1
Satish G. Kandlikar
Gleason Professor of Mechanical Engineering,
Rochester Institute of Technology,
Rochester, NY 14618
e-mail: [email protected]
Stéphane Colin
Université de Toulouse,
INSA, ICA (Institut Clément Ader),
31077 Toulouse, France
e-mail: [email protected]
Yoav Peles
Mechanical, Aerospace, and Nuclear Engineering,
Rensselaer Polytechnic Institute,
Troy, NY 12180
e-mail: [email protected]
Srinivas Garimella
George W. Woodruff School
of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
e-mail: [email protected]
R. Fabian Pease
Electrical Engineering Department,
Stanford University,
Stanford, CA 94305
e-mail: [email protected]
Juergen J. Brandner
Karlsruher Institut fuer Technologie (KIT),
Campus North,
D-76344 Eggenstein-Leopoldshafen,
Karlsruhe, Germany
e-mail: [email protected]
David B. Tuckerman
Tuckerman & Associates, Inc.,
Lafayette, CA 94559
e-mail: [email protected]
1
Heat Transfer in
Microchannels—2012
Status and Research Needs
Heat transfer and fluid flow in microchannels have been topics of intense research in the
past decade. A critical review of the current state of research is presented with a focus on
the future research needs. After providing a brief introduction, the paper addresses six
topics related to transport phenomena in microchannels: single-phase gas flow, enhancement in single-phase liquid flow and flow boiling, flow boiling instability, condensation,
electronics cooling, and microscale heat exchangers. After reviewing the current status,
future research directions are suggested. Concerning gas phase convective heat transfer
in microchannels, the antagonist role played by the slip velocity and the temperature
jump that appear at the wall are now clearly understood and quantified. It has also been
demonstrated that the shear work due to the slipping fluid increases the effect of viscous
heating on heat transfer. On the other hand, very few experiments support the theoretical
models and a significant effort should be made in this direction, especially for measurement of temperature fields within the gas in microchannels, implementing promising
recent techniques such as molecular tagging thermometry (MTT). The single-phase liquid
flow in microchannels has been established to behave similar to the macroscale flows.
The current need is in the area of further enhancing the performance. Progress on implementation of flow boiling in microchannels is facing challenges due to its lower heat
transfer coefficients and critical heat flux (CHF) limits. An immediate need for breakthrough research related to these two areas is identified. Discussion about passive and
active methods to suppress flow boiling instabilities is presented. Future research focus
on instability research is suggested on developing active closed loop feedback control
methods, extending current models to better predict and enable superior control of flow
instabilities. Innovative high-speed visualization and measurement techniques have led to
microchannel condensation now being studied as a unique process with its own governing influences. Further work is required to develop widely applicable flow regime maps
that can address many fluid types and geometries. With this, condensation heat transfer
models can progress from primarily annular flow based models with some adjustments
using dimensionless parameters to those that can directly account for transport in intermittent and other flows, and the varying influences of tube shape, surface tension and
fluid property differences over much larger ranges than currently possible. Electronics
cooling continues to be the main driver for improving thermal transport processes in
microchannels, while efforts are warranted to develop high performance heat exchangers
with microscale passages. Specific areas related to enhancement, novel configurations,
nanostructures and practical implementation are expected to be the research focus in the
coming years. [DOI: 10.1115/1.4024354]
Keywords: microscale thermal transport, heat transfer, single-phase flow, rarefaction
effects, slip flow, flow boiling, enhancement, instabilities, condensation, review, research
needs
Introduction
As has been observed in natural systems such as lungs and kidneys in humans and other living animals, transport processes
become more efficient at microscale passage dimensions. The
increase in the area/volume ratio of the passages and the change
in the relative importance of different forces create a new class of
transport processes that can lead to significant size reductions in
practical devices utilizing these processes. Although these benefits
have been well-known, as demonstrated by the pioneering work
of Tuckerman and Pease [1], significant research in this area
1
Corresponding author.
Contributed by the Heat Transfer Division of ASME for publication in the
JOURNAL OF HEAT TRANSFER. Manuscript received July 31, 2012; final manuscript
received March 13, 2013; published online July 26, 2013. Assoc. Editor: Zhuomin
Zhang.
Journal of Heat Transfer
started only after their successful application in high heat flux
electronics cooling and microfluidic devices. The definition of
microscale is somewhat flexible, depending on the dimensions at
which the transport characteristics are affected. In general, channel dimensions of 10–200 lm constitute the bulk of the microscale
focus; larger dimensions of up to 1–3 mm are also of interest in
some applications such as single-phase liquid flow, boiling and
condensation.
The resurgence in microscale transport research started in its
earnest in the first decade of the new century, marking the period
2000–2012 for a large number of publications dealing with thermal transport in microchannels. This was aided by a number of
dedicated conferences, such as ASME International Conference
on Nanochannels, Microchannels and Minichannels started in
2003, and the European MicroFlu conference on microfluidics
started in 2008 highlighting the increased research activity worldwide in this area.
C 2013 by ASME
Copyright V
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This paper is aimed at capturing the recent advances in the field
of microscale convective transport, focusing on four main topics:
single-phase gas flows, single-phase liquid flows, flow boiling,
and flow condensation. A brief survey of the current status is presented, followed by a critical evaluation of research opportunities
in the respective areas. Two specific applications, electronics
cooling and microscale heat exchangers, are considered in more
detail as they seem to be the most promising candidates benefitting from microscale transport process advancements. The need to
shift the research focus to a more fundamental approach is highlighted in recognizing some of the unique characteristics of the
microscale phenomena, and utilizing them in further enhancing
the thermal transport processes.
2
Single-Phase Gas Flow in Microchannels
A large number of recent investigations have been undertaken
to analyze convective heat transfer in gas microflows addressing
various new applications connected to the increasing development
of MEMS. Gas microflows with heat transfer occur, for example,
in microscale heat exchangers, pressure gauges, mass flow and
temperature microscale sensors, micropumps and microsystems
devoted to mixing or separation for local gas analysis, mass
spectrometers and Knudsen micropumps. The main elements of
these microsystems which are subject to heat transfer are long or
short, possibly bent, microchannels with various possible crosssections.
In these microchannels, due to rarefaction effects, a local thermodynamic nonequilibrium is observed within the Knudsen layer
close to the wall. It results in a velocity slip and a temperature
jump at the wall, with thermal antagonist effects: compared with
the classic behavior in microchannels, the first phenomenon
increases, whereas the second one decreases, convective heat
transfer. In addition, a third mechanism has to be taken into
account in microchannels: shear work due to gas slip at the wall
increases the contribution of viscous heating to the convective
heat transfer.
@T T Tw ¼ fT k @n w
(3)
In Eq. (2), the difference between the fluid velocity at the wall, u,
and the wall velocity, uw, depends on both the velocity and temperature gradients. The first term of the RHS is the velocity slip
which results from the normal gradient, @u=@n, of the stream-wise
velocity and also from the tangential gradient, @v=@t, of the spanwise velocity, which should be taken into account in case of
curved surfaces. The viscous slip coefficient, rP, is in practical
cases of the order of unity and it depends on the wall nature and
roughness, as well as on the gas species.
The thermal creep effects due to the tangential temperature gradient, @T=@t, are taken into account by the second term of the
RHS of Eq. (2). The thermal slip coefficient, rT, is close to 3/4 for
specular reflection and of the order of unity in case of diffuse
reflection. A detailed discussion on the values of rP and rT can be
found in Ref. [5]. The temperature jump is proportional to the normal gradient, @T=@n, of the temperature and can be calculated by
Eq. (3). The temperature jump coefficient, fT, has a value of the
order of 2 [5]. The accurate determination of the values of rP, rT
and fT in real situations remains, however, an open issue and the
experimental data provided in the literature can sometimes be
contradictory. The velocity slip and temperature jump of Eqs.
(2)
and (3) are of #ðKnÞ while the thermal creep term is of # Kn2 .
Higher order boundary conditions, where the velocity slip and
temperature
jump involve second order derivatives and are of
# Kn2 , have also been considered in a few papers devoted to
convective heat transfer in microchannels.
The Nusselt number is increased by the slip velocity, due to an
increase of the flow rate, and it is decreased by the temperature
jump which reduces the temperature gradient within the gas at the
wall. In most practical cases, however, the second effect is predominant and the Nusselt number is decreased when rarefaction is
increased. A review of the analytical and numerical studies on
convective heat transfer within microchannels in the slip flow
regime is provided in Ref. [6].
2.1 Specificities of Heat Transfer in Gas Microflow
2.1.1 Rarefaction and Slip Flow Regime. In addition to compressibility, rarefaction of the flow in these microchannels has a
significant impact on heat transfer. Shrinking down the dimensions of fluidic microsystems under an internal gas flow leads to
an increase of the Knudsen number
Kn ¼
k
Dh
(1)
defined as the ratio of the mean free path, k, of the molecules over
the hydraulic diameter Dh of the microchannel. The Knudsen
number encountered in typical microsystems is frequently
between 103 and 101, which is the typical range of the wellknown slip flow regime [2]. In this moderately rarefied regime,
the Navier-Stokes equations are still valid in the bulk flow, but a
local nonequilibrium is observed within the Knudsen layer. This
thin wall layer, the thickness of which is on the order of the
molecular mean free path, experiences complex nonlinear phenomena that result in velocity slip, temperature jump and thermal
creep at the wall [3], which strongly influence convective heat
transfer.
2.1.2 Boundary Conditions and Heat Transfer. Several
kinds of boundary conditions are proposed in the literature to
take into account this nonequilibrium near the wall surface [4].
The main ones are based on the Maxwell-Smoluchowski
conditions
@u @v lR @T þ
þ rT
u uw ¼ rP k
@n @t w
P @t w
(2)
2.2 Main Theoretical and Experimental Results. A large
number of recent papers have been devoted to the analysis of
pressure driven flows of gases with heat transfer in straight microchannels with constant cross-section, focusing on the determination of the Nusselt number. Most of them concern circular or
parallel-plate microchannels, and to a lesser extent, microchannels
with rectangular, trapezoidal and triangular sections, frequently
encountered in fluidic microsystems. In these studies, the flow is
assumed laminar and the regime is the slip flow regime. Investigations relate to thermally fully developed and thermally developing
flows, with uniform heat flux (UHF) or constant wall temperature
(CWT) conditions. The most significant contributions and results
are summarized in Secs. 2.2.1 to 2.2.3.
