum, such as
energy balance. Uncertainties in such an energy balance as
well as wall temperature measurement may cause a
significant error as well as data scatter.
Despite that there are a number of experimental works on
flow boiling heat transfer in minichannels and
microchannels, there are only a few empirical correlations
that one can easily use to predict heat transfer coefficients.
There are also more physicsbased flow boiling models
available (Qu and Mudawar, 2003; Thome et al., 2004), but
these models require extensive numerical calculations to get
the heat transfer coefficients.
Therefore, the first attempt was to choose three
correlations of flow boiling heat transfer and to compare
each prediction for water flow in mini and microchannels.
These are Gungor & Winterton (1987), Yu et al. (2002), and
Kandlikar & Balasubramanian (2003), and are given below.
Gungor & Winterton (1987)
S075/ ,041
h=h, l+3000Bio 6+1.12X
P x p (1)
S .023G( ) d
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Table 1: Summary of past investigations on flow boiling in minichannels and microchannels
Channel Size Mass Flux Heat Flux Pressure
Authors Year Fluid
[Yearmm] Fd [kg/m2s] [kW/m2] [bar]
Wambsgasss et al. 1993 2.4, 2.9, round, square R12, R113 50830 3.690 sat
Tran et al. 1996 2.4, 2.9, round, square R12, R113 50830 3.690 sat
Yan and Lin 1998 2.0, round R134a 50200 520 sat
Bao et al. 1999 1.95, round R11, R123 501800 5200 sat
Yu et al. 2002 2.98, round water 50200 50300 12
Bang and Choo 2004 1.66, round R22 300600 530 sat
Bang et al. 2009 1.73, round water 100200 50160 216
Lin et al. 2001 1.1, round R141b 510 1872 sat
Yen et al. 2003 0.190.51, round R123, FC72 50300 113 sat
Qu & Mudawar 2003 0.231x0.713, rect., 21 ch. water 135402 5001500 1.17
Steinke & Kandlikar 2003 0.214x0.2, rect., 6 ch. water 1501800 50900 2
Bang & Yoon 2005 0.31, round water 110305 2086 <0.5
Yu et al. (2002)
02
h = (6.4 x 106)(Bo2We)027
Kandlikar & Balasubramanian (2003)
h max(hD,hc BD), Re, >100
h [ hBD, Re, < 100
h, = [0.6683Co2(1 x)08 + 1058Bo7 (1 x) 0sF ]ho
hBD = 1.136Co 9(1 x)8 + 667.2Bo7 (1 x)SFL ]hLO
The first one has been applied to conventional larger
size tubes and the latter two have been tested with the data
from minichannels and microchannels. It is noted that the
vapor, quality is not a parameter in the correlation of Yu et
al. and the Kandlikar's is basically his correlation for
conventional channels (Kandlikar, 1990) with some
classification for microchannels, where hLo is single phase
convective heat transfer coefficient for laminar or turbulent
depending on Reynolds number.
First, the predictions of flow boiling of water in 1.73
mm diameter circular tube by these correlations are
compared in Figure 1. The mass flux of 300 kg/m2s in this
comparison corresponds to Re=1600 at 1 atm laminarr
flow) for liquidonly flow. Figure 1 shows that there are
large differences between the predictions by the three
correlations. It is noted that the Yu et al. correlation is not a
function of vapor quality. The other two correlations show
the typical rise of convection dominant flow boiling heat
transfer coefficient as a function of vapor quality.
For a microchannel of diameter of 0.3 mm, Figure 2
shows the prediction of the correlations for water and the
mass flux of 100 kg/m2s. Again, it is shown that Yu et al.
correlation is not a function of vapor quality. The
Kandlikar correlation shows decreasing trend of heat
transfer and this is because for this value of mass flux,
liquid Re number is below 100 and the correlation
indicates nucleate boiling dominant regime. It is noted that
the Kandlikar correlation has a discontinuity at liquid
Re=100. For example, for liquid Re=100 and the
conditions of Figure 2, the nucleate boiling dominant value,
hND, is 44600 W/m2K and the convection dominant value,
(2) hcBD, is 70992 W/m2K. In convection dominant regime,
the Kandlikar correlation gives increasing heat transfer
coefficient as the vapor quality increases.
