Proceedings of the Fifth International Conference on Nanochannels, Microchannels and Minichannels
Proceedings of ASMEICNMM2007
ICNMM2007
th
5 International Conference on Nanochannels,June
Microchannels
and
Minichannels
18-20, 2007,
Puebla,
Mexico
June 18-20, 2007, Puebla, Mexico
ICNMM2007-30027
ICNMM2007-30027
FURTHER EVALUATION OF A FLOW BOILING CORRELATION FOR
MICROCHANNELS AND MINICHANNELS
Julian V. S. Peters
Thermal Analysis Laboratory, RIT
[email protected]
ABSTRACT
Flow boiling in microchannels and minichannels is being
investigated for its potential for high heat flux removal in
electronics and other devices. The small channel dimensions
characteristic of these channels result, under most
circumstances, in laminar flow at the flow rates used in these
applications. The present work investigates the applicability of
the correlation developed by Kandlikar and Balasubramanian
[1] to some of the recent data for plain as well as enhanced
microchannels using artificial nucleation cavities.
The
correlation is able to provide insight into the effect of the
nucleation cavities on the heat transfer coefficient during flow
boiling in microchannels. Modifications to the use of the
correlation with deep laminar flows are suggested based on
comparison with new data.
Satish G. Kandlikar
Thermal Analysis Laboratory, RIT
[email protected]
G – mass flux
htp – two-phase heat transfer coefficient
hlo – liquid-only heat transfer coefficient
kl – liquid thermal conductivity
Nu – Nusselt number
Prl – liquid Prandtl number
q” – heat flux
Relo – liquid-only Reynolds number
x – vapor quality
ORIGINAL CORRELATION
The two-phase heat transfer coefficient, htp, is determined
differently for nucleate boiling dominant (NBD) and convective
boiling dominant (CBD) regions:
0. 8
INTRODUCTION
As work continues both in generating experimental data on
flow boiling in mini- and microchannels, and in designing heat
transfer systems making use of small-diameter channels,
designers will be well served by empirical correlations
spanning a range of data sets and possessed of wide
applicability. In his 1991 and 1998 papers, Kandlikar [2, 3]
developed a flow boiling map and two-phase heat transfer
coefficient correlation for turbulent flow (Re > 2300) in
channels 3 millimeters and up in diameter. That work was
extended in 2004 by Kandlikar and Balasubramanian [1] to
apply to smaller channel diameters by use of a laminar liquidonly heat transfer correlation. The objective of this work is to
review Kandlikar and Balasubramanian’s correlation with more
recent experimental data on plain and enhanced channels in the
mini- and microchannel regions.
NOMENCLATURE
Bo – boiling number
Co – convection number
D – circular channel diameter
Dh – noncircular channel hydraulic diameter
f – friction factor
Ffl – fluid parameter
Frlo – liquid-only Froude number
htp , NBD = 0.6683Co −0.2 (1 − x )
f 2 (Frlo )hlo
(1)
0.8
+ 1058 Bo 0.7 (1 − x ) F fl hlo
0.8
htp ,CBD = 1.136Co −0.9 (1 − x ) f 2 (Frlo )hlo
0.8
+ 667.2 Bo 0.7 (1 − x ) F fl hlo
(2)
The first term in each of the two equations is referred to as
the convective boiling term; the second term in each equation is
referred to as the nucleate boiling term.
The use of these two equations in determining the two-phase
heat transfer coefficient during flow boiling depends on the
particular flow regime and is subject to modifications in
microchannels.
Details for each flow regime and for
microchannels are given below.
Determination of htp:
The liquid-only heat transfer coefficient, hlo, should be
calculated with a single-phase heat transfer coefficient
appropriate to the conditions in the tube. Furthermore, any
properties or dimensionless quantities used in the calculation of
hlo should be taken as if the full mass flux were liquid.
Suggested correlations for each flow regime are given below.