2.2.1 Analytical Solutions for Simplest Configurations.
Analytical solutions can be derived in the simplified case of a
fully laminar developed flow in a straight microchannel, assuming
incompressible fluid with constant properties and without taking
into account thermal creep and viscous heating. For a flow in a
circular (C) microtube with UHF, this analytical solution reads [6]
NuðC;1;UHFÞ ¼
KnfT þ
11 þ 128KnrP þ 384ðKnrP Þ2
48ð1 þ 8KnrP Þ2
!1
(4)
For the same problem with CWT, the analytic solution has no
explicit formulation, but its resolution leads to tabulated results
[7]. For a flow in a parallel-plate (PP) microchannel with one
insulated wall and one heated wall with uniform heat flux
(UHF-1IW), the analytical solution with the same simplifying
hypothesis reads:
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NuðPP;1;UHF1IWÞ ¼
KnfT þ
13 þ 294KnrP þ 1680ðKnrP Þ2
!1
70ð1 þ 12KnrP Þ2
(5)
and in the case of a symmetrically uniformly heated microchannel
(UHF)
NuðPP;1;UHFÞ ¼
KnfT þ
17 þ 336KnrP þ 1680ðKnrP Þ2
!1
140ð1 þ 12KnrP Þ2
(6)
These solutions can be extended to the case of two unsymmetrically heated walls by combining the solutions of two subproblems
similar to the above problem [8]. A review on heat transfer analysis of gas microflows in microchannels with rectangular, triangular or trapezoidal sections is provided in Ref. [6]. Analytical
solutions have been obtained in an implicit form for the eight versions of UHF in rectangular microchannels [9] and for the CWT
case [10], as well as in isosceles triangular microchannels [11].
2.2.2 Additional Effects. The above analytical solutions give
a trend but neglect some important additional effects. The first
one is the viscous heating, which has been taken into account by
Jeong and Jeong [12] for UHF heat transfer in a microtube. They
defined the Brinkman number as
Bru ¼
l
u2
uw Dh
(7)
where u is the mean velocity and uw the uniform heat flux at
the wall transmitted to the fluid. The influence of the Brinkman
number on the Nusselt number was analyzed and the following
analytical solution was obtained
NuðC;1;UHF;Bru 6¼0Þ
¼
C21
6C21
48C21
þ 4C1 þ 1 þ 48C21 C2 þ 8Bru 2C21 þ 3C1 þ 1
(8)
with C1 ¼ 1 þ 8rP Kn and C2 ¼ fT Kn. As evidenced by Fig. 1(a),
for a heated surface (Bru > 0), an increase of viscous heating
logically leads to a decrease of the Nusselt number, whereas for
a cooled surface (Bru < 0), the opposite is observed. The effect
of viscous dissipation significantly decreases as rarefaction
increases. As compared to macrochannels, microchannels experience a lower convection: Nu decreases when Kn increases, i.e.,
when the channels section decreases, except in the case of a
heated surface with significant viscous dissipation (see case
Bru ¼ 0:1). In this case, a maximum value of Nu is reached for a
particular value of Kn, i.e., a specific value of the microchannel
hydraulic diameter. A similar result is found in a parallel-plate
microchannel [13]
NuðPP;1;UHF;Bru 6¼0Þ
¼
C23
35C23
420C23
þ 14C3 þ 2 þ 420C23 C2 þ 4Bru 42C23 þ 33C3 þ 6
(9)
with C3 ¼ 1 þ 12rP Kn. The analytic solution of the CWT case
with viscous heating is given in Ref. [12] for a microtube and in
Ref. [13] for a parallel-plate microchannel. In the previous studies, the Nusselt number was deduced assuming that the heat flux
at the wall uw ¼ kð@T=@nÞw is fully transmitted by conduction in
the fluid. However, in case of slip flow, the heat transfer at the
Journal of Heat Transfer
Fig. 1 Nusselt number for a fully developed flow in a microtube (a) or in a parallel-plate microchannel and (b) with uniform
wall heat flux as a function of Knudsen and modified Brinkman
numbers, rP 5 1, fT 5 1.67
wall should be modified to include the shear work done by the
slipping fluid and should read [14]
@T @u
uw ¼ k þ lu (10)
@n w
@n w
This condition has rarely been implemented in slip flow heat
transfer analysis. Miyamoto et al. [15] analyzed the effect of viscous heating in UHF heat transfer between parallel plates in the
slip flow regime using Eq. (10) and obtained
NuðPP;1;UHF;Bru 6¼0Þ
"
# 11
0
9Bru 3 þ 84rP Kn þ 560ðrP KnÞ2
2
þ 8rP fT Kn C
B 2
C
B C3
35C3
C
¼B
C
B
A
@ 17 þ 336rP Kn þ 1680ðrP KnÞ2
þ
f
Kn
þ
T
2
140C3
(11)
This equation gives the same results as Eq. (9) in the case of no
rarefaction (Kn ¼ 0) and in the case of no viscous dissipation
(Bru ¼ 0), which was expected as shear work in the Knudsen
layer scales with the Brinkman number [16]. On the other hand,
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when rarefaction and viscous heating are both taken into account,
the influence of rarefaction is stronger when shear work is taken
into account (Fig. 1(b)). Comparing with macrochannels, the
decrease of hydraulic diameter leads to a decrease of convective
heat transfer efficiency (Nu decreases as Kn increases) but the
work of shear stress due to slip at the wall –which is observed
only in the case of microchannels—increases the role of viscous
dissipation and results in a higher heat transfer in the case of
cooled surface.
Developing flows have also been analyzed by a number of
authors who have treated the so-called extended Graetz problem
[6]. In some papers, such as Refs. [12,13], the axial conduction
(finite Peclet number) is taken into account in addition to viscous
dissipation. The influence of the variation of gas properties (l, k)
within the cross-section due to temperature variations has been
considered by Hooman et al. [17] who observed negligible effect
on Nu in the UHF case in a microtube.
2.2.3 Experimental Studies. There are very few published
experimental data on convective slip flow heat transfer in microchannels. Some experiments have revealed very low Nusselt numbers, compared to the expected ones, but the huge discrepancy
between experiment and theory can be explained by experimental
errors discussed in Ref. [18]. The most accurate available data
concern flows between parallel plates. The group of Miyamoto
measured the surface temperature distribution of a slip chocked
flow of low-density air through a millimeter-size parallel-plate
channel with adiabatic walls [19] and with uniformly heated walls
[15]. In the configuration with uniform heat flux at the wall, the
relative deviation between the measured and calculated wall temperature distribution was very small, of the order of 1% or 2% for
the reported data, with an increased discrepancy for increasing
Knudsen number. The experimental Knudsen number, however,
was limited to values lower than 5 104 at the inlet and
5 103 at the outlet for the reported data and in this range slip
flow and temperature jump effects are not very significant. In the
configuration with adiabatic walls, a few data were reported for
higher Knudsen numbers, up to 6 103 at the inlet and 6 102
at the outlet, well in the slip flow regime. There was a very good
agreement with the simulated wall temperature distribution, taking into account shear work at the wall. On the contrary, when
this shear work was not taken into account, the wall temperature
was underestimated with a deviation of a few percent. This analysis confirms that Eq. (10) should be used and that most of the analytical and numerical models proposed in the literature for
convective heat transfer in gas microflows should be corrected to
take into account the shear work at the wall.
2.3 Single-Phase Gas Flow—Research Needs. The literature on slip flow heat transfer is now well stocked, with a series of
available analytical solutions or numerical analysis for various
heat conditions and microchannel geometries. The limits of the
analytical solutions, based on simplifying assumptions, are not,
however, always well documented. Concerning the influence of
gas properties temperature dependence on heat transfer, there are
still few studies in the slip flow regime [20]. When viscous dissipation has to be taken into account, the effect of shear work at the
wall is generally not considered, and most of the analytical solutions should be extended to include its non-negligible effect. In
addition, the thermal creep is not analyzed, except in a few numerical papers [21]. On the other hand, although the theory of gas
hydrodynamics in the slip flow regime is now supported by smart
experiments, there is a crucial lack of experimental data concerning heat transfer in this regime. Providing accurate experimental
data on slip flow heat transfer is a challenge for the next years,
which would allow a real discussion on the validity of velocity
slip and temperature jump boundary conditions, on the appropriate values of accommodation coefficients, as well as on the limits
of applicability of slip flow theory, in terms of degree of rarefaction. Some promising emerging techniques such as MTT and
interferometry should be developed for this analysis of heat transfer in gas microflows. Up to now, these techniques are successfully used for thermography in liquids microflows [22,23] and
their application to gas microflows is a challenging goal. Preliminary results detailed in Ref. [22] give high hopes that MTT could
be soon implemented for successful analyze of temperature fields
in gas microflows. Even if the technique is limited to millimetersize channel sections, due to the minimal achievable size of the
laser beam –typically a few tens of micrometers–, the same flow
and heat transfer configurations than those observed in microchannels can be obtained by reducing the pressure. Current research,
for example, at the Stokes Research Institute, also shows that
interferometry could be an operative tool for gas thermometry in a
couple of years.
3 Enhancement in Single-Phase Flow and Flow
Boiling in Microchannels
The basic liquid flow behavior at microscale remains
unchanged for as small as 10 lm passage dimensions. The liquid
molecules are closely packed together compared to the channel
dimensions and the equations developed for macroscale applications, such as Navier-Stokes equation and convective heat transport equations are still applicable. During flow boiling, however,
the bubble sizes are quite comparable to the channel dimensions
and are responsible for changes in the two-phase flow behavior
and thermal characteristics. The main issue has been instability,
which is being addressed in Sec. 4. The overall progress made in
the area of liquid flow and flow boiling in microchannels in the
last three decades has been reviewed recently by Kandlikar [24].
Recent publications indicate that there is a need for further
enhancing heat transfer in microchannels. This section is therefore
devoted to reviewing the literature in this field and identifying
specific research directions.
3.1 Single-Phase Liquid Flow. Among the excellent reviews
available on this topic, the work by Goodling [25], Sobhan and
Garimella [26], Palm [27], and Guo and Li [28] are noteworthy.
By 2005, it was well accepted that the liquid flow in microchannels follows the continuum theory, and the discrepancies were
mainly attributed to the experimental errors, axial conduction
effects, roughness effects. A recent exhaustive review of the
early work on heat transfer during single-phase flow is given by
Kandlikar [24].
In addition to the work on fundamental aspects of friction factor
and heat transfer at microscale, considerable progress has been
made in applying the high heat removal capability of microchannels with liquid flow. Microchannels are sought after in high heat
flux dissipation applications. A heat flux in excess of 1 kW/cm2 is
anticipated in advanced electronic cooling applications. To meet
this cooling demand, employing single-phase liquid with an average temperature difference of 20 C would require a heat transfer
coefficient of 500,000 W/m2 C. Thus, heat transfer enhancement
has been identified as a major research thrust for future research.
Microchannels used in heat transfer applications with singlephase liquid flow are generally operated in the laminar region.