60000
50000
S40000
g 30000
20000
10000
 Kandlikar (2003) Water, 1 atm, D=1 73 mm
Yu metal (2002) G100 kg/m s, q"=80 kW/m
A Gungor & Winterton (1987)kq8k
0.1 0.2 0.3 0.4 0.5
Vapor Quality, x
Figure 1: Comparison of flow boiling heat transfer
correlations for water in minichannel (d=1.73 mm)
10000
U 0
Kandlikar (2003) Water, 1 atm, D=0 3 mm
Yu et al (2002) G=100 kg/m s, q"=80 kW/m2
Gungor & Winterton (1987)
A/ /./ 1 < 
0.1 0.2 0.3
Vapor Quality, x
0.4 0.5
Figure 2: Comparison of flow boiling heat transfer
correlations for water in microchannel (d=0.3 mm)
Paper No
Paper No
Experiment
For water flow in a microchannel and a minichannel, two
sets of experiments have been conducted using round tubes
of 0.31 mm and 1.73 mm in diameter. A brief description of
experimental apparatus and the experimental results are
given here and more details are found in the articles of Bang
et al. (2007) for microchannel and Bang et al. (2009) for
minichannel.
Microchannel Experiment
The experimental apparatus consisted mainly of
degassing devise, peristaltic pump, preheater, test section of
single microchannel, and vacuum chamber for control of the
operating pressure. The microchannel was a round stainless
steel tube with 0.31 mm of inner diameter, 0.1 mm thickness,
and 75.7 mm in length (53.4 mm heated length). To
minimize heat loss at the both ends of the tube and to
construct a leakproof connection of micro size tube, two
polyethylene blocks held the two ends of the tube with
flanges and micro orings. The end blocks were also
machined to provide thermocouples and pressure gauge
ports.
Heat flux was provided by heating wire wound over the
tube and variable DC power was connected. The voltage and
current were measured to obtain heat flow rate to the test
tube. The tube exit was connected to the vacuum chamber of
which pressure was controlled at a preset pressure. A small
but stable flow rate of water through a microchannel was
possible using a variable speed peristaltic pump and the
flow rate was measured using a precision balance on which
the water supply container was put on.
Deionized water was used as the working fluid. To
obtain degassed water, the water was first boiled in a
separate water heater and cooled quickly with minimum
contact with the ambient air. Then it was transferred to a
water container with the top cover sealed and moving up as
the water was filled in from the bottom to minimize the
contact of water with air. When the water level was lowered
as water flowed out to the test tube the top cover was also
lowered accordingly.
The water inlet temperature was controlled at the
preheater. The inlet and the outlet pressures were measured
to obtain pressure drop across the channel and the tube outer
wall temperatures were measured at two locations using
thermocouples spotwelded on the tube surface. The heat
transfer coefficient was obtained from the heat flux, wall
temperature and the bulk fluid temperature (or saturation
temperature for flow boiling).
One of the major findings in the present work was the
effect of operating pressure on the trend by the wall heat
flux (or vapor quality). At the lower operating pressure (11
kPa) the heat transfer coefficient increased as the wall heat
flux increased, but at the higher operating pressure (20
kPa) it decreased as the wall heat flux increased. At 15 kPa
the heat transfer coefficient did not change in terms of the
heat flux. The cause of such different trends of the operating
pressure can be attributed to the twophase flow parameters
such as vapor velocity and liquid film thickness. Figure 3
and 4 show the measured flow boiling heat transfer
coefficients.
In the subatmospheric pressure range, the specific
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
volume of the saturated vapor changes significantly as the
pressure changes. The ratio of the specific volumes of
saturated vapor for the pressure of 11 kPa to 20 kPa is 1.8,
indicating that the vapor velocity in the lower pressure is
almost double of that in the higher pressure. The liquid film
in annular flow, for example, must be thinner in lower
pressure due to the higher vapor velocity and this enhances
the contribution of the convective boiling mode. It is also
interesting to note in Figure 3 and 4 that the effect of the
operating pressure is diminishing as the heat flux increases
and the heat transfer coefficient appears to be independent
of the heat flux (or the vapor quality) at higher heat fluxes.
