Proceedings of the ASME 2013 International Mechanical Engineering Congress & Exposition
IMECE2013
November 13-21, 2013, San Diego, California, USA
IMECE2013-64463
Preliminary Results of Pressure Drop Modeling During Flow
Boiling in Open Microchannels with Uniform and Tapered
Manifolds (OMM)
Ankit Kalani, Satish G. Kandlikar*
Department of Mechanical Engineering
Rochester Institute of Technology
Rochester, NY, USA
*[email protected]
ABSTRACT
Flow boiling with microchannel can dissipate high heat
fluxes at low surface temperature difference. A number of
issues, such as instabilities, low critical heat flux (CHF) and
low heat transfer coefficients, have prevented it from reaching
its full potential. A new design incorporating open
microchannels with uniform and tapered manifold (OMM) was
shown to mitigate these issues successfully. Distilled, degassed
water at 80 mL/min is used as the working fluid. Plain and open
microchannel surfaces are used as the test section s. Heat
transfer and pressure drop performance for uniform and tapered
manifold with both the surfaces are discussed. A low pressure
drop of 7.5 kPa is obtained with tapered manifold and
microchannel chip at a heat flux of 263 W/cm2 without
reaching CHF. The pressure drop data is further compared with
the homogenous model and the initial results are presented.
1.
INTRODUCTION
Flow boiling in microchannel can provide efficient heat
transfer due to the high surface area to volume ratio and latent
heat effects. Since the introduction of microchannel [1], flow
boiling using microchannel has been extensively studied in
literature. The current work is focused on flow boiling with
microchannel using water and a new geometry introduced for
mitigating flow instabilities.
Flow instability [2,3], low heat transfer coefficient [4], and
early CHF [5] were some of the key issues related to the poor
performance of flow boiling. A number of researchers have
used different techniques to obtain stable flow boiling
performance. Kandlikar et al. [6] used a combination of
pressure drop element and artificial nucleation sites to obtain a
stable flow in their study. Kuo and Peles [7] studied the effects
of pressure on flow boiling using microchannel with reentrant
cavities. Wang et al. [8] studied flow boiling instability using
three different inlet/outlet configurations. Diverging, parallel
microchannels and artificial nucleation sites were used by Lu
and Pan [9] to achieve stable flow boiling. Balasubramanian et
al. [10] used expanding microchannel to obtain 30% lower
pressure drop. Recently, Alam et al. [11] used microgap on a
printed circuit board to obtain low pressure drop in the system.
Cross-linked microchannels [12] and trapezoidal microchannels
[13] have also been studied to reduce the ins tability. Zhang et
al. [14] studied the flow instability in microchannels and
concluded that multiple factors like inlet restrictors, increase in
the system pressure and channel diameter can lead to a more
stable system.
A maximum heat flux of 130 W/cm2 was reported by Qu
and Mudawar [15] with a microchannel heat sink having 21
parallel channels. Kuo and Peles [16] used microchannel with
reentrant cavities for high heat dissipation. The authors
recorded a heat flux of 643 W/cm2 with 303 kg/m2 s mass flux
at a wall superheat of around 70 °C. Liu and Garimella [17]
experimentally investigated with varying inlet water
1
Copyright © 2013 by ASME
temperature and mass fluxes. A heat flux of 129 W/cm2 was
dissipated at an exit quality of 0.2. Recently, Kandlikar et al.
[18] proposed a novel open microchannel with tapered
manifold configuration and dissipated a heat flux of 506 W/cm2
at a wall superheat of 26.2°C without reaching CHF.
Preliminary work with tapered manifold showed low pressure
drop and high heat transfer performance. Kalani and Kandlikar
[19] experimentally investigated the pressure drop performance
on the above mentioned manifolds. They observed that the
pressure drop with tapered manifold (3-10 kPa) showed
significant reduction compared to the pressure drop with
uniform manifold (>50 kPa) with the microchannel chip.
A number of models and correlations exist in literature for
two-phase pressure drop modeling, e.g., the Lockhart and
Martinelli correlation [20] using the separated flow model, the
homogeneous model, the Chisholm correlation, and Friedel
correlation among the more widely used ones . The
homogeneous model has been shown to consistently predict the
pressure drop reasonably well over a wide range of conditions,
especially for low exit qualities. In the current work, tapered
microchannel configuration (200 µm taper over a 10 mm flow
length) is further investigated and its effect on heat transfer
performance and pressure drop are studied. The pressure drop
performance is evaluated by comparing it with the wellestablished homogeneous model. Plain and microchannel
copper chips are used as the boiling surfaces with distilled
water at a flow rate of 80 mL/min.