Heat transfer coefficient in the fully developed laminar region is
inversely related to the channel hydraulic diameter. Under a constant heat flux boundary condition, in order to obtain the desired
heat transfer coefficient of 500,000 W/m2 C, a hydraulic diameter
of around 5 lm is needed with a plain microchannel. However,
the pressure drop increases as D4 and an extremely large pressure drop would result with this configuration. The need for
enhancement within microchannels was identified earlier in
2004 by Kandlikar and Grande [29], who proposed different
enhancement features in silicon substrates. Employing enhancement features in microchannels offers a practical solution to meet
this high heat flux dissipation demand. Tuckerman [30] in 1984
had generated tall pin fins of aspect ratios 8:1 by using precision
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Fig. 3 Oblique fin geometry for enhancing single-phase liquid
flow. Adapted from Ref. [37].
Fig. 2 Example of enhancement technique proposed by
Steinke and Kandlikar [32]
sawing to enhance the performance of microchannels. As the heat
transfer coefficient increases over the fin surface, fin efficiency
decreases with fin height, and longer fins may not be desirable. A
good review of various enhancement studies is given by Tullius
et al. [31]. Steinke and Kandlikar [32] presented a list of enhancement techniques applicable in microchannels. Figure 2 shows one
of their proposed designs with cross mixing of adjacent liquid
streams. Some of the other promising designs include surface
roughness, flow disruptions, and secondary flows. The two
enhancement techniques that have received attention in the recent
literature are fins and roughness elements. These are reviewed in
greater detail.
Fabrication techniques for the enhancement features have been
developed for low cost production. A review of fabrication techniques for silicon substrates is provided by Kandlikar and Grande
[29], and Jasperson et al. [33] provide a detailed review for metal
substrates.
3.1.1 Fins in Single-Phase Liquid Flow. Fins increase the
available heat transfer surface area and are used extensively in
macroscale heat transfer applications. Tuckerman [30] first
employed high aspect ratio pin fins to enhance microchannel
performance. A number of researchers have recently applied this
geometry in microchannels. Kosar and Peles [34] studied circular
pin fins, 99.5 lm in diameter and placed at a pitch of 150 lm in a
staggered configuration on a silicon chip inside an 1800 lm wide
and 10 mm long channel. A heater was placed on the backside of
the silicon chip. Using water flow, they obtained a maximum heat
transfer coefficient of around 55,000 W/m2 C. John et al. [35]
compared the performance of square and circular pin fins and
noted that the figure of merit, defined as the heat transfer performance to pressure drop penalty, was higher for circular pin fins at
Re < 300, while reverse was true at higher Re. Vanapalli et al.
[36] studied additional fin shapes of ellipse and diamond in gas
flow, but these have not been studied in liquid flows. Lee et al.
[37] studied their patented parallelogram cross-sectional fins with
the side walls parallel to the flow and the oblique front and rear
sides facing at an angle. Their fin geometry is depicted in Fig. 3.
This design is similar to that shown in Fig. 2, except the secondary
flow is induced in only one direction. This geometry was implemented on a copper cooler base of 25 mm 25 mm with a fin
height of 1.2 mm and a channel width of 300 lm. The secondary
flow induced in the oblique interconnecting passages resulted in
an eighty percent enhancement in heat transfer with little pressure
drop penalty. However, the heat transfer coefficient was relatively
low due to the large hydraulic diameter employed. Implementing
this geometry at microscale seems to be attractive.
Journal of Heat Transfer
Prasher et al. [38] studied various square and circular pin fin
geometries of diameters (or side walls for square fins) ranging
between 55 and 153 lm. Their results indicate that the area
enhancement combined with the improvement in heat transfer
coefficient provided a maximum enhancement factor of 25 as
compared to the channel without any fins. They presented correlations for heat transfer and friction factor as a function of geometrical parameters and flow rate.
Among other fin shapes, offset strip fins have been widely utilized for heat transfer enhancement. Colgan et al. [39] used this
geometry in their silicon chip cooler to dissipate over 500 W/cm2
with water and over 250 W/cm2 with a fluorinated liquid. The fin
length was 500 lm with a pitch of 50–100 lm. The heat transfer
coefficients for these fins were measured by Steinke and Kandlikar [40] and were seen to be one of the highest reported (in excess
of 500,000 W/m2 C). An SEM image of one of the fin geometries
used in these two studies is shown in Fig. 4.
From the literature discussed above, it is seen that the offset
strip-fin geometry provides significant heat transfer enhancement
in microchannels. The increased pressure drop due to the tortuous
path followed by the liquid has been countered by reducing the
flow length with multiple inlet and outlet headers [39]. This multiple header concept was originally suggested by Tuckerman [30]
with alternate input and output headers that were placed along the
flow length in the cover plate over the microchannels. It is also
noted that the similarity between microscale and macroscale flows
provides an opportunity to explore the fin geometries that have
Fig. 4 SEM image of one of the offset strip-fin geometries
employed by Colgan et al. [39] and Steinke and Kandlikar [40].
Fin length 5 250 lm, fin and channel widths 5 50 lm, channel
depth 5 200 lm.
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Fig. 5 Temperature nonuniformity along the coolant flow
length for an open gap, a conventional microchannel, and a
variable density fin structure. Adapted from Ref. [41].
been successful in macroscale applications be investigated for
microscale liquid flow systems. The added constraints due to manufacturability and more stringent pressure drop limitations may be
applied as additional selection criteria.
Another important aspect in the cooling of electronic devices is
the uniformity of temperature along the coolant flow path. As the
coolant flows, its temperature rises, which in turn causes the substrate temperature to rise almost in the same proportion since the
heat transfer coefficient is uniform along the flow length from inlet
to outlet (except in the entrance region). To reduce the temperature
variation, Rubio-Jimenez et al. [41] numerically investigated a
microscale pin-fin structure with increasing fin density along the
flow direction. The resulting increase in the surface area and heat
transfer coefficient compensate for the decrease in the available
temperature difference between the fluid and the substrate along the
flow direction, and a more uniform substrate temperature is
obtained as shown in Fig. 5. Here the fin density is changed twice
along the flow length in the MF-50 100 200-66 fin structure
with variable fin density. For comparison, the temperature variation
in a conventional microchannel and an open gap of the same height
without the fins are also shown. The variable fin density design also
offers a lower pressure drop as higher fin density is employed only
toward the exit where the temperature difference is smaller.
3.1.2 Roughness in Single-Phase Flow. Surface roughness to
improve heat transfer at microscale is a relatively simple technique. Preliminary work on the effect of uniform roughness was
conducted by Kandlikar et al. [42]. Stainless steel tubes were
chemically etched to produce different surface roughness. The
results showed that for a 0.62 mm diameter circular tube, a surface
roughness of 0.355% enhanced heat transfer by about 50% over a
smooth tube with little pressure drop penalty in the Re range from
900 to 2800. The effect of roughness on friction factor in laminar
and turbulent flows was investigated by Kandlikar et al. [43], who
proposed a modified Moody diagram based on the concept of
constricted flow diameter. Weaver et al. [44] conducted an experimental study with rectangular channels 500 lm high with a roughness height of 6.1 lm resulting from their manufacturing process.
They noted that the heat transfer was enhanced by only a factor of
1.1 to 1.2, while friction factor increased by a factor of 2.2 in the
Re range 1000–3000. Lin and Kandlikar [45] conducted a systematic study to investigate the effect of structured roughness on heat
transfer and pressure drop in a 10 mm wide channel with a gap of
1 mm. Figure 6 shows a surface profile that was generated on the
stainless steel sidewalls.
For a roughness element height of 96.3 lm shown in Fig. 6, an
enhancement of about 1.8 was obtained in the laminar region over
a plain surface. However, transition to turbulent flow occurred
earlier and a significantly higher heat transfer coefficient of
150,000 W/m2 C was obtained. This geometry represents one of
Fig. 6 SEM image of the roughness profile on the sidewall of
the channel, adapted from Ref. [45]
the best performing enhancement techniques available in the
literature (regular twisted tapes, coiled wire insert, alternate clockwise and anticlockwise twisted tapes, and porous media insert).
Figure 7 shows the heat transfer performance comparison of three
roughness profiles studied by Lin and Kandlikar [45]. Structured
roughness provides a very effective way for enhancing heat
transfer at microscale. A number of numerical studies are available that provide further insight, e.g., Refs. [46,47], but are not
reviewed here due to space constraint. Further research on designing specific roughness features to match the fluid properties and
operating flow rate is warranted.
3.2 Research Needs in Single-Phase Liquid Flow in
Microchannels. Although efforts are needed for developing a
fundamental perspective of microscale heat transfer, enhancing
heat transfer in microchannels is of critical importance in successful development of microscale thermal devices. The heat transfer
coefficient needs to be further increased, while dramatic reductions in pressure drop are warranted. This leads to another concern
regarding the small area available for manifolds. Another area recommended for research is the development of high performance/
large heat duty heat exchangers at competitive costs using microscale passages to replace those using macroscale passages.
Fig. 7 Heat transfer performance of three structured roughness profiles with water, adapted from Ref. [45]
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3.3 Flow Boiling in Microchannels. Since boiling phenomenon is in general considered to be more efficient than the singlephase flow due to the large latent heat transfer at a constant
temperature in a liquid, the advantages have not yet been realized
in microchannels. Some of the fundamental work on flow boiling
was presented by Tuckerman and Pease [1] in 1981, followed by
Moriyama et al. in 1992 [48], Peng and Wang [49] in 1993,
Bowers and Mudawar [50] in 1994 for minichannels, and Hetsroni
[51] in 2000. The heat transfer coefficients were reported to
be low during flow boiling in microchannels by Steinke and
Kandlikar [52] in 2004. In 2001, Kandlikar [53,54] visualized the
explosive bubble growth that is responsible for instability and low
critical heat flux. High-speed visualization was employed by a
number of researchers to understand the link between flow patterns and heat transfer performance, e.g., Schilder et al. [55] and
Harirchian and Garimella [56] and Cheng et al. [57]. Although
these efforts have shed considerable light on the two-phase flow
behavior, a clear path toward enhancing the heat transfer performance still remains elusive. Recent work by Kandlikar [58] shows
the similarities between pool flow boiling and flow boiling in
microchannels, while it is seen that the enhanced pool boiling
with an open microchannel surface by Cooke and Kandlikar
[59,60] has significantly outperformed flow boiling in microchannels with water. This indicates an immediate need to focus future
research on flow boiling enhancement in microchannels. The
complexity of a flow boiling system cannot be justified when the
performance of a simpler pool boiling system or a single-phase
system is superior. In Secs. 3.3.1 and 3.3.2, two enhancement
techniques will be reviewed to evaluate their potential in enhancing heat transfer coefficient and CHF.