The measured heat transfer coefficients are shown in
terms of vapor quality in Figure 5. Also shown in the figure
is the single phase convective heat transfer coefficient of
laminar liquid flow, h=4.36k/Dh=9.0 kW/m2K. The
saturated flow boiling showed poorer performance than the
single phase convection when the operating pressure is as
low as 10 kPa. But in the case of operating pressure of 20
kPa, the flow boiling performance is better than single phase
flow. The combined presentation of heat transfer
coefficients for the two mass fluxes showed that the effect
of mass flux is small.
25
20
15
10
,
5
G =203 kglm2s( Re = 168)
SP =11. kPa
Pu= 15.0 kPa
SP = 19.8 kPa
A
A A
A O
* .
10 20 30 40 50 60 70 80 90
Heat Flux (kW/m2)
Figure 3: Effect of operating pressure in microchannel flow
boiling (G=203 kg/m2s)
25
20
 15
"E
10.
5
G = 112 kg/m2s (Re = 87)
SPout,=11.0kPa
Pout =15.0 kPa
A Put =19.8kPa
A
A A
U U
A A
A
U
70 80 90
10 20 30 40 50 60
Heat Flux ( kW/m2)
Figure 4: Effect of operating pressure in microchannel flow
boiling (G= 112 kg/m2s)
. *
0 0
* 0
Paper No
25
20
 15
E
10
5
5
Single
Phase
A&
LA
a0
U** 0
do5 DD
0.00 0.05 0.10 0.15
quality, x
0.20 0.25
Figure 5: Flow boiling heat transfer coefficients v.s. vapor
quality in microchannel (water, d=0.3 mm)
The prediction of flow boiling heat transfer coefficients
using the correlations are compared with the experimental
data in Figure 6. It appears that the discrepancy between the
Kandlikar's prediction and the present data is large,
compared to the Yu et al.'s correlation. The correlation of Yu
et al. showed a similar trend as the data for the case of 11
kPa, but failed to show the decreasing trend of 20 kPa
pressure.
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
supply various vapor quality at the inlet of the test tube, an
evaporator is installed before the test tube. It is a 2m long
tube of the same tube size with the test tube and heated by
passing direct DC current. In the connecting part to the test
tube, the same flow cross sectional area is kept to prevent
twophase flow regime change.
The test tube is a 300mm long, SS316 round tube and its
inner diameter is 1.73 mm and the wall thickness is 0.72
mm. The heat flux is provided by passing direct DC current.
At the both ends of the test tube a short PFA
(PerFluoroAlkoxy) tube is connected to provide electrical
insulation between the test tube and the rest of the loop. The
temperature of the test tube wall is measured at five
locations using thermocouples bonded to the outer wall
using high thermal conductivity cement.
The fluid temperature measurement at the exit of
preheater, at the inlet of evaporator, at both the inlet and the
exit of test tube, and the exit of the condenser are made by
direct insertion of the thermocouples into the tube. The
differential pressure across the test tube and the absolute
pressure at the inlet of the test tube are measured.
The influence of heat flux on the flow boiling heat
transfer coefficient for water at 2 bars is shown in Figure 7.
The dryout occurred at about 0.6 of vapor quality. The
measured flow boiling heat transfer coefficients are in the
general trend of convection dominant flow boiling such that
at low vapor quality the change of the heat transfer
coefficient versus vapor quality is small or nearly plateau
and at higher quality the heat transfer coefficient increases
as the quality increases. It is interesting to observe that the
higher heat flux reduces the heat transfer coefficient.
G = 112kg/m2s( Re= 87)
U P =11.OkPa
P = 15.0kPa ,.="
A Pt =19.8kPa ,,<.'
Correlations
Yu et al. (2002)
 Kandlikar (2004)
A A
A^'^
40000
30000
E 20000
10000
10 20 30 40 50 60 70 80 90 100
Heat Flux( kW/m2)
D=1.73 mm, 2 bars, G=100 kg/m2s
A .