1
Copyright © 2007 by ASME
Turbulent Flow Region (Relo ≥ 3000):
htp , NBD
htp = larger 
 htp ,CBD
(3)
0 .8
htp = htp , NBD = 0.6683Co −0.2 (1 − x ) hlo
(Re lo − 1000 ) Prl  f 2  k l D 

hlo =

2
1 + 12 .7 Prl 3 − 1  f 
 2
(
)

0 .5
+ 1058 Bo 0.7 (1 − x ) F fl hlo
(4)
100 < Re lo < 410
(Re lo ) Prl  f 2  k l D 
For very low Reynolds numbers, generally under 100, the
convective boiling term is removed from the NBD correlation:
0.8
htp = 1058 Bo 0.7 (1 − x ) F fl hlo



0 .5
2
f


1 + 12 .7 Prl 3 − 1 

 2
(
)
(5)
104 < Relo ≤ 5x106. (Petukhov and Popov)
where
f = [1.58 ln (Re lo ) − 3.28]
−2
(6)
Horizontal and
htp , NBD
htp = larger 
 htp ,CBD
Vertical or
hlo taken as a linear interpolation for the given Relo between
the Gnielinski correlation at Relo=3000 and the laminar value
at Relo=1600 as given by Equation (7). Note that for
microchannels in the Transition and Laminar regions the
Froude number effect is removed – . f 2 (Frlo ) = 1
Frlo > 0.04 : f 2 (Frlo ) = 1
(10)
(11)
Fluid parameter:
Fluid
Ffl
Water
1.00
R-11
1.30
R-12
1.50
R-13B1
1.31
R-22
2.20
R-113
1.30
R-114
1.24
R-134a
1.63
R-152a
1.10
R-32/R-132
3.30
R-141b
1.80
R-124
1.00
R-123
0.616
Nitrogen
4.70
Neon
3.50
Kerosene
0.488
All fluids with a
1.00
stainless steel surface
Table 1. Fluid parameters in Kandlikar [4] correlation.
(Adapted from Kandlikar and Balasubramanian [1] Table 1,
Kandlikar [4] Table 4, and Kuan [8].)
htp , NBD
htp = larger 
 htp ,CBD
(7)
The Nusselt number, Nu, must be appropriate to the channel
geometry and heat transfer boundary conditions (i.e. constant
heat flux or constant surface temperature.)
For example, for circular tubes under constant heat flux
boundary conditions, Nu=4.36. For other geometries and other
boundary conditions, the suitable value of the Nusselt number
must be determined from handbooks and/or literature.
Alternatively, carefully obtained experimental values of hlo
may be employed under the given mass flux, channel geometry
and operating conditions.
Deep Laminar Flow Modifications:
Kandlikar and Balasubramanian [1] suggest two
modifications in the use of the correlation at low Reynolds
numbers. However, comparison with new data leads us to
suggest the following modifications to the use of the
correlation.
0.3
Frlo ≤ 0.04 : f 2 (Frlo ) = (25 Frlo )
Note that for microchannels the liquid-only Froude number
will almost always be larger than 0.04, and f 2 (Frlo ) = 1 .
Laminar Flow (Relo < 1600):
Nu ⋅ k
Dh
(9)
Re lo < 100
Froude number dependence:
The form of the dependency on the liquid-only Froude
number, f 2 (Frlo ) , depends on the orientation of the tube and
on the liquid-only Froude number:
Transition Flow Region (1600 ≤ Relo < 3000):
hlo =
(8)
0 .8
3000 ≤ Relo ≤ 104. (Gnielinski)
hlo =
For liquid-only Reynolds numbers between 100 and 410,
only the NBD correlation given by Eq. (1) applies. Also note
that the Froude number dependence is removed per Equation
(11) which follows:
The fluid parameter Ffl accounts for the effects of
fluid/surface interactions in nucleate boiling heat transfer.