2.
NOMENCLATURE
kCu
q”
x
Tsat
Tc
Twall
ΔTsat
h
3.
thermal conductivity of copper, W/m K
heat flux, W/m2
distance, m
saturation temperature, K
chip temperature, K
wall temperature, K
wall superheat, K
heat transfer coefficient, W/m2 K
fluid path. The ceramic base plate with the test section was
bolted together with manifold block to form a single unit.
A Micropump © pump was used to provide a flow rate of 80
mL/min. Distilled and degassed water was used as the fluid
medium. The supply line from the supply tank to the manifold
block was wrapped in fiber glass insulation to minimize the
heat losses. A subcooling of 10 °C was employed at the inlet
into the test section.
Figure 1. Schematic of the flow boiling test setup [18].
The manifold block provided the tapered or the uniform
manifold configuration. The uniform manifold had no recess
over the test section area, and the 0.127 mm thick gasket
provided the uniform gap. The tapered manifold had a
gradually increasing taper as seen in Fig. 2 over the test section.
The inlet thickness (h 1 ) of the tapered manifold was 0.127 mm
fixed by the gasket, while the exit thickness (h 2 ) varied
depending on the size of the taper machined in the manifold.
The tapered manifold provided an increasing flow crosssectional area along the flow direction. In the current work, the
tapered manifold used had a recess of 200 µm on the exit side.
EXPERIMENTAL SETUP
Figure 1 shows the schematic of flow boiling setup used
for the current study. A similar test setup was used by Kandlikar
et al. [18] in a previous study. The setup consisted of three main
parts: heater, test section and a manifold block. A copper block
having eight 200 W cartridge heaters formed the heater. The top
half of the copper heater was machined to have a 10 mm × 10
mm square section and had three equally spaced holes (5 mm)
for k-type thermocouple probes for measuring heat flux. A
polysulfone manifold block with the desired uniform gap or
taper was placed over the test section. A ceramic base plate was
used to support the manifold block with the test section in the
center. The test section was a copper chip that was placed over
the base plate. A silicone gasket of 0.127 mm thickness was
used to provide sealing and also acted as the manifold gap. The
manifold block consisted of inlet and outlet opening s for the
Figure 2. Schematic of the tapered manifold (not to
scale).
One-dimensional heat transfer conduction equation was
used for the calculation of heat flux supplied to the test section.
dT
q" = −k Cu
(1)
dx
The temperature gradient, dT/dx, in the above equation was
calculated using the three-point backward Taylor’s series
approximation.
dT
dx
2
=
3T1 − 4T2 + T3
2∆x
(2)
Copyright © 2013 by ASME
A differential Omega® pressure sensor was used for the
pressure drop reading. An NI cDaq-9172 data acquisition
system with NI-9213 temperature module was used to record
the temperatures. A LabVIEW® virtual instrument (VI) was
used to display and record temperature and heat flux.
4.
TEST SECTION
Two copper chips (plain and microchannel), 20 mm × 20
mm × 3 mm, were used as test sections in the current work. The
surface area exposed to the fluid was restricted to the central 10
mm × 10 mm. A 2 mm × 2 mm groove was machined on the
underside of the chip as shown in Fig. 3 so that the heat transfer
was mainly directed to the 10 mm × 10 mm area exposed to the
heater. This also helped in reducing the heat spreading effect.
The microchannel was fabricated using a CNC machine. The
dimensions of the microchannel were 195 µm channel width,
180 µm fin width and 450 µm channel depth.
Figure 3 Schematic of the microchannel copper chip.
The wall temperature at the top of the chip surface was
calculated using the heat flux obtained from the measured chip
temperature Tc and the temperature drop in the copper substrate
over the distance x1 , which is the distance between the
thermocouple location and the top surface.
Twall = Tc − q"(
5.
x1
k Cu
)
at the top of the microchannel and the saturation temperature.
CHF was not reached for any of the test runs.
The uncertainty analysis for the current work is reported in
detail by Kandlikar et al. [18]. The flow uncertainty at the
tested flow rate was 5%. The uncertainty in the temperature
measurements was 0.1 °C. The estimated uncertainty in heat
flux and surface temperature at high heat fluxes were 4% and
0.2 °C, respectively. The details of the manifolds that were used
are presented in the table below.