A. /
A. A
..
q"=50 kW/m
q"=80 kW/m2
q"=115 kW/mn
q"=150 kW/m
0.0 0.1 0.2 0.3 0.4 0.5 0.6
Figure 6: Comparison of flow boiling heat transfer
coefficients with empirical correlations (d=0.31 mm)
Minichannel Experiment
The experimental apparatus consists mainly of pump,
preheater, pressurizer, evaporator, test tube, and condenser.
The pump is a magnetic gear pump with variable speed and
a coriolistype flow meter is installed to measure the mass
flow rate. To control the system pressure, a pressurizer is
installed at the pump suction side. The pressurizer is a
rectangular chamber of which both side walls are made of
transparent quartz plates in order to visually check the liquid
water level of the loop. At the top of pressurizer is nitrogen
gas tank connected to control the system pressure. To
Figure 7: Flow boiling heat transfer coefficients of water at
2 bars (d=1.73 mm)
The present flow boiling heat transfer data for water in
minichannel are compared with the predictions of the three
selected correlations. First, the prediction of Gungor and
Winterton correlation does not look good and this is
probably because this correlation is based on the data for the
conventional larger size channels. The best prediction is by
Kandlikar correlation as shown in Figure 8. This correlation
has been developed based on flow boiling data for
minichannels and microchannels. However, the heat flux
increases the heat transfer coefficient but the experimental
data shows the reversed trend.
40
35
30
25
E 20
 15
10
5
Paper No
40000
30000
E 20000
q"=50 kW/m
q"=80 kW/m2
q"=115 kW/m2
q"=150 kW/m2
Line: Kandlikar (2003)
A
0 0.1 0.2 0.3 0.4 0.5 0.6
Figure 8: Comparison of flow boiling heat transfer
coefficients with Kandlikar's correlations (d=1.73 mm)
Annular Flow Boiling Model
The dominant flow pattern in flow boiling in small
channels has largely known to be annular flow, thus the
liquid film thickness is the controlling parameter for the
magnitude of flow boiling heat transfer coefficient. As for
the flow pattern of flow boiling in small channels, Barajas
and Panton (1993) studied on the effects of contact angle on
twophase flow in capillary tubes and suggested that the
flow pattern in small tubes is greatly affected by the contact
angle of the wall and the fluid and the surface tension of
liquid and vapor. This observation of contact angle effect
seems one of very important aspects of flow boiling in
minichannels and microchannels.
Using the flow regime map proposed by Barajas and
Panton, the locus of the flow regime change for water in the
minichannel of 1.73 mm diameter, mass flux of 100 kg/m2s
and vapour quality of 0.050.6 is shown in Figure 9. It
shows that flow patter changes from slug flow to annular
flow at the vapour quality between 0.1 and 0.2.
10
o
1
0 0.1
0.01
_j
0.1 i 10
100 1000
Gas Velocity U GS, m/s
Figure 9: Flow pattern on Barajas and Panton map for water
in 1.73 mm diameter channel, G=100 kg/m2s, x=0.050.6
Twophase flow pattern in minichannel or microchannel
is dominated by slug flow in low vapor quality and annular
flow in high vapor quality. Thome et al. (21"i 14 proposed a
threezone flow boiling model to describe evaporation of
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
elongated bubbles of slug flow in microchannels. Their heat
transfer model describes the transient variation in local heat
transfer coefficient during the sequential and cyclic passage
of (i) a liquid slug, (ii) an evaporating elongated bubble and
(iii) a vapor slug. Besides, however, this detailed modeling
of slug bubble seems to be applicable to the very short
length of entry part of heated channels since the flow
quickly becomes annular as the vapor quality increases, the
model is strongly dependent on empirical data such as
bubble frequency.
In annular twophase flow the heat transfer at the inner
wall is dominated by the heat transfer across the liquid film
and the prediction of liquid film thickness is the key in
determining the heat transfer coefficient.
An experimental measurement of liquid film thickness
has been conducted by Han and Shikazono (2009) for slug
flow in microchannels. They used laser focus displacement
meter to measure liquid film thickness inside round tubes of
0.5, 0.7 and 1.0 mm diameter and the working fluids were
ethanol, water, and FC40. Based on the experimental
measurement of liquid film thickness, they proposed the
following empirical correlation for the liquid film thickness
under slug bubble acceleration.