Values of Ffl, for copper and brass surfaces, have been
published by Kandlikar and other researchers and have been
2
Copyright © 2007 by ASME
tabulated below. Note that Ffl=1 for all fluids on stainless steel
surfaces. Methods for experimentally determining Ffl for other
fluid/surface combinations have been discussed in Kandlikar
[4, 7].
The correlation has shown good agreement with many sets
of experimental data. The correlation was originally developed
using a bank of over 10,000 data points. Figure 1 gives an
example of the parametric depdendence that is well predicted
by the correlation for the data of Schrock and Grossman’s [9,
10] . The correlation predicts the experimental data within 10%
and matches the trends very well. Especially note that the
increasing trend in htp with x at lower pressures, and the
decreasing trend in htp with x at higher pressures is well
matched.
study shows much better agreement than they found. Possible
reasons for this discrepancy are discussed at the end of this
section.
Due to the low Reynolds numbers of the flows in Yen’s
study, the Eqs. (8) and (9) have been used here. For the data
with very low Reynolds numbers (400 kg/m2s, Relo ~ 245), Eq.
(9) was used. This is a higher Reynolds number than suggested
by Kandlikar and Balasubramanian [1] for this modification,
but it yields excellent agreement. Further study of this
boundary is warranted. Equation (8) has been used with the
800 kg/m2s data (Relo ~ 500), which is fundamentally in
agreement with Kandlikar and Balasubramanian [1].
2
2
R-123, Circular, 210 µm diameter, 400 kg/m s, 37.53 kW/m
5000.00
4000.00
2
(W/m K)
Two-phase heat transfer coefficient, htp
6000.00
3000.00
2000.00
Yen 2006
Kandlikar Correlation
1000.00
0.00
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Quality, x
Figure 2. Kandlikar correlation compared with Yen’s 2006
data: R-123, 210 µm diameter circular channel, 400 kg/m2s,
37.53 kW/m2.
Figure 1. Variation of two-phase heat transfer coefficient with
vapor quality, x. Comparison of Schrock and Grossman’s
experimental data (points) with Kandlikar’s correlation (lines).
Adapted from [1]
2
2
R-123, Circular, 210 µm diameter, 400 kg/m s, 26.33 kW/m
4000
3500
3000
2
(W/m K)
COMPARISON WITH NEW DATA
New microchannel flow boiling data have been published
since Kandlikar and Balasubramanian extended the correlation
to low Reynolds numbers in mini- and microchannels. In
recent years understanding of the issues attendant to
experimental work in microchannels has developed.
The present work compares the Kandlikar and
Balasubramanian’s modified correlation with new data sets
spanning a range of channel sizes, mass fluxes, heat fluxes, and
with several working fluids. Table 3 summarizes the studies
considered and presents the pertinent experimental parameters.
Two-phase heat transfer coefficient, htp
4500
2500
2000
1500
1000
Yen 2006
Kandlikar Correlation
500
0
0
0.1
0.2
0.3
0.4
0.5
0.6
Quality, x
Fluid properties used in evaluating the correlation are taken
from NIST REFPROP 7.0, Database 23, at saturation at
pressures as given in the experimental papers.
Figure 3. Kandlikar correlation compared with Yen’s 2006
data: R-123, 210 µm diameter circular channel, 400 kg/m2s,
26.33 kW/m2.
Yen, et. al. 2006
Yen, et. al. [11] studied flow boiling of R-123 in circular
and square Pyrex microchannels at mass fluxes of 400 and 800
kg/m2s and heat fluxes from 25.32 to 84.72 kW/m2. They did
compare their results with Kandlikar’s correlation, but our
3
Copyright © 2007 by ASME
Author, Year
Yen, et. al.,
2006
Yen, et. al.,
2006
Kuo and Peles
(in Review)
2
Fluid
Channel Specifications
G, kg/m s
Relo
R-123
Circular, 210 µm
400
243
R-123
Square, 214 µm
400, 800
247, 495
Water
Rectangular, 223 µm
Plain and with
Reentrant Cavities
86-303
68-240
q”, kW/m
26.33,
37.53
25.3284.72
2
x
0-0.7
0-0.7
175-1918
0-0.37
Table 3. Experimental studies for comparison with the Kandlikar correlation.