Taper
height
(exit)
Inlet
thickness
(µm)
Exit
thickness
(µm)
kg/m2s
Ginlet
Goutlet
Uniform
0
127
127
394
394
Taper A
200
127
327
394
247
Manifold
kg/m2s
5.1 Uniform manifold testing:
Results of the uniform manifold with plain and
microchannel chips testing are discussed in this section.
Uniform manifold consisted only of the manifold area provided
by a gap resulting from the gasket over the chip. Both the inlet
and exit regions had a gap of 0.127 mm.
The boiling performance with uniform manifold is shown
in Fig. 4. The heat flux for the plain chip shows a linear
increase with the wall superheat. A s light overshoot is observed
for increasing heat flux. A maximum of 227 W/cm2 was
dissipated at a wall superheat of 22 °C. For the microchannel
chip, a distinct improvement in boiling performance is seen. A
similar heat flux of plain chip was reached at a much lower
wall superheat. Both the chips did not reach CHF.
(3)
RESULTS
Flow boiling heat transfer performance with uniform and
tapered manifold is discussed in this section. Plain and
microchannel chip were tested with distilled water as the fluid
medium at atmospheric pressure. The micropump kept a
constant flow rate of 80 mL/min in the system. A gap of 0.127
mm was maintained between the heater surface and the top
cover for all test runs with the help of a gasket. Water at
atmospheric pressure and a subcooling of 10 °C was introduced
at the inlet. Heat flux was calculated for the projected area of
100 mm2 using Eq. 1. Flow boiling performances shown below
are presented as heat flux versus wall superheat. Wall superheat
was calculated as the difference between the wall temperature
Figure 4. Boiling performance showing heat flux versus
wall superheat for plain and microchannel chip with
uniform manifold.
5.2 Tapered manifold testing:
3
Copyright © 2013 by ASME
The concept of tapered manifold was introduced to provide
improved heat transfer performance with low pressure drop.
This was accomplished by increasing the cross-sectional area
along the flow direction toward the exit, which would allow the
vapor to be removed without disrupting the fluid path. Figure 5
compares the boiling performance for the uniform and tapered
manifolds (200 µm) for the microchannel and the plain chips.
For the plain chip, tapered manifold showed improved
performance compared with the uniform manifold.
Uniform manifold with microchannel chip shows improved
performance compared to the tapered manifold, however at
higher heat fluxes (500 W/cm2 ), it is seen from the trend that
the taper would outperform the uniform manifold as seen in the
previous publication [18].
along the flow direction was able to accommodate the increased
vapor flow and resulted in an extremely low pressure drop.
Figure 6. Effect of tapered and uniform manifolds on
pressure drop.
5.4 Pressure Drop Analysis
The differential pressure sensor was located at the inlet and
the exit sections of the manifold block. Since the degassed
water had 10 °C subcooling, the initial frictional pressure drop
was single phase and was calculated using the formula below.
Figure 5. Boiling performance with tapered and
uniform manifold.
5.3 Pressure drop performance with tapered and uniform
manifold:
High pressure drop across the microchannels has been one
of the key issues with the microchannel flow boiling systems.
The tapered manifold provided extremely low pressure drop
compared to the microchannels and the uniform gap
microchannel configurations as discussed in this section.
Figure 6 shows pressure drop versus the corresponding
heat flux with uniform and tapered manifolds. The highest
pressure drop was observed with a uniform manifold with a
plain chip. At high heat fluxes (~225 W/cm2 ), a pressure drop
of 160 kPa was recorded with the plain chip. At a similar heat
flux, the microchannel chip with a uniform manifold recorded a
pressure drop of 50 kPa. The reduction in the pressure drop was
mainly due to the increase in the flow cross -sectional area
provided by the manifold. The tapered manifold (200 µm)
showed the lowest pressure drop of 10 kPa at a heat flux of
225W/cm2 . The combination of tapered manifold with
microchannel showed significant pressure drop reduction over
the entire range of heat flux. The expanding cross-sectional area
𝛥𝑃 =
𝑢𝑚 =
2𝑓𝜌 𝑢 2𝑚 𝐿
(4)
𝐷
𝑚̇
𝜌𝐴𝑐
𝑎𝑛𝑑 𝑃𝑜 = 𝑓𝑅𝑒
(5)
Where f is the fanning friction factor, u m is the mean
velocity and Po is the Poiseuille number. The above equations
were used to calculate the single phase pressure drop.