3.3.1 Fins With Flow Boiling. Fins have been used extensively in flow boiling application at macroscale. Krishnamurthy
and Peles [61] employed 100 lm circular pin fins in 250 lm tall
microchannels. They obtained a maximum heat transfer coefficient of around 75,000 W/m2 C. Their video images indicated the
presence of vapor patches which led to premature CHF. Qu and
Siu-Ho [62] studied 200 lm square pin fins in 670 lm high microchannels with water. A maximum heat flux of 248.5 W/cm2 was
attained with a mass flux of 417 kg/m2s. The highest heat transfer
coefficient obtained was 125,000 W/m2 C at lower qualities
(vapor fractions). Xue et al. [63] employed 30 lm square pin fins
in 60 lm high silicon microchannels. They obtained a CHF of
around 65 W/cm2 with FC-72. The flow boiling heat transfer
coefficients improved over pool boiling with increasing flow
velocities.
Although fins are attractive in macroscale flow boiling applications, the existing studies show that they are not able to compete
with the high heat transfer coefficients obtainable with single-phase
liquid flow. Further research is warranted on developing new fin
geometries that will provide stable high performance (high heat
flux and high heat transfer coefficient) under flow boiling conditions. Such studies are needed for both silicon and copper substrates
because of their application in electronics cooling and high performance heat exchangers, respectively.
3.3.2 Nanostructures With Flow Boiling. Nanowires have
been shown to enhance pool boiling due to their improved surface
wettability characteristics. Khanikar et al. [64] employed carbon
nanotubes (CNT) on copper microchannel surfaces. They found a
modest improvement in heat transfer at low heat fluxes, but only a
marginal improvement in heat transfer characteristics at high heat
fluxes. Since CNTs yielded a hydrophobic surface, the nucleation
characteristics improved but the large contact angles adversely
affected the performance at higher heat fluxes. Similar results
were obtained by Singh et al. [65] with CNTs on silicon substrates. Recently, Kousalya et al. [66] employed ultraviolet light
on the CNT structures and reported an improvement in heat transfer performance with a 4.6 C reduction in the wall superheat at a
heat flux of around 50 W/cm2. The ultraviolet light was utilized to
Journal of Heat Transfer
make a CNT surface hydrophilic as originally reported by Takata
et al. [67]. Morshed et al. [68] employed carbon nanowires on
silicon substrates and tested for flow boiling enhancement with
water. Their reported results for heat transfer coefficients that
have been erroneously reported as around 5000 W/cm2 C, while
the correct units are believed to be 5000 W/m2 C. The surface
became hydrophilic with the introduction of nanowires and the
heat transfer performance improved. The wall superheat was
reduced by about 8 C at a heat flux of 55 W/cm2 under a mass
flux of 251 kg/m2s. The maximum heat fluxes employed in their
tests were below 60 W/cm2.
The nanostructures are seen to be effective in increasing boiling
performance through an increase in the surface wettability. This is
an area where further research is warranted.
3.4 Research Needs in Flow Boiling Heat Transfer
Enhancement in Microchannels. Heat transfer enhancement
during flow boiling in microchannels has not been extensively
investigated in literature as the instability issues were of prime
concern. With their current low heat transfer coefficient and CHF
limits, flow boiling in plain microchannels does not compete
favorably with single-phase and pool boiling techniques. The fins
are promising as they enhance the CHF limit, but the high wall
superheat noted in tall fins make them unsuitable. Shorter fins are
desirable from the wall superheat standpoint, but the associated
area increase becomes limited. Porous surfaces are attractive, but
care has to be taken to limit the additional thermal resistance
introduced by the porous matrix. The nanostructures seem to be
an attractive option, as they are able to alter and enhance the heat
transfer mechanism. The benefits of microscale have not yet been
fully realized for flow boiling in microchannels, and progress in
that direction can be made only through a fundamental understanding of the boiling phenomena at microscale. Further benefits
can be realized by combining such high performing microscale
techniques with nanoscale surface features.
4
Flow Boiling Instabilities in Microchannels
Flow boiling instabilities are well recognized as a hindrance
to the realization of evaporative microscale heat exchangers.
They introduce temperature oscillations, thermal stress cycling,
vibration, and they can compromise the structural integrity of
the system. More importantly, they can lead to premature transition to the limiting CHF condition [69,70]. To overcome this difficulty, an effort to better understand the mechanisms controlling
flow instabilities at the microscale and to develop methods to
suppress their deleterious effects have been undertaken by several independent research groups. As detailed in a recent book
dedicated to this topic [71], much is qualitatively known about
the nature of flow instabilities in microscale domains because of
these studies. However, quantitative measures and models to better predict the occurrence and magnitude of these flow instabilities are far from being satisfactory. In addition, better methods
need to be developed to overcome the challenges presented by
flow instabilities.
4.1 Instability Modes. Studies performed over the last decade suggest that five instability modes control the small scale
[49–51], namely, rapid bubble growth, Ledinegg (excursive),
parallel channel, upstream compressible volume, and the CHF
condition. Only the rapid bubble growth instability is unique to
the microscale. The other four were initially identified for conventional scale channels; some dating back to the late 1930 s, such as
the Ledinegg instability [72]. However, the manifestations of
these instabilities in microchannels are somewhat different than in
their large scale counterparts.
4.1.1 Rapid Bubble Growth Instability. When a nucleation
site inside a microchannel is activated, a bubble will form and
very often will grow very rapidly before occupying the entire
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channel’s cross-sectional area. Once this occurs, the bubble will
continue to grow explosively downstream and upstream as well, if
preventive means are not properly taken, causing flow reversal.
As discussed by Kuo and Peles [73] and detailed by Peles [71],
two mechanisms control this instability: the high liquid superheat
sustained in microchannels made of silicon and the pressure
waves generated during the growth and collapse of a bubble.
4.1.2 Ledinegg Instability. The first successful attempt to
systematically study flow boiling instabilities was published by
the German scientist M. Ledinegg who formulated the basis
for the widely known static instability that bears his name [72].
From the various flow boiling instability modes this is perhaps the
most important and most extensively studied. It is therefore, not
surprising that it is also one of the first instability modes that were
revealed in the course of studying flow boiling in microchannels.
Many papers and books have detailed this instability that arises
from the pressure drop-mass flux characteristics in a channel with
flow boiling. This instability can only occur when the slope of the
pressure drop-mass flux curve is negative.
4.1.3 Parallel Channel Instability. Connecting two or more
channels in parallel to the same inlet and exit manifolds can modify the stability of the individual channel in two distinct ways. It
can change the mass flow rate supply curve of the channel and, if
the channels are connected through a conductive solid along their
length, it induces thermal interaction that can modify the stability
condition.
If the slope of the channel’s supply curve moderates, the system
stability—the Ledinegg instability—will deteriorate. Because
microchannel heat sinks are formed by etching many deep
trenches into a silicon chip or a metal slab, the inlet manifold to
exit manifold pressure drop will not be significantly affected by a
temporary change in an individual channel, such as a temporary
change in the mass flux. It follows that the system cannot react to
changes occurring in a single channel, and the nominal supply
curve of a single channel is flat (i.e., the inlet to exit pressure drop
is constant irrespective of mass flux). This makes microchannels
very susceptible to the parallel channel instability, which in this
case, is directly related to the Ledinegg instability. On the other
hand, thermal interaction between adjacent channels tends to stabilize the flow at the microscale [74].
4.1.4 Upstream Compressible Volume. This instability is
common in systems with a significant volume of noncondensable
gas trapped upstream or in a heated section. Since gas is compressible, changes to the inlet pressure will cause the section
upstream a heated channel to become compressible—the extent of
the compressibility depends on the volume of trapped gas
upstream the channel relative to the channel’s volume. For very
small channels, Bergles and Kandlikar [70] noted that a large
volume of degassed liquid is sufficient to introduce considerable
compressibility. It is often associated with pressure drop oscillations, having a characteristic frequency of about 0.1 Hz, combined
with density wave oscillations, having a characteristic frequency
of about 1 Hz.
4.1.5 Critical Heat Flux Condition. The critical heat flux
condition is perhaps one of the most deleterious instability that
can occur in flow boiling system. It marks the transition from a
very effective heat transfer process to a very ineffective process.
Since the heat transfer coefficient drops very rapidly following the
CHF condition, the surface can reach unacceptable temperatures
causing complete burnout of the channel under uncontrolled heating conditions.
Because of the importance of the CHF conditions—primarily
avoiding it—literature concerning CHF conditions at the microscale are plentiful (e.g., Ref. [75]). After examining available
literature and superimposing microchannel CHF data on Gambill
and Lienhard [76] CHF limits, Carey [77] speculated that CHF at
the microscale is hindered in comparison to the conventional
scale. However, Kuo and Peles [78] suggested that the low CHF
values in microchannels might be the results of suboptimal experimental conditions used in early studies, such as low mass fluxes
and long channels. They used some of their own data to suggest
that higher CHF values can be achieved in microchannels if apposite conditions prevail.
4.2 Mitigating Instabilities. Because instabilities are detrimental in the implementation of flow boiling systems, several
methods have been developed and proposed to suppress, or at
least delay, their appearance. Most of these techniques are aimed
at suppressing the Ledinegg instability, parallel channel instability, upstream vapor compressibility, and the critical heat flux conditions, but, several can also be used to suppress the rapid bubble
growth.
Inlet restrictors have been used in conventional scale channels
to overcome the Ledinegg instability and parallel channel instability. They add pressure drop that increases linearly with mass flow
rate and, therefore, reduces the negative slope of the pressure
drop-mass flux demand curve. This technique was found to be
equally effective in microchannels [69,79]. Diverging channels is
a variation of inlet restrictors used to suppress the Ledinegg instability and was successfully demonstrated to be effective at the
microscale (e.g., Ref. [80]).
Fractal tree-like microchannels [81] were studied partly as a
method to mitigate flow boiling instabilities. Although not immediately apparent, this flow configuration is yet another variation of
the inlet restrictors as far as flow instabilities are concerned. This
is because the cross-sectional flow passage increases downstream
and, therefore, shifts the demand for the channel’s pressure drop
toward the inlet where the flow is either single-phase flow or at
low quality.
Extraction of vapor from a microchannel (Fig. 8) in an effort to
reduce the void fraction and, by proxy, reduce the apparent effect
of the boiling process on the overall channel’s pressure drop
demand curve was proposed by David et al. [82]. This intriguing
Fig. 8 The vapor venting microchannel to suppress flow boiling instabilities
0proposed by David et al. [82]
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Efforts pertinent to active flow control should include both open
loop and closed loop control.
Regardless of the effort to develop new techniques, fundamental studies need to be continued to map flow boiling instabilities
and identify their modes. This is desirable because instabilities are
multidimensional problems with many variables controlling their
occurrence. Experimental and numerical studies should be conducted to expand available data under large operating conditions,
different geometries, and different types of fluids. In addition,
multiscale numerical models need to be further developed to predict instabilities, such as the rapid bubble growth. These models
should span length scales starting from the nanoscale to several
millimeters, and will require a range molecular dynamic simulations coupled with continuum models. Such studies should have
an eye toward current and future applications.