2
2
R-123, 214 µm Square, 400 kg/m s, 39.25 kW/m
2
Yen 2006
9000.00
14000.00
Kandlikar Correlation
2
Two-phase heat transfer coefficient, htp (W/m K)
2
Two-phase heat transfer coefficient, htp (W/m K)
2
R-123, 214 µm Square, 400 kg/m s, 25.32 kW/m
16000.00
12000.00
10000.00
8000.00
6000.00
4000.00
2000.00
0.00
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
8000.00
7000.00
6000.00
5000.00
4000.00
3000.00
2000.00
Yen 2006
1000.00
0.00
Quality, x
0
Figure 4. Kandlikar correlation compared with Yen’s 2006
data: R-123, 214 µm side length square channel, 400 kg/m2s,
39.25 kW/m2.
2
Kandlikar Correlation
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Quality, x
Figure 5. Kandlikar correlation compared with Yen’s 2006
data: R-123, 214 µm side length square channel, 400 kg/m2s,
25.32 kW/m2.
2
R-123, 214 µm Square, 800 kg/m s, 61.59 kW/m
2
12000
9000
Two-phase heat transfer coefficient, htp (W/m K)
8000
2
2
Two-phase heat transfer coefficient, htp (W/m K)
2
R-123, 214 µm Square, 800 kg/m s, 84.72 kW/m
10000
7000
6000
5000
4000
3000
2000
Yen 2006
Kandlikar Correlation
1000
0
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
The correlation fits the circular tube data shown in Figures 2
and 3 extremely well. The mean absolute errors for those data
sets are 10.5% and 7.89%, respectively. The mean absolute
errors of the fits in Figures 4-7 are 48.2%, 92.2%, 21.1%, and
11.2%, respectively.
The mean absolute errors for the data shown in Figures 4-7
have been calculated excluding the first data point of each set.
The high heat transfer coefficient at the first point is due to the
onset of nucleate boiling near that location.
8000
6000
4000
2000
Yen 2006
Kandlikar Correlation
0
Quality, x
Figure 6. Kandlikar correlation compared with Yen’s 2006
data: R-123, 214 µm side length square channel, 800 kg/m2s,
61.59 kW/m2.
10000
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Quality, x
Figure 7. Kandlikar correlation compared with Yen’s 2006
data: R-123, 214 µm side length square channel, 800 kg/m2s,
84.72 kW/m2.
The square channel data are generally underpredicted by
Kandlikar’s correlation. The large heat transfer coefficients
shown by the square channel data at low qualities is likely due
to the sudden release of liquid superheat at the onset of nucleate
boiling. The underprediction in the moderate quality regions of
Figures 4 and 5 can be ascribed to the enhanced nucleation
present in square and rectangular channels in the corner
regions. Kandlikar’s correlation was originally developed for
4
Copyright © 2007 by ASME
circular tubes, and the relative accuracy of the correlation in
predicting circular and rectangular channel data reflects this.
Rectangular channels can be treated as enhanced channels for
the purposes of Kandlikar’s correlation, with a method similar
to the one presented in Kandlikar [12].
It bears mention that in their paper, Yen, et. al. [11]
presented their Figure 19, which showed Kandlikar’s
correlation overpredicting the circular data by a large margin.
However, in this study the correlation was found to very closely
match Yen’s experimental data. The likely cause of this
discrepancy is that Yen, et. al. may have used a fluid factor Ffl
= 1.0. This is the value for water, and is often used when a
value for the working fluid has not been determined by the
experimenter or is not available in the literature. In this study,
Kuan’s [8] value of 0.616 yielded much better agreement with
Yen’s data. Furthermore, given the low Reynolds number in
the circular channels, the convective boiling contribution
should be disregarded, which Yen, et. al. may have neglected to
do.