The total pressure drop between the inlet measurement port
to the location where the two-phase begins consisted of the
single phase pressure drop in the inlet pipes, the losses in
bends, entrance losses and the core frictional losses along the
single phase length.
𝛥𝑃 =
𝐷ℎ =
2𝜌𝑢 2𝑚
2
4𝐴𝐶
𝑃
[(
𝐴𝑐
𝐴𝑝
2
) 2𝐾90 + 𝐾𝑐 + 𝐾𝑒 +
4𝑓𝑎𝑝𝑝 𝑧′
𝐷ℎ
]
(6)
(7)
where Ac is the channel area, Ap is the total plenum cross sectional area, K90 is the loss coefficient at the 90° bend, Kc and
4
Copyright © 2013 by ASME
Ke are the contraction and expansion losses coefficient due to
area changes repectively, Dh is the hydraulic diameter, Ac is the
cross-sectional area, P is the wetted perimeter and z’ is the
single phase length.
The length, z’ at which the water becomes saturated is
calculated by
𝑧′ =
𝑚̇ 𝐶𝑝𝛥𝑇
(8)
𝑄𝑊
where W is the channel width, ∆T is the degree of
subcooling and Q is the total heat transferred.
The two phase region length z, was given by
𝑧 = 𝐿 − 𝑧′
(9)
where L is the total channel length and z’ is the single
phase region length.
Homogenous model was used for the two phase pressure
drop calculations[21]. For the uniform manifold, the core
frictional and acceleration component was given by the formula
below. The formula shown also consisted a gravitational term
which was zero in the current work as the test section was
horizontal.
−𝟐𝑮𝟐 𝒗𝒇
𝒗
𝒅𝑨
[𝟏 + 𝒙 ( 𝒇𝒈 )]
𝒅𝑷
𝑨
𝒗𝒇 𝒅𝒛
)=
−(
𝒅𝒗𝒈
𝒅𝒛 𝒕𝒂𝒑𝒆𝒓,𝒂𝒄𝒄𝒆𝒍
)
𝟏 + 𝑮𝟐 𝒙 (
𝒅𝒑
where A is the cross-sectional area and dA/dz is the change
in cross-sectional area along the channel length (two phase
region).
Similar to the initial single phase, at the exit with two
phase pressure drop due exit losses and frictional pressure drop
in the rest of the non-active region was calculated. Equations
𝛥𝑃𝑒 = 𝐺 2 𝜎𝑒 (1 − 𝜎𝑒 )𝜓𝑠
(14)
𝜌𝐿
𝜓𝑠 = 1 + ( − 1) [ 0.25𝑥 (1 − 𝑥) + 𝑥 2 ]
𝜌𝑉
(15)
where σe is the expansion ratio which is given by the area
ratio of channel to plenum, ψs is the two phase multiplier, ρl
liquid density and ρg is the vapor density. The frictional
component of the pressure drop is given by:
𝛥𝑃 =
𝟐𝒇𝑻𝑷 𝑮𝟐 𝒗𝒇
𝒗
𝒗
𝒅𝒙
[𝟏 + 𝒙 ( 𝒇𝒈 )] + 𝑮𝟐 𝒗𝒇 ( 𝒇𝒈 )
𝒅𝑷
𝑫𝒉
𝒗𝒇
𝒗𝒇 𝒅𝒛
−( ) =
(𝟏𝟎)
𝒅𝒗𝒈
𝒅𝒛
)
𝟏 + 𝑮𝟐 𝒙 (
𝒅𝒑
where x is the exit velocity, vf is the specific volume of
liquid, vfg is the difference in the specific volume of saturated
liquid and vapor, G is the mass flux and fTP is the two phase
friction factor. The two phase friction factor was calculated
using the two phase viscosity which is given by:
𝟏
̅
µ
=
𝒙
µ𝒈
𝑓𝑇𝑃 =
+
(𝟏 − 𝒙 )
𝑃𝑜 µ
̅
𝐺𝐷ℎ
µ𝒇
(𝟏𝟏)
(12)
where µf is liquid viscosity, µg is vapor viscosity. For the
tapered manifold, similar equation (Eq. 10) as the uniform
manifold was used with the addition of the below given term.
