SINGLE-PHASE CONVECTIVE HEAT TRANSFER
IN MICROCHANNELS
A State-of-the-Art Review
by
S. Kakaç, Y. Yener, W. Sun and T. Okutucu
14th INTERNATIONAL CONFERENCE
ON
THERMAL ENGINEERING AND THERMOGRAMMETRY
(THERMO)
June 22-24, 2005
Budapest, HUNGARY
14th THERMO
OUTLINE
 Introduction
 Experimental Investigations, Analytical
and Numerical Contributions
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INTRODUCTION
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In recent years various silicon-base systems having
dimensions of the order of microns have been
developed, such as
• Micro-heat sinks
• Micro-biochips
• Micro-reactors
• Micro-fuel cells
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Trend toward miniaturization
Significantly
the requirements
for higher level of performance
from cooling technology
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Existing heat flux levels > 100 W/cm2
Many ideas for effective cooling methods
have been proposed,
including a microchannel heat sink
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The microchannel heat sink
was first introduced by
Tuckerman and Pease*
A microchannel heat sink is a
structure with many
microscale channels machined
on the electrically inactive
face of the microchip.
*Tuckerman, D.B. and Pease, R. F., IEEE Electron Device Letter, 2 (1982), 126-129.
*Tuckerman, D.B. and Pease, R. F., J. Electrochem. Soc., 129, (1982), C98.
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Tuckerman and Pease*
demonstrated that
• Water-cooled
microchannels are
capable of dissipating
790 W/cm2.
• h for laminar flow > h
for tubulent flow in
macrochannels.
ww=wc=57m & z=365m
*Tuckerman, D.B. and Pease, R. F., J. Electrochem. Soc., 129 (1982), C98.
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Since the work of Tuckerman and Pease (1981, 1982),
there has been an unprecedented upsurge in research
to understand the fluid flow and heat transfer
characteristics in microchannels for better design of
various types of microsystems
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• Over the last two decades, experimental studies of
friction factors and Nusselt numbers in microchannels
have demonstrated that there is a great deal of
discrepancies between the experimental data and the
classical values, which are based on the continuum
hypotheses.
• Experimental data also appear to be inconsistent with
one another.
• Various reasons have been proposed to account for the
differences.
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• One reason may be attributed to various surface
conditions:
 Surface roughness
 Channel cross-section shape
 Surface hydrophilic property, etc.
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• Depending on the etching method and etching time, two
kinds of microchannels,