Kuo and Peles (in review)
Kuo and Peles [13] performed water flow boiling
experiments with five parallel rectangular channels, with and
without reentrant cavities. The data were provided by Peles
and are currently in review and are used here with their
permission. The experiments were performed at mass fluxes
from 86 to 303 kg/m2s and heat fluxes from 247 to 1297
kW/m2. The experimental procedure in this study was to set a
mass flux and vary the heat flux on the test fixture.
Measurements were taken at one fixed location in the channels;
the quality varied as the heat flux changed. Thus, the variation
of quality does not correlate to position along the channel, as in
other studies, but to changing heat flux.
The deep laminar flow modification to Kandlikar’s
correlation has been made for comparison with these data sets.
This form has been previously presented as equation 9.
2
2
Water, Plain, Rectangular, Dh=223 µm, 86.3 kg/m s
Water, Plain, Rectangular, Dh=223 µm, 161.02 kg/m s
2
Two-phase heat transfer coefficient, htp (W/m K)
120000
2
Two-phase heat transfer coefficient, htp (W/m K)
140000
120000
100000
80000
60000
40000
20000
0
0.00
Peles 2006
Kandlikar Correlation
0.05
0.10
0.15
0.20
100000
80000
60000
40000
20000
0
0.00
0.25
Peles 2006
Kandlikar Correlation
0.02
0.04
0.06
Quality, x
Figure 8. Kandlikar correlation compared with Kuo and Peles’
data: Water, plain channels, 223 µm Dh, 86.3 kg/m2s, 247-417
kW/m2 (Higher heat fluxes applied to achieve higher qualities).
0.10
0.12
0.14
0.16
Figure 9. Kandlikar correlation compared with Kuo and Peles’
data: Water, plain channels, 223 µm Dh, 161.02 kg/m2s, 286564 kW/m2 (Higher heat fluxes applied to achieve higher
qualities).
2
2
Water, Plain, Rectangular, Dh=223 µm, 230.92 kg/m s
Water, Plain, Rectangular, Dh=223 µm, 303.36 kg/m s
140000
2
2
Two-phase heat transfer coefficient, htp (W/m K)
140000
Two-phase heat transfer coefficient, htp (W/m K)
0.08
Quality, x
120000
100000
80000
60000
40000
20000
0
0.00
Peles 2006
Kandlikar Correlation
0.05
0.10
0.15
0.20
100000
80000
60000
40000
20000
0
0.00
0.25
Quality, x
Figure 10. Kandlikar correlation compared with Kuo and
Peles’ data: Water, plain channels, 223 µm Dh, 230.92 kg/m2s,
437-1013 kW/m2 (Higher heat fluxes applied to achieve higher
qualities).
120000
Peles 2006
Kandlikar Correlation
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
Quality, x
Figure 11. Kandlikar correlation compared with Kuo and
Peles’ data: Water, plain channels, 223 µm Dh, 303.36 kg/m2s,
573-1297 kW/m2 (Higher heat fluxes applied to achieve higher
qualities).
5
Copyright © 2007 by ASME
2
Water, Rectangular w/ Reentrant Cavities, Dh=223 µm, 86.3 kg/m s
2
Water, Rectangular w/ Reentrant Cavities, Dh=223 µm, 161.02 kg/m s
2
Two-phase heat transfer coefficient, htp (W/m K)
140000
2
Two-phase heat transfer coefficient, htp (W/m K)
140000
120000
100000
80000
60000
40000
20000
0
0.00
Peles 2006
Kandlikar Correlation
0.05
0.10
0.15
0.20
0.25
0.30
120000
100000
80000
60000
40000
20000
0
0.00
Quality, x
Peles 2006
Kandlikar Correlation
0.05
0.10
0.15
0.20
0.25
0.30
0.35
Quality, x
Figure 12. Kandlikar correlation compared with Kuo and
Peles’ data: Water, reentrant cavities, 223 µm Dh, 86.3 kg/m2s,
175-461 kW/m2. MAE = 62.1%.