The following term was added to the numerator to account for
the increase in the cross-sectional area due to the taper.
(𝟏𝟑)
2𝑓𝑇𝑃 𝐿𝑚2̇
𝐷𝜌𝑇𝑃
𝜌𝑇𝑃 = 𝜌𝐿 (1 − 𝜖𝐻 ) + 𝜌𝐺 𝜖𝐻
𝜖𝐻 =
1
𝑢 1 − 𝑥 𝜌𝐺
)
1+ 𝐺(
𝑢𝐿
𝑥
𝜌𝐿
(16)
(17)
(18)
where ρTP is the two phase density, ϵH is the homogeneous
void fraction and u G/ u L is the velocity ratio and is equal to 1 for
the homogeneous flow.
Homogeneous model was used to obtain the theoretical
pressure drop values which were compared with the
experimentally obtained pressure drop. The next section
discusses the result from the comparison.
5.5 Uniform manifold pressure drop comparison
Figure 7 shows the comparison of the pressure drop
modeling results for the uniform manifold using plain chip with
the experimental the data. The model shows good agreement
(within ±10%) with the experimental values at higher heat
fluxes (>100 W/cm2 ). A higher deviation is observed at lower
heat fluxes, this may be due to the earlier onset of nucleate
boiling in the subcooled liquid.
5
Copyright © 2013 by ASME
Figure 7. Comparison of data for uniform manifold and
plain chip with the model.
Figure 8 compares the pressure drop data for the
microchannel chip and uniform manifold with the
homogeneous model results. The model underpredicts as
compared to the experimental data. At lower heat fluxes, the
two-phase length is only 2 mm (total length is 10 mm),
indicating high subcooled boiling effect. The current model
does not account for this effect.
Figure 9. Comparison of data for taper manifold and
plain chip with the model.
The comparison of the pressure drop data for microchannel
chip and the model using tapered manifold is shown in Fig. 10.
The introduction of the addition term from Eq. 13 to account
for the increase in the cross -sectional works well and the model
predicts the data within 2-3 kPa. Since the total pressure drop is
extremely low, the percentage deviations are seen to be high, up
to 40 percent.
Figure 8. Comparison of data for uniform manifold and
microchannel chip with the model.
5.5 Tapered manifold pressure drop comparison
Pressure drop results for the tapered manifold with both
plain and microchannel chip are compared with the
homogeneous model predictions. Figure 9 compares the plain
chip experimental values with the model. The model overall
shows good agreement, at higher heat fluxes larger deviations
are observed.
Figure 10. Comparison of data for taper manifold and
microchannel chip with the model.
CONCLUSIONS
Heat transfer and pressure drop performance of uniform
and plain manifolds with plain and microchannel chips were
investigated. Distilled water at atmospheric pressure at a flow
rate of 80 mL/min was used for all test runs.
1.
6
The tapered manifold with a taper height of 200 µm
and uniform manifold was tested with plain and
microchannel chips at a flow rate of 80 mL/min.
Copyright © 2013 by ASME
2.
3.
4.
5.
6.
The combination of the microchannel chip and the
tapered manifold significantly reduced the pressure
drop in the system. The 200 µm taper with
microchannels showed the best performance with the
lowest pressure drop of 10 kPa compared to the 160
kPa pressure drop with the plain chip and the uniform
manifold.
Experimentally obtained pressure drop value of both
manifolds for plain and microchannels chips were
compared with the homogeneous model. For the
tapered manifold, good agreement with the model was
observed for both chips.
Further refinement in the model, in terms of addition
of subcooled boiling effect is recommended.
The testing was not conducted to the CHF limit, which
was reported to be higher that 500 W/cm2 in an earlier
publication.
Additional data and comparison with other pressure
drop models is recommended.
[8]
[9]
[10]
[11]
[12]
ACKNOWLEDGEMENTS
The work was conducted in the Thermal Analysis,
Microfluidics and Fuel Cell Laboratory at the Rochester
Institute of Technology in Rochester, NY and supported by the
National Science Foundation under Award No. CBET-1236062.
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
Tuckerman D. B., and Pease R. F. W., 1981, “Highperformance heat sinking for VLSI,” Electron Device
Lett. IEEE, 2(5), pp. 126–129.
Kandlikar S. G., 2002, “Fundamental issues related to
flow boiling in minichannels and microchannels,” Exp.