J 0.968Ca23Bo0414
d 1+4.838Ca2/3Bo 414
Here, Ca is capillary number and Bo is Bond number.
For annular flow, liquid film thickness can be related with
void fraction, hence if one can obtain an empirical relation
for void fraction, liquid film thickness can be calculated.
For a liquid film of thickness 6 in a round tube,
4nd8 48
(1 a) d =
nd2 d
Following the LockhartMartinelli approach on annular flow
(Collier and Thome, 1994), the relationship between the
twophase frictional multiplier and the void fraction is
) = (1 a)2
And the LockhartMartinelli correlation for the twophase
multiplier is
C 1
2 = 1++
X X2
Where X is the Martinelli parameter and the constant C is 12
for the case of laminar liquid flow and turbulent vapor flow
which is a typical case for flow boiling in minichannels. Yu
et al. (2002) proposed an empirical expression for the
Martinelli parameter.
pg 1 0 x Re
X 18.65 g1
S5x Re 5
Using equations (5) to (8), the liquid film thickness can be
calculated.
Must.
Riv.
II,
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Annular flow model
 Slug flow model
01 02 03
Vapor Quality
50000
40000
S30000
E
20000
10000
04 05 06
A Measured
 Annularflow model
 Slug flow model
0.1 0.2 0.3 0.4 0.5 0.6
Figure 10: Prediction of liquid film thickness for slug flow
and annular flow (d=1.73 mm, G=100 kg/m2s)
Using the two models above of Han and Shikazono
correlation and the relation of void fraction and twophase
frictional multiplier, the liquid film thicknesses were
calculated for slug flow and annular flow and the results are
shown in Figure 10. It is interesting to observe in the figure
that the flow pattern changes at about x=0.15 and this
transition point is similar to the value found from the flow
pattern map (Figure 9). In the annular flow regime, the
liquid film thickness becomes an order of tens of
micrometer.
The liquid film in minichannels is typically thin as seen
above, the heat transfer across the liquid film can be
approximated by conduction dominant with linear
temperature profile. Based on this assumption, the heat
transfer coefficient can be given by
h =k (9)
Using the proposed liquid film thickness models for slug
flow and annular flow, the flow boiling heat transfer
coefficients were calculated for water flow in minichannel.
The calculated heat transfer coefficients were shown in Fig.
11 together with the measured data. It is shown that the
proposed annular flow model reasonably predicts the
convection dominant trend of the measured data in higher
vapor quality where the annular flow is obvious. At lower
vapor quality where slug flow seems dominant, the annular
flow model underpredicts the data while slug flow model
shows better the trend of the data. Combining the slug flow
model and the annular flow model over the appropriate
range of vapor quality can give a good agreement with the
experimental data.
In slug flow, the contribution of nucleate boiling can not
be neglected, and this is why the slug flow model yet
underpredicts the data. Addition of nucleate boiling
contribution to the slug flow model would result in better
prediction, although a formulation of nucleate boiling heat
transfer is more complex. This will be the work for the
future..
Figure 11: Comparison of the proposed heat transfer model
prediction with experimental data (d= 1.73 mm)
Conclusions
An experimental study on flow boiling of water in a
minichannel of 1.73 mm innerdiameter round tube and in a
microchannel of 0.31 mm diameter round tube has been
conducted and the measured flow boiling heat transfer
coefficients were compared with available correlations. The
comparison shows that there are yet a large discrepancy
between the data and the correlation predictions.
Liquid film is generally very thin in minichannel and
microchannel flow and it envisages that liquid film
characteristics plays a major role in constructing a model for
flow boiling heat transfer coefficient. Two approaches were
carried out: an empirical correlation of liquid film thickness
for slug flow and a relation between void fraction and
twophase frictional multiplier for annular flow. Combining
the slug flow model and the annular flow model over the
appropriate range of vapor quality gives a good agreement
with the experimental data.
Acknowledgements
This work was supported by the MKE (The Ministry of
Knowledge Economy), Korea, under the ITRC (Information
Technology Research Center) support program supervised
by the NIPA (National IT Industry Promotion Agency
(NIPA2009C109009030007).
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