Figure 13. Kandlikar correlation compared with Kuo and
Peles’ data: Water, reentrant cavities, 223 µm Dh, 161.02
kg/m2s, 290-853 kW/m2. MAE = 55.9%.
2
Water, Rectangular w/ Reentrant Cavities, Dh=223 µm, 230.92 kg/m s
2
Water, Rectangular w/ Reentrant Cavities, Dh=223 µm, 303.36 kg/m s
160000
2
140000
Two-phase heat transfer coefficient, htp (W/m K)
2
Two-phase heat transfer coefficient, htp (W/m K)
160000
120000
100000
80000
60000
40000
20000
0
0.00
Peles 2006
Kandlikar Correlation
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
140000
120000
100000
80000
60000
40000
20000
0
0.00
Quality, x
Peles 2006
Kandlikar Correlation
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
Quality, x
Figure 14. Kandlikar correlation compared with Kuo and
Peles’ data: Water, reentrant cavities, 223 µm Dh, 230.92
kg/m2s, 443-1546 kW/m2. MAE = 59.7%.
100000
90000
Plain, 86.3 kg/m2s
Reentrant, 86.3 kg/m2s
80000
Plain, 230.92 kg/m2s
Reentrant, 230.92 kg/m2s
70000
2
Experimental htp, W/m K
Kandlikar’s correlation does not predict Kuo and Peles’ data
as well as it did Yen’s [11] data, and in fact shows the opposite
trend. This indicates a basic difference in the mechanism
captured in Kandlikar’s model and what is taking place in Kuo
and Peles’ experiments. This deviation is not currently
understood, but it will be investigated in future work. Some
possibilities include the effects of the stabilizing flow
restrictions used at the entrances of Kuo and Peles’ channels
and the effects of periodic dryout on the heat transfer
coefficient. Figures detailing the comparison of Kandlikar’s
correlation to Kuo and Peles’ data follow.
Generally,
Kandlikar’s correlation matches the data from Kuo and Peles’
plain channels better than the data from the channels with
reentrant cavities. The discrepancy between the plain channels
and the channels with reentrant cavities is exacerbated by the
fact that under similar conditions (quality and mass flux) the
channels with reentrant cavities display lower heat transfer
coefficients than do the plain channels. This effect is shown in
Figure 16 (open markers denote plain channels, filled markers
denote channels with reentrant cavities.)
Figure 15. Kandlikar correlation compared with Kuo and
Peles’ data: Water, reentrant cavities, 223 µm Dh, 303.36
kg/m2s, 570-1918 kW/m2. MAE = 48.1%.
60000
50000
40000
30000
20000
10000
0
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
Quality, x
Figure 16. Comparison of Kuo and Peles’ plain and reentrant
cavity data.
6
Copyright © 2007 by ASME
It is not known at present why the presence of reentrant
cavities would, in fact, degrade the heat transfer characteristics
of these microchannels. The cavities were incorporated to
encourage nucleation at lower wall superheats, thus leading to
higher heat transfer coefficients. Further investigation into this
effect is merited.
As a concluding remark, it is seen that the high heat flux
data is consistently below the predicted values. This needs to be
further investigated.
CONCLUSIONS
Kandlikar’s correlation, with the modifications suggested
by Kandlikar and Balasubramanian [1] and the present authors,
shows good agreement with one of the two data sets examined
in this study. Better agreement is seen with only the nucleate
boiling term of the nucleate boiling correlation, so it is
proposed that the use of the correlation in deep laminar flow be
modified as shown with equations 8 and 9. Additional data is
needed to further confirm these changes.
The correlation overpredicts Kuo and Peles’ data for channels
with inlet restrictors and enhancement features using nucleation
cavities along the channel walls, and predicts the opposite trend
of heat transfer coefficient with quality. It is hypothesized that
the effects of periodic dryout in the channels could account for
the different behavior of the two-phase heat transfer coefficient.