Therm. Fluid Sci., 26(2–4), pp. 389–407.
Kandlikar S. G., 2004, “Heat Transfer Mechanisms
During Flow Boiling in Microchannels,” J. Heat Trans f.,
126(1), p. 8.
Steinke M. E., and Kandlikar S. G., 2004, “An
Experimental
Investigation
of
Flow
Boiling
Characteristics of Water in Parallel Microchannels,” J.
Heat Transf., 126(4), pp. 518–526.
Bergles A. E., and Kandlikar S. G., 2005, “On the
Nature of Critical Heat Flux in Microchannels,” J. Heat
Transf., 127(1), pp. 101–107.
Kandlikar S. G., Kuan W. K., Willistein D. A., and
Borrelli J., 2006, “Stabilization of Flow Boiling in
Microchannels Using Pressure Drop Elements and
Fabricated Nucleation Sites,” J. Heat Transf., 128(4), pp.
389–396.
Kuo C.-J., and Peles Y., 2009, “Pressure effects on flow
boiling instabilities in parallel microchannels,” Int. J.
Heat Mass Transf., 52(1–2), pp. 271–280.
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
7
Wang G., Cheng P., and Bergles A. E., 2008, “Effects of
inlet/outlet configurations on flow boiling instability in
parallel microchannels,” Int. J. Heat Mass Transf., 51(910), pp. 2267–2281.
Lu C. T., and Chin P., 2009, “A highly stable
microchannel heat sink for convective boiling,” J.
Micromechanics Microengineering, 19(5), p. 055013.
Balasubramanian K., Lee P. S., Jin L. W., Chou S. K.,
Teo C. J., and Gao S., 2011, “Experimental investigations
of flow boiling heat transfer and pressure drop in straight
and expanding microchannels – A comparative study,”
Int. J. Therm. Sci., 50(12), pp. 2413–2421.
Alam T., Lee P. S., Yap C. R., Jin L., and
Balasubramanian K., 2012, “Experimental investigation
and flow visualization to determine the optimum
dimension range of microgap heat sinks,” Int. J. Heat
Mass Transf., 55(25–26), pp. 7623–7634.
Cho E. S., Koo J.-M., Jiang L., Prasher R. S., Kim M. S.,
Santiago J. G., Kenny T. W., and Goodson K. E., 2003,
“Experimental study on two-phase heat transfer in
microchannel heat sinks with hotspots,” Ninteenth
Annual IEEE Semiconductor Thermal Measurement and
Management Symposium, 2003, pp. 242–246.
Wu H. Y., and Cheng P., 2004, “Boiling instability in
parallel silicon microchannels at different heat flux,” Int.
J. Heat Mass Transf., 47(17–18), pp. 3631–3641.
Zhang T., Tong T., Chang J.-Y., Peles Y., Prasher R.,
Jensen M. K., Wen J. T., and Phelan P., 2009, “Ledinegg
instability in microchannels,” Int. J. Heat Mass Transf.,
52(25–26), pp. 5661–5674.
Qu W., and Mudawar I., 2003, “Measurement and
prediction of pressure drop in two-phase micro-channel
heat sinks,” Int. J. Heat Mass Transf., 46(15), pp. 2737–
2753.
Kuo C.-J., and Peles Y., 2007, “Local measurement of
flow boiling in structured surface microchannels,” Int. J.
Heat Mass Transf., 50(23–24), pp. 4513–4526.
Liu D., and Garimella S. V., 2007, “Flow Boiling Heat
Transfer in Microchannels,” J. Heat Transf., 129(10), pp.
1321–1332.
Kandlikar S. G., Widger T., Kalani A., and Mejia V.,
2013,
“Enhanced
Flow
Boiling
Over
Open
Microchannels With Uniform and Tapered Gap
Manifolds,” J. Heat Transf., 135(6), p. 061401.
Kalani A., and Kandlikar S. G., 2013, “Experimental
Investigation of Flow Boiling Performance with Tapered
Microchannel
Manifolds ,”
ASME
Conference
Proceedings,2013.
Lockhart R. W., and Martinelli R. C., 1949, “Proposed
correlation of data for isothermal two-phase, twocomponent flow in pipes,” Chem. Eng. Prog., 45(1), pp.
39–48.
Collier J. G., 1972, Convective boiling and
condensation, McGraw-Hill, London, U.K.
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