5
Fig. 9 A SEM image of the microchannel and the reentrant cavities used by Kuo and Peles to suppress flow boiling instabilities [73]
and novel idea is in its infancy and will require much effort, innovation, design, and careful microfabrication processes to become
a viable and superior solution for flow instabilities in microscale
domains.
Several methods to address the rapid bubble growth have been
studied. Forming reentrant cavities along a microchannel, such as
the one shown in Fig. 9, in an effort to promote nucleation and
reduce the wall superheat at the onset of nucleate boiling (ONB),
was proposed by several groups [73,78,80,83]. Since one of the
mechanisms responsible for the rapid bubble growth is the liquid
superheat, reduction in the liquid temperature at ONB helps suppress this instability. However, since other mechanisms can also
trigger the rapid growth of a bubble, i.e., the bubble dynamics and
elevated pressures, this remedy might not be sufficient.
Since reentrant cavities reduce the liquid superheat, they also
tend to suppress the oscillation generated by the bubble ebullition
process. Macroscale studies [84] have shown that flow oscillations
tend to prematurely trigger CHF conditions. Microscale studies
[73] confirmed that the reduction in flow oscillation attributed to
surface reentrant cavities can also be used to augment the CHF
conditions.
Analytical efforts to study the stability of flow boiling in microchannels and develop techniques to suppress flow instabilities
were recently reported by Zhang et al. [85,86]. Active feedback
control models were used to simulate modulation of the supply
pump and the inlet valve in an effort to suppress the Ledinegg and
the upstream compressible volume instabilities in a single channel. Based on these models a controller design was presented. In a
subsequent paper [86], the stability and active flow and temperature control of parallel channel system were analyzed. With identical channels, the system was shown to be uncontrollable. For
nonidentical channels, instabilities can be controlled through
modulating the pump. A controller design approach for such cases
was presented.
4.3 Research Needs—Flow Boiling Instabilities. Despite
the several efforts to suppress flow boiling instabilities detailed
above, methods developed so far are far from being perfected
either because they introduce drawbacks, such as increased
pressure drop (e.g., inlet restrictors to suppress the Ledinegg instability), or they lack sufficient capabilities to suppress them. Some
of the most advanced techniques suggested may be superior, but,
they have not been successfully proven and are not mature
enough.
New active and passive methods need to be developed to overcome penalties associated with current proven techniques and at
the same time provide robust inexpensive suppression techniques.
Journal of Heat Transfer
Condensation in Microchannels
5.1 Recent Advances. Condensation, evaporation and boiling share several underlying aspects; however, the drivers for
research in these fields have been different. While boiling and
evaporation have been critical for the advancement of high-heatflux heat removal from compact devices in applications such as
electronics cooling, condensation is usually associated with heat
rejection, typically coupled with larger thermal resistances from
single-phase coupling fluids or ambient air. With the increasing
emphasis on system-level metrics such as overall energy efficiency, reductions in heat transfer equipment size, and the use of
environmentally friendly working fluids, obtaining a fundamental
understanding of condensation at the microscale assumes increasing importance. As the flow passage size decreases, the relative
importance of surface tension compared to gravity increases.
Therefore, condensation models developed for larger tubes (where
gravity and inertial forces dominate) are not expected to reliably
predict the behavior at small scales. Thus, there is a critical need
for robust condensation heat transfer and pressure drop models
applicable to a wide variety of working fluids, microscale geometries and operating conditions. Measurements and modeling of
condensation processes pose challenges different from those
encountered in boiling and evaporation, even in the most basic
aspect of measuring heat transfer rates. Over the past decade,
advances in experimental and modeling techniques have gradually
begun to establish the groundwork for an in depth understanding
of condensation at the microscale.
5.1.1 Condensation Flow Regimes and Void fractions in
Microchannels. Heat transfer and pressure drop in microchannel
condensation depend strongly on the mechanisms for two-phase
flow (e.g., stratified, intermittent, annular, and their variants) as
well as corresponding phase distributions characterized by void
fraction, slip ratio, etc. Thus, heat and momentum transfer models
require knowledge of the flow regimes for the applicable operating conditions and geometries. Over the past decade, flow regime
mapping has progressed from visualization of air/water mixtures
under adiabatic, ambient pressure conditions, to phase change of
representative fluids at operating conditions of interest. These
advances are slowly reducing the need for unreliable extrapolations of findings on air–water mixtures with their large phase
property differences (e.g., liquid/vapor density ratio, surface
tension) to typical condensing fluids with completely different
properties and the accompanied phase change. One of the first visualizations of the actual condensation process in microchannels
was the work of Coleman and Garimella [87–89] on R134a using
an innovative pressurized transparent enclosure around glass
microchannels to enable visualization at high pressures, representing a departure from adiabatic air–water mixtures. They classified
flow regimes into annular, wavy, intermittent, and dispersed
flows, with further subdivisions into patterns, and developed empirical flow regime transition criteria as functions of G, x, and Dh
for circular (D ¼ 4.91 mm) and rectangular (1 < Dh < 4.8 mm;
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Fig. 10
Description of two-phase flow regimes and patterns [90]
0.5 < AR < 2) microchannels at 150 < G < to 750 kg m2 s1. In
addition to the documentation of intermittent and other flows during condensation, their most significant observation was that as
Dh decreased, the intermittent and annular flow regimes increased
in extent at the expense of stratified/wavy flow regimes, due to the
increased importance of surface tension over gravity. Following
up on that initial work from the early 2000 s, Keinath and Garimella [90] extended the visual documentation of condensation
(Fig. 10) in two important aspects: operation at high reduced pressures (0.38 < Pr < 0.77) approaching the critical pressure, and b)
the use of azeotropic refrigerant mixture R404A. In addition, they
extended the range of geometries (0.5 < D < 3 mm), and used
advanced image processing techniques to obtain quantitative information about the dynamic phase distributions in such flows.
Such visualizations of condensation at the microscale with high
spatial and temporal resolution have also enabled the measurement and modeling of local void fractions, with working fluids of
interest operating at the relevant conditions. For example, Winkler
et al. [91] developed an edge-detecting and spline-fitting tech-
Fig. 11 Comparison of vapor–liquid distribution on a (a) frame
and (b) local basis for Tsat 5 30 C, G 5 200 kg m22 s21 [92]
nique to identify the vapor–liquid interface in wavy and intermittent flow during condensation of R134a for 1 < Dh < 4.8 mm,
which was used to obtain void fractions based on video frames of
the respective regimes. Keinath and Garimella [90,92] extended
the work of Winkler et al. further through the use of better optical
resolution and image processing to obtain data for diameters as
small as Dh ¼ 0.5 mm, and for a wider range of reduced pressures
(0.38 < Pr < 0.77) for condensing R404A. This wide range of PR
enabled the assessment of the influence of fluid property variation
on void fraction. In their experiments with 200 < G < 800 kg m2
s1 in round tubes with D ¼ 0.5, 1.0, and 3.0 mm, the vapor core
is assumed to be circular or circular on top with a flat bottom at
the appropriate height (Fig. 11(a)). Like Winkler et al. [91] and
others before, Keinath and Garimella [92] did not find a significant influence of G on void fraction, particularly at low x. The
bulk average void fraction also did not depend appreciably on Dh;
however, Dh did affect the distribution of the liquid and vapor
within the flow. This is evident in Fig. 11, which shows axial
and bulk average void fractions for G ¼ 200 kg m 2 s1 flow at
Tsat ¼ 30 C in tubes with D ¼ 1 and 3 mm. For both tubes, the
bulk average void fraction is the same, even though one image
shows intermittent flow, and the other wavy flow. Such emerging
insights show that basing transport models only on bulk average
void fractions is inadequate; different interfacial areas, even at the
same void fraction, would lead to different DPs and heat and mass
transfer coefficients.
5.1.2 Microchannel Condensation Pressure Drop. Due to the
strong coupling of heat and momentum transfer, accurate determination and modeling of microchannel condensation pressure drop
is essential for the development of heat transfer models. Cavallini
and co-workers [93–97] have, during the past decade, achieved
progress on condensation DP at small Dh. They investigated DP
in a rectangular multiport minichannel (Dh ¼ 1.4 mm) for R-134a
and R-404A [93] and R-134a, R-236ea, and R-410A [95] for
200 < G < 1400 kg m2 s 1 at 40 C. The refrigerants spanned a
range of reduced pressures, high (PR ¼ 0.49, R410A), medium
(PR ¼ 0.25, R134a) and low (PR ¼ 0.14, R236ea). They found that
most correlations could not predict the frictional gradient over
the range of fluids and operating conditions, and developed a
two-phase multiplier correlation [97] based on the Friedel [98]
model for annular flow using data from several studies of condensation in microchannels. They concluded that gravitational
effects were not important in annular minichannel flow and
eliminated the Froude number dependence in the model, and
also attempted to account for liquid entrainment. More recently,
Cavallini et al. obtained DP data for R134a [94] and R1234yf
[96] in a single circular microchannel with D ¼ 0.96 mm for
200 < G < 1000 kg m 2 s1. With this, they extended the above
model [97] to account for surface roughness and to nonshear
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Fig. 12
Intermittent flow unit cell [101]
dominated flow regimes through modifications in the liquid film
friction factor.
Condensation DP models with specific attention to the applicable flow regime include the initial multiregime model of Garimella et al. [99] for condensing R134a in circular microchannels,
followed by Agarwal and Garimella [100] for circular and noncircular microchannels (0.42 < Dh < 0.8 mm). This model was in
turn based on models of DP in intermittent flow by Garimella
et al. for circular [101] and noncircular [102] microchannels, and
for annular flow [103]. The intermittent flow DP model was based
on the unit cell shown schematically in Fig. 12. The insights about
intermittent flow structure gained from their earlier flow visualization studies enabled them to idealize the total DP in each unit cell
as the sum of the DP in the liquid slug, vapor bubble and transitions between the two (Eq. 12)). A correlation for slug frequency
was then developed as a function of slug Reynolds number for circular and noncircular tubes.
Lslug
dP
dP
Lbubble
dP
þ
¼
dz
dz film
dz slug LUC
LUC
bubble
NUC
þ DPtransition
(12)
L
For the annular flow model [103], the frictional DP is related to
the interfacial friction factor as shown in Eq. (13), where the void
fraction, a, is calculated from the Baroczy [104] model
DP 1
G2 x 2 1
¼ fi
L
2 qV a2:5 D
(13)
The interfacial friction factor (fi) is then correlated to the liquidphase Darcy friction factor, by the expression in Eq. (14), where X
is the Martinelli parameter and w is the ratio of viscous-to-surface
tension forces
fi
¼ A Xa RebL wc
fL
(14)
5.1.3 Microchannel Condensation Heat Transfer. Accurate
measurement of condensation heat transfer in microchannels
poses unique challenges. Unlike boiling experiments, heat transfer
rates cannot be measured through the electrical input, and must
therefore be inferred from secondary measurements. This is in
turn made difficult by the small mass flow rates in microchannels
that lead to small condensation heat duties, especially when
experiments must be conducted with small changes in x across the
vapor–liquid dome to achieve enough resolution to track flow
regime variations. Further compounding the challenges is the fact
that the low heat duties coupled with the high h in microchannels
Journal of Heat Transfer
leads to a very small DT upon which h measurements must be
based.
Models for microchannel condensation have focused predominantly on annular flow, with adjustments and interpolations
with single-phase heat transfer to account for intermittent flow.
Cavallini and co-workers conducted condensation measured heat
transfer in concert with their DP studies [93,95–97] in circular
and rectangular channels with Dh < 3 mm. From these data and
their DP model, they developed a heat transfer model based on
the heat and momentum analogy [97]. Cavallini et al. [105] then
developed a model from a database for tubes with D > 3 mm.
Despite being comprised of data for large tubes, Del Col et al.
[96] found that the model predicted condensation for R1234yf for
D ¼ 0.96 mm well.
An innovative solution to the issue of accurate measurement of
condensation h, the “thermal amplification” technique, was developed by Garimella and Bandhauer [106]. In this technique, heat of
condensation is removed by a high flow rate primary coolant,
which provides a low thermal resistance, followed by rejection
of this heat of condensation to a secondary coolant at a low thermal capacitance rate. This approach decouples, and separately
addresses, the conflicting challenges of measurement of accurate
heat duties of a few Watts, while also accurately deducing
condensation h from the measured overall conductance values
without intrusive temperature measurements. The resulting
heat transfer coefficients were then used to develop models for
condensation of R134a in circular (0.506 D 1.524 mm) [107]
and noncircular (0.424 Dh 0.839 mm) [108] channels for
150 < G < 750 kg m 2 s1. To predict the shear-driven annular
condensation, they used an approach similar to Traviss et al.
[109]. To account for microchannel effects, the DP and interfacial
shear for this model were determined from the corresponding
annular DP models (Eqs. (13) and (14)).
Advances in the measurement of h at even smaller scales
(0.1 Dh 0.4 mm) were made by Agarwal and Garimella
[110,111] for condensing R134a in rectangular geometries using
photolithography and diffusion bonding for the fabrication of the
test sections. Heat transfer coefficients were obtained from the
data through spatially and temporally resolved analyses of
the conjugate heat transfer between the copper channels and the
refrigerant and coolant, including developing a closed-form solution to address the effect of intermittent vapor and liquid flow
over the channel surface. These heat transfer coefficients yielded
a flow regime based model, in which the heat transferred in the
vapor bubble and liquid slug regions were combined to obtain a
composite time-averaged h, as a function of the correlated slug
length ratio (Eq. (15)). For highly annular flows (high x, G), the
liquid slug length is very small compared to the vapor bubble, and
the heat transfer is dominated by that occurring across the thin annular film.
lslug
h ¼ hs lslug þ lbubble
lslug
þ hf 1 lslug þ lbubble
(15)
Such a technique allows for the modeling of a wide range of
conditions with inherently smooth transitions between the two
dominant regimes in microchannels, intermittent and annular.
Numerical models for predicting microchannel condensation
heat transfer for laminar annular flow have been developed by
Wang and Rose [112,113], Nebuloni and Thome [114] and Da
Riva and Del Col [115]. Wang and Rose’s model accounts for the
streamwise shear stress on the condensate film and the transverse
pressure gradient due to surface tension. The transverse pressure
gradient is particularly important in noncircular microchannels,
where fluid is preferentially drawn to sharp corners resulting in
local thinning of the condensate film and high h. This phenomenon is generally not accounted for in correlations for large channels. Closure to the model is provided through an empirical
prediction of DP. Their technique enables the investigation of the
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individual contributions of gravitational, surface tension and viscous effects by “switching on or off” the corresponding terms.
They use this model to identify surface tension and viscosity
dominated regions where h can be predicted via a Nusselt-type
correlation for a variety of fluids, with good agreement with the
data of several investigators including Cavallini et al. [95] and
Bandhauer et al. [107]. Nebuloni and Thome [114] investigate
laminar annular condensation in microchannels with varying internal shape using a finite volume formulation of the energy equations in the liquid phase. They showed that as Dh decreases, the
effect of axial conduction on local tube wall temperature and h
can be significant. Da Riva and Del Col [115] simulate condensation of R134a in a 1-mm diameter circular channel using a volume
of fluid method to assess the influence of surface tension. For the
circular channel, they found condensation to be gravity dominated. This is in contrast to the other numerical studies [112–114],
which show a surface tension effect when condensation occurs in
geometries with sharp corners.
in intermittent and other flows, and the varying influences of tube
shape, surface tension and fluid property differences over much
larger ranges than currently possible.
Finally, almost all the focus in this arena has been on pure fluids or azeotropic fluids. But increasingly, zeotropic fluid mixtures
will find a way into the choices of working fluids due to their ability to match temperature gradients on the source side, in advanced
thermodynamic cycles, and in applications such as waste heat
recovery, where temperature pinches exert large penalties. Even if
flow mechanisms are not appreciably affected by the zeotropic
nature of the fluid mixtures, the heat and mass transfer processes
will be significantly different, with species transport and
concentration gradients in one or both phases, requiring substantially different accounting of the latent and sensible heat transfer
across the phases, especially in high temperature glide (e.g.,
ammonia–water) mixtures. Clearly, the next decade and more
presents ample interesting challenges in the field of microscale
condensation.
5.2 Research Needs—Condensation in Microchannels.
The above discussion shows that the past decade has seen a substantial increase in the understanding of condensation at the
microscales, where investigators are not simply extrapolating
from air–water two-phase flows, or proposing minor modifications
to models originally developed for large Dh. Microchannel condensation is now being studied as a unique entity with its own
governing influences. Innovative high-speed visualization techniques have yielded detailed qualitative and quantitative information about the prevalent flow regimes, the criteria for transitions
between them, and the liquid–vapor phase distribution information needed for void fraction models. Flow mechanism information, together with shear and momentum balance analyses in
different regions of intermittent and annular flow, has yielded
models that specifically account for microscale phenomena. Measurement techniques developed to address challenges specific to
high flux heat transfer at low heat duties have yielded heat transfer
coefficients that appear to be in agreement across different groups
of investigators. Computational treatments have been successful
in highlighting the regions of dominance of surface tension, gravitational, viscous, and inertial forces, including substantiation for
the increased h in surface tension dominated flows in channels
with sharp corners.
Optical flow visualization has its limits; as Dh gets progressively smaller, the interfaces become harder to identify. Techniques that can yield quantities such as void fraction at such small
scales, without the need to optically track intractable interfaces,
perhaps through nonintrusive capacitance/impedance measurements, are necessary for further progress on this front. Also, heat
transfer measurements become progressively difficult at the
smaller scales, due to the reduction in heat duties as well as the
increase in h. The key challenge will be to measure small DT
values ( 0.1 K) with high enough accuracy, without disturbing
the flows.
Flow regime maps and transition criteria continue to proliferate;
however, their predictive capabilities deteriorate as they are
applied to different fluids, geometries, and operating conditions.
Thus, it is vital to develop a flow regime map that can address
different fluid types such as synthetic refrigerants and their azeotropic mixtures, natural fluids such as ammonia, steam, CO2,
water, and hydrocarbons over a wide range of PR and Dh. This
will require more representative idealizations of the governing
forces that make the flow tend to one regime or the other across
the many transition boundaries visualized by researchers. Such
transition criteria will lead to correspondingly better multiregime
models for phase distributions and will minimize the need to arbitrarily pick void fraction correlations to provide closure to h and
DP models. Heat transfer models can then progress from primarily
annular flow based models with some adjustments using dimensionless parameters to those that can directly account for transport
6 Applications of Microchannels in Electronics
Cooling
6.1 Brief Timeline of Advances. The need to cool electronics has been a recognized issue for as long as electronics has been
around, see e.g., Ref. [116]. Vacuum tubes with their ohmically
heated cathodes were the most obvious source of heat which led
to unreliability of both the tubes themselves but also of nearby
components. Capacitors were the usual victims.
The replacement of vacuum tubes with semiconductor devices
greatly eased the problem. However, the advent of computers
brought an enormous increase in the density and total population
of heat dissipating devices and simple spreading was no longer
effective and various forms of liquid cooling were introduced.
Probably the best known example was introduced publicly in
1980 when IBM announced the “thermal conduction module”
[116]. By coincidence, Tuckerman and Pease [1,30] recognized
that the thermal resistivity of silicon was not the problem. The
problem was heat removal from the back surface.
Somewhat surprisingly (at the time) this advance was not
exploited by the computer manufacturers. This was because at
the same time the scaling down of dimensions in ICs led to faster,
less power- hungry and cheaper computing circuitry. Complementary metal oxide semiconductor (CMOS) circuits became attractively fast and, more importantly, eliminated static power
dissipation, and so displaced emitter-coupled logic (ECL) circuits in
computers. So this eliminated the need for water cooling in most
computers. An additional factor was that the use of computers had
evolved from a few expensive, fast, central computers to many
cheaper ones but not quite so fast. Thus, computing electronics did
not need the Tuckerman heat sink. The only market for many years
was for cooling laser diode arrays.
By the mid 1990 s, further scaling of CMOS led to increasingly
fast clock frequencies, and so dynamic power (the power dissipated
by the switching of logic states charging and discharging parasitic
capacitances) was now approaching the levels requiring something
more than passive, or even active (fan driven), air cooling.
As a result microchannel cooling was revived. As an example
Colgan et al. [39] at IBM have described a large variety of the
microchannel structures to allow rational choices for different
conditions and a demonstrated specific thermal conductance of
about 5 W/K/cm2 for single chip modules. One contribution to the
thermal resistance is that of the interfaces. This was avoided in
the original configuration of Tuckerman and Pease by fashioning
the heat sink into the chip itself. Such an approach was not well
received by those manufacturing ICs, so a novel interface structure based on microcapillaries was introduced. This was the first
use of microstructures to improve a thermal interface and
was very effective, with an interfacial conductance of more than
30 W/K/cm2 [30], but has been little used since then.
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As a second example, the company Cooligy was formed specifically to develop aggressive technologies for cooling high-speed
chips. Cooligy technology not only employed microchannels but
also employed phase change (originally used in heat pipes) and
novel pumping technology [117]. The cooling liquid was directly
pumped into the “microstructure heat collector” attached on the
back of a silicon chip. The rest of the cooling loop consisted of a
pump and an air-to-coolant heat exchanger with a fan. Cooligy
technology was used initially in the Apple G4 table top computer.
3D integrated circuitry is now being developed in various
forms. In its simplest and most widely used form, completed chips
are stacked on top of each other and are interconnected at the
periphery. The next level being considered is to arrange interchip
connections by using an array of through silicon vias; this is
under very active development. These two techniques can be
regarded as advanced packaging. A further development is “wafer
stacking” in which prefabricated layers of active circuitry are
laminated together [118]. This allows larger number of interconnects between the layers of circuitry. Finally there is monolithic
3D-IC in which the layers of circuitry are fabricated in situ [119].
This approach allows the highest density of interconnects between
the two layers of active circuitry. All forms of 3D-ICs have the
challenge of removing heat from the upper layers. Anomalous,
usually lower, thermal conductivity of materials in thin film form
is one complication. This is yet another example of the importance of developing an understanding of thermal transport at
the atomic level. Another related issue is the tortuous route of
removing heat from the upper layers, i.e., through many interfaces. Numerical simulation is starting to play a big role in modeling these interfaces. Improved simulation using more powerful
computers and imaginative new algorithms should be a really
fruitful area of research. Microchannels are uniquely suited to
provide cooling between two IC layers. However, the issues
related to thermal vias and interconnects require close collaboration among the circuit designers, thermal engineers and fabricators [120].
In cooling of high power electronics, many microchannel devices now use either evaporative cooling of water or refrigerants, or
impingement jet cooling [121]. The heat fluxes reached with these
technologies are in the range of some hundred W cm2 and, thus,
not significantly higher than those reached a decade ago. The
same values have been successfully obtained with single-phase
laminar cooling to obtain low pressure losses [122–124]. Figure 13
shows an example of such a microstructure fabricated in copper.
However, high power electronics will be further developed.
While in former times the key application for cooling was computing processors, it is now changed to full computers (i.e., blade
server systems) and high power electronics for automotive industry. Especially in the latter, a combination of very high heat flux
and low pressure losses, obtained at minimum volume, is targeted.
For any type of electronic cooling application, the quality and reliability of the thermal interface between the electronic device (e.g.,
a semiconductor chip) and the microchannel heat sink or “cold
plate” is of critical importance, and there is ongoing research
employing nanotechnology to improve the heat transfer coefficients of such interfaces while maintaining minimal mechanical
stress on the chips [125].
6.2 Research Needs in Application of Microchannels in
Electronics Cooling. Advances in thermal management are
needed for the development of further generations of electronics
to continue. Such advances can be brought about by exploiting the
opportunities afforded by new materials and structures and by
greatly improved modeling techniques that themselves rely on
advanced computing electronics and by a resurgence in new algorithms and related techniques emanating from computer science
departments. Inventions of new configurations are hard to predict
but funding agencies should also be ready to review, and fund,
seed projects to test out new ideas that offer rational promise of
meeting some of the above challenges. Cooling solutions in the
future will require more collaboration among the electronics
circuit designer, microfabrication engineers, reliability experts,
material scientists and thermal engineers. Novel solutions that
dramatically extend the cooling capabilities may be explored
independently in laboratory setting, but their ultimate success
depends on our ability to manufacture functional devices in a
cost-competitive manner.
7
Applications of Microchannels in Heat Exchangers
7.1 Microscale Heat Exchangers: Theory, Design and
Applications. Microscale heat exchangers have been the subject
of research and application for more than 30 yr now. The developments of the last 10 yr are briefly described in the following text.
7.1.1 Theoretical Overview. The potential advantages of
miniaturization for improving heat transfer have been appreciated
for many decades; publication of the book “Compact Heat
Exchangers” by W. M. Kays and A. L. London in 1955 was particularly influential in educating the engineering community of
that era. By miniaturization, the dimensions of geometrical elements of heat transfer devices are changed. The influence of the
change of dimensions can be quantified by using a scaling factor
S. Based on the physical base units mass, length and time, the volume is scaled by S3, the surface area by S2 and the characteristic
length (i.e., the hydraulic diameter) by S1. Flow velocity is scaled
by S0. A detailed description of the influences of scaling is provided in Ref. [126].
Many theoretical and experimental results have been published
within the last 10 yr dealing with the validity of classical heat transfer correlations, as applied to the prediction of heat transfer behavior in microchannel heat exchangers [43,126–128]. Looking at this
literature, it is obvious that there is no consensus on this topic yet,
neither for laminar nor turbulent flow. However, Morini et al.
Fig. 13 Surface microscale cooler for high power electronics cooling obtained with laminar flow. Left: Assembled copper
device; Center: Copper device without lid; Right: SEM of internal structure. Reproduced with permission from KIT.
Journal of Heat Transfer
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Dh ¼
f¼
G¼
h¼
K¼
k¼
L¼
LUC ¼
n¼
P¼
Pr ¼
R¼
S¼
s¼
t¼
T¼
u¼
v¼
x¼
X¼
hydraulic diameter, m
friction factor
mass flux, kg m2 s1
heat transfer coefficient, W m2 K1
free variable
thermal conductivity, W m1 K1
length, m
length of unit cell, m
normal coordinate, m
pressure, Pa
reduced pressure
specific gas constant, J kg1 K1
scaling factor
length, m
streamwise tangential coordinate, m
temperature, K
streamwise velocity, m s1
velocity component normal to the wall, m s1
quality or length (in Sec. 7)
Martinelli parameter
Dimensionless Numbers
Bru ¼
Ca ¼
Ec ¼
Gr ¼
Kn ¼
Ma ¼
Nu ¼
Pe ¼
Pr ¼
Re ¼
modified Brinkman number
capillary number
Eckert number
Graetz number
Knudsen number
Mach number
Nusselt number
Peclet number
Prandtl number
Reynolds number
Greek Symbols
a¼
q¼
w¼
k¼
K¼
l¼
r¼
rP ¼
rT ¼
u¼
fT ¼
void fraction
density, kg m3
dimensionless surface tension term
mean free path, m
dimensionless length
dynamic viscosity, Pa s
surface tension, N m1
viscous slip coefficient, dimensionless
thermal slip coefficient, dimensionless
heat flux, W m2
temperature jump coefficient, dimensionless
Subscripts
D¼
I, j ¼
L¼
n¼
SAT ¼
t¼
V¼
w¼
z¼
1¼
dimensionless
index
liquid
normal
saturated
tangential
vapor
at the wall
in z-direction
fully developed conditions
Acronyms
C ¼ circular microtube
CHF ¼ critical heat flux
CWT ¼ constant wall temperature
PP ¼ parallel-plate microchannel
UHF ¼ uniform heat flux
1IW ¼ one insulated wall
References
[1] Tuckerman, D. B., and Pease, R. F., 1981, “High Performance Heat Sinking
for VLSI,” IEEE Electron Device Lett., EDL-2, pp. 126–129.
[2] Colin, S., 2005, “Rarefaction and Compressibility Effects on Steady and Transient Gas Flows in Microchannels,” Microfluid. Nanofluid., 1(3), pp. 268–279.
[3] Young, J. B., 2011, “Calculation of Knudsen Layers and Jump Conditions
Using the Linearized G13 and R13 Moment Methods,” Int. J. Heat Mass
Transfer, 54(13-14), pp. 2902–2912.
[4] Zhang, W.-M., Meng, G., and Wei, X., 2012, “A Review on Slip Models for
Gas Microflows,” Microfluid. Nanofluid., 13(6), pp. 845–882.
[5] Sharipov, F., 2011, “Data on the Velocity Slip and Temperature Jump on a
Gas-Solid Interface,” J. Phys. Chem. Ref. Data, 40(2), p. 023101.
[6] Colin, S., 2012, “Gas Microflows in the Slip Flow Regime: A Critical Review
on Convective Heat Transfer,” ASME J. Heat Transfer, 134(2), p. 020908.
[7] Sparrow, E. M., and Lin, S. H., 1962, “Laminar Heat Transfer in Tubes Under
Slip-Flow Conditions,” ASME J. Heat Transfer, 84, pp. 363–369.
[8] Zhu, X., Xin, M. D., and Liao, Q., 2002, “Analysis of Heat Transfer Between
Two Unsymmetrically Heated Parallel Plates With Microspacing in the Slip
Flow Regime,” Microscale Thermophys. Eng., 6(4), pp. 287–301.
[9] Kuddusi, L., and Cetegen, E., 2007, “Prediction of Temperature Distribution
and Nusselt Number in Rectangular Microchannels at Wall Slip Condition for
All Versions of Constant Heat Flux,” Int. J. Heat Fluid Flow, 28(4), pp.
777–786.
[10] Yu, S., and Ameel, T. A., 2001, “Slip-Flow Heat Transfer in Rectangular
Microchannels,” Int. J. Heat Mass Transfer, 44(22), pp. 4225–4234.
[11] Zhu, X., Liao, Q., and Xin, M., 2004, “Analysis of the Heat Transfer in
Unsymmetrically Heated Triangular Microchannels in Slip Flow Regime,”
Sci. China, Ser. E: Technol. Sci., 47(4), pp. 436–446.
[12] Jeong, H., and Jeong, J., 2006, “Extended Graetz Problem Including Axial
Conduction and Viscous Dissipation in Microtube,” J. Mech. Sci. Technol.,
20(1), pp. 158–166.
[13] Jeong, H.-E., and Jeong, J.-T., 2006, “Extended Graetz Problem Including
Streamwise Conduction and Viscous Dissipation in Microchannel,” Int. J.
Heat Mass Transfer, 49(13-14), pp. 2151–2157.
[14] Hong, C., and Asako, Y., 2010, “Some Considerations on Thermal Boundary
Condition of Slip Flow,” Int. J. Heat Mass Transfer, 53(15-16), pp.
3075–3079.
[15] Miyamoto, M., Shi, W., Katoh, Y., and Kurima, J., 2003, “Choked Flow and
Heat Transfer of Low Density Gas in a Narrow Parallel-Plate Channel With
Uniformly Heating Walls,” Int. J. Heat Mass Transfer, 46(14), pp. 2685–2693.
[16] Hadjiconstantinou, N. G., 2003, “Dissipation in Small Scale Gaseous Flows,”
ASME J. Heat Transfer, 125, pp. 944–947.
[17] Hooman, K., Hooman, F., and Famouri, M., 2009, “Scaling Effects for Flow
in Micro-Channels: Variable Property, Viscous Heating, Velocity Slip, and
Temperature Jump,” Int. Commun. Heat Mass Transfer, 36(2), pp. 192–196.
[18] Morini, G. L., Yang, Y., Chalabi, H., and Lorenzini, M., 2011, “A Critical
Review of the Measurement Techniques for the Analysis of Gas Microflows
Through Microchannels,” Exp. Therm. Fluid Sci., 35(6), pp. 849–865.
[19] Shi, W., Miyamoto, M., Katoh, Y., and Kurima, J., 2001, “Choked Flow of
Low Density Gas in a Narrow Parallel-Plate Channel With Adiabatic Walls,”
Int. J. Heat Mass Transfer, 44(13), pp. 2555–2565.
[20] Qazi Zade, A., Renksizbulut, M., and Friedman, J., 2011, “Heat Transfer
Characteristics of Developing Gaseous Slip-Flow in Rectangular Microchannels With Variable Physical Properties,” Int. J. Heat Fluid Flow, 32(1), pp.
117–127.
[21] Sun, Z., and Jaluria, Y., 2010, “Unsteady Two-Dimensional Nitrogen Flow in
Long Microchannels With Uniform Wall Heat Flux,” Numer. Heat Transfer,
Part A, 57(9), pp. 625–641.
[22] Hu, H., Jin, Z., Nocera, D., Lum, C., and Koochesfahani, M., 2010,
“Experimental Investigations of Microscale Flow and Heat Transfer Phenomena by Using Molecular Tagging Techniques,” Meas. Sci. Technol., 21(8),
p. 085401.
[23] Garvey, J., Newport, D., Lakestani, F., Whelan, M., and Joseph, S., 2008,
“Full Field Measurement at the Microscale Using Micro-Interferometry,”
Microfluid. Nanofluid., 5(1), pp. 77–87.
[24] Kandlikar, S. G., 2012, “History, Advances, and Challenges in Liquid Flow
and Flow Boiling Heat Transfer in Microchannels: A Critical Review,” ASME
J. Heat Transfer, 134, p. 034001.
[25] Goodling, J. S., 1993, “Microchannel Heat Exchangers: A Review,” Proceedings of High Heat Flux Engineering II, July 12–13, San Diego, CA, 1997, pp.
66–82.
[26] Sobhan, C. B., and Garimella, S. V., 2001, “A Comparative Analysis of Studies on Heat Transfer and Fluid Flow in Microchannels,” Microscale Thermophys. Eng., 5(4), pp. 293–311.
[27] Palm, B., 2001, “Heat Transfer in Microchannels,” Microscale Thermophys.
Eng., 5(3), pp. 155–175.
[28] Guo, Z.-Y., and Li, Z.-X., 2003, “Size Effect on Single-Phase Channel Flow
and Heat Transfer at Microscale,” Int. J. Heat Fluid Flow, 24(3), pp. 284–298.
[29] Kandlikar, S. G., and Grande, W. J., 2004, “Evaluation of Single Phase Flow
in Microchannels for High Heat Flux Chip Cooling—Thermohydraulic
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relatively new trend is to use so-called nanofluids to increase the
heat transfer [133]. Nanofluids are suspensions of nanoparticles
(i.e., Al2O3 or similar) in liquids. They can provide an improvement in heat transfer from several percent up to roughly an order
of magnitude, but may be prone to fouling inside the microstructures. As might be expected, it has been observed that fouling
and blocking is an even more serious problem for microscale
heat exchangers than for macroscale ones. For example, accelerated fouling led to abandonment of an otherwise promising
attempt to develop an energy-efficient microscale milk pasteurizer [134] A reliable solution for this problem has not yet been
found. In another study for the same topic, a simple microscale
heat exchanger design was used for homogenization and pasteurization of dairy products, but did not succeed very well. However, a solution was suggested and tested, and proofed to work,
at least for the fouling problems. Recently, the thermal treatment
of hydrocarbon monomers to create polymerized hydrocarbons
have been performed successfully. This is an especially interesting accomplishment, considering the fouling problems that can
occur during polymerization processes. By careful device and
process design, fouling effects were completely avoided. Some
countermeasures used successfully in macroscale (such as antifouling coatings) do not work at microscale due to the fact that
the shear forces for the drag-off of fouling layers or particles are
simply too low in laminar flow. However, stainless steel microscale heat exchangers have successfully been applied to biotech
processes with living cells as well as in the nutrition industry,
showing no increased tendency to fouling. Here, precise design
and process control seems to be more important than antifouling
precautions.
7.2 Research Needs in Microchannel Heat Exchangers.
Within the last 10 yr, the theoretical description of heat transfer in
microscale has advanced only gradually. The same is true for
development of new devices, with the exception of some very specific devices. Several basic tasks, such as the validity of conventional models at the microscale, are still not completely clarified,
as well as the influence of the surface quality or how to overcome
fouling. However, the technical applicability of microstructure
heat exchangers has been widely enhanced owing to the emergence of commercial providers of such devices, which makes it
easier to apply them to a wide variety of applications and technologies. In the future, a homogenization of the model description as
well as many more applications are expected.
Some of the most interesting future applications may result
from the very short thermal time constants of microchannel structures (resulting from the combination of very high heat transfer
coefficient and very low heat capacity), coupled with their very
short diffusion times (high mass transfer coefficients) and the
short residence times inside the devices which can allow acceleration of various physical and chemical process flows. One example
of exploiting the short thermal time constant (about 10 ms) of the
microchannel heat sink coupled with a high thermal conductance
compliant interface is currently being developed to improve the
accuracy of “nanoimprint lithography,” a technology which may
be key to future progress in semiconductor manufacturing. The
idea is to use locally controlled expansion to assure accurate overlay in large area (e.g., 300 mm diameter) nanoprinting. In this
technique, a quartz template with a relief image of the required
pattern is pressed into a liquid polymer on top of the wafer, which
sits on a microchannel heat sink chuck. The pattern on the template is accurately positioned over the existing structure on the
wafer, then a laser pulse crosslinks the polymer into a solid resist
film. With appropriate chemistry, the quartz template can be
removed without damaging the polymeric resist pattern. Features
finer than 10 nm can be patterned in this manner. Achieving accurate overlay over the entire pattern requires that local distortion of
template and wafer match. By using an array of light microscopes
to monitor local overlay errors and feeding back to local heating
Journal of Heat Transfer
elements within the microchannel heat sink chuck, one can rapidly
correct these errors [135].
As mentioned before, the influences of surface roughness are
not described in a homogeneous way yet. Due to the fact that technical heat transfer systems (at least those not made from silicon)
always show a certain level of surface roughness, there is need for
a consistent description of the influences of surface roughness on
the heat transfer. More generally, a consistent model description
of the heat transfer in microscale is needed, which is still under
discussion. In many cases, effects like entrance lengths or developing flows as well as flow mal-distributions by parallelization of
microstructures with inadequate distribution systems at the
entrance and outlet manifolds (plenums) are not given sufficient
attention with when designing and manufacturing microscale heat
exchangers. This is of special importance when dealing with modular systems like those already mentioned for chemical process
engineering or energy-efficient processes. Moreover, there is no
standardized method for the characterization of microscale heat
exchangers yet. Together with a homogenized and accepted theoretical description (which could be implemented into numerical
models) this could improve the precision of experimental work
and the comparability between numerical simulation results and
experimental results worldwide. Most likely this would also
improve the business possibilities for manufacturers of microstructure heat exchanger devices, which can be fairly large sized
units employing microscale passages.
8
Conclusions and Outlook
Fundamental issues related to transport processes—singlephase gas flow, single-phase liquid flow, flow boiling and
condensation—have been extensively explored and a sound
understanding of these processes is available through the published literature. New opportunities are being presented with the
simultaneous exploration of nanoscale features and transport
processes. Advances in microfluidicis, MEMS technology and
nanomaterial fabrication and characterization are opening up new
possibilities in making the microchannel transport processes more
efficient and applicable to practical devices. As seen from the
surge in research in the last decade, fundamental research and
practical implementation are expected to synergistically lead the
advancement in this area. After presenting a brief overview of the
current status, research needs in these areas are listed for the respective microchannel application. Research needs and product
development opportunities for electronics cooling as well as heat
exchangers employing microscale passages are also highlighted.
Acknowledgment
The authors would like to thank U.S. federal agencies for the
encouragement and support they have provided through research
grants to a number of researchers working in the area of microscale transport processes. In particular, the support provided by
National Science Foundation in supporting conferences, specifically the ASME International Conference on Nanochannels,
Microchannels. and Minichannels, is gratefully acknowledged.
Special thanks to the NSF CBET Program Director Professor
Sumanta Acharya for his encouragement in writing this status
report. The progress has been truly made possible by the large
number of researchers worldwide through their creative endeavors. The support of the European Community under Grant No.
PITN-GA-2008-215504 is gratefully acknowledged by the authors
Stéphane Colin and Juergen Brandner.
Nomenclature
A¼
AR ¼
C¼
D, d ¼
surface, m2
aspect ratio, W/H
free variable
diameter, m
SEPTEMBER 2013, Vol. 135 / 091001-15
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Dh ¼
f¼
G¼
h¼
K¼
k¼
L¼
LUC ¼
n¼
P¼
Pr ¼
R¼
S¼
s¼
t¼
T¼
u¼
v¼
x¼
X¼
hydraulic diameter, m
friction factor
mass flux, kg m2 s1
heat transfer coefficient, W m2 K1
free variable
thermal conductivity, W m1 K1
length, m
length of unit cell, m
normal coordinate, m
pressure, Pa
reduced pressure
specific gas constant, J kg1 K1
scaling factor
length, m
streamwise tangential coordinate, m
temperature, K
streamwise velocity, m s1
velocity component normal to the wall, m s1
quality or length (in Sec. 7)
Martinelli parameter
Dimensionless Numbers
Bru ¼
Ca ¼
Ec ¼
Gr ¼
Kn ¼
Ma ¼
Nu ¼
Pe ¼
Pr ¼
Re ¼
modified Brinkman number
capillary number
Eckert number
Graetz number
Knudsen number
Mach number
Nusselt number
Peclet number
Prandtl number
Reynolds number
Greek Symbols
a¼
q¼
w¼
k¼
K¼
l¼
r¼
rP ¼
rT ¼
u¼
fT ¼
void fraction
density, kg m3
dimensionless surface tension term
mean free path, m
dimensionless length
dynamic viscosity, Pa s
surface tension, N m1
viscous slip coefficient, dimensionless
thermal slip coefficient, dimensionless
heat flux, W m2
temperature jump coefficient, dimensionless
Subscripts
D¼
I, j ¼
L¼
n¼
SAT ¼
t¼
V¼
w¼
z¼
1¼
dimensionless
index
liquid
normal
saturated
tangential
vapor
at the wall
in z-direction
fully developed conditions
Acronyms
C ¼ circular microtube
CHF ¼ critical heat flux
CWT ¼ constant wall temperature
PP ¼ parallel-plate microchannel
UHF ¼ uniform heat flux
1IW ¼ one insulated wall
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