This possibility will be explored in future work.
It is noted that in Kuo and Peles’ study, the presence of
reentrant cavities resulted in lower two-phase heat transfer
coefficients than were observed in otherwise identical plain
channels with only inlet restrictors present. This is an effect
that must be carefully studied if future designers of
microchannel heat exchange systems will consider the use of
reentrant cavities. The mechanism of heat transfer is altered and
effectively the performance is degraded. Further investigation
in this area is warranted
[4] Kandlikar, S.G., 1990, “A General Correlation for Saturated
Two-Phase Flow Boiling Heat Transfer in Horizontal and
Vertical Tubes,” Journal of Heat Transfer, 112, pp. 219228.
[5] Gnielinski, V., 1976, “New Equations for Heat and Mass
Transfer in Turbulent Pipe and Channel Flow,”
International Chemical Engineer, 16, pp. 359–368.
[6] Petukhov, B. S., and Popov, V. N., 1963, “Theoretical
Calculation ofHeat Exchange in Turbulent Flow in Tubes
of an Incompressible Fluid with Variable Physical
Properties,” Teplofiz. Vysok. Temperature (High
Temperature Heat Physics), 1(1), pp. 69–83.
[7] Kandlikar, S.G. 1983, “An Improved Correlation for
Predicting Two-phase Flow Boiling Heat Transfer
Coefficient in Horizontal and Vertical Tubes,” Heat
Exchangers for Two-phase Applications, ASME, HTD, 27,
pp. 3-10.
[8] Kuan, Wai Keat, 2006, “Experimental Study of Flow
Boiling Heat Transfer and Critical Heat Flux in
Microchannels,” PhD Dissertation, Rochester Institute of
Technology, Rochester, NY.
[9] Schrock, V. E., and L. M. Grossman, 1962. “Forced
Convective Boiling in Tubes,” Nuclear Science and
Engineering, 12, pp. 474–481.
[10] Kandlikar S. G., and H. Nariai, “Flow Boiling in Circular
Tubes,” in Handbook of Phase Change, ed. S. G.
Kandlikar, Chapter 15, pp. 367–441, Taylor and Francis,
Philadelphia, PA, 1999.
[11] Yen, T., Shoji, M., Takemura, F., Suzuki, Y., and N.
Kasagi, 2006, “Visualization of Convective Boiling Heat
Transfer in Single Microchannels with Different Shaped
Cross-Sections,” International Journal of Heat and Mass
Transfer, 49, pp. 3884-3894.
[12] Kandlikar, S.G., 1991, “A Model for Correlating Flow
Boiling Heat Transfer in Augmented Tubes and Compact
Evaporators,” Journal of Heat Transfer, 113, pp. 966 – 972.
[13] C.-J. Kuo and Yoav Peles. In Review. Received as
personal communication January 2007.
ACKNOWLEDGEMENTS
This work was done with the support of the Thermal
Analysis and Microfluidics Laboratory at the Rochester
Institute of Technology. The authors would also like to thank
Professor Yoav Peles and his coworkers [13] at the Rensselear
Polytechnic Institute for generously providing the water boiling
data.
REFERENCES
[1] Kandlikar, S.G., and Prabhu Balasubramanian, 2004 “An
Extension of the Flow Boiling Correlation to Transition,
Laminar, and Deep Laminar Flows in Minichannels and
Microchannels,” Heat Transfer Engineering, 25(3), pp. 8693.
[2] Kandlikar, S.G., 1991, “Development of a Flow Boiling
Map for Subcooled and Saturated Flow Boiling of
Different Fluids Inside Circular Tubes,” Journal of Heat
Transfer, 113, pp. 190-200.
[3] Kandlikar, S.G., 1998, “Heat Transfer Characteristics in
Partial Boiling, Fully Developed Boiling, and Significant
Void Flow Regions of Subcooled Flow Boiling,” Journal
of Heat Transfer, 120, pp. 390-401.
7
Copyright © 2007 by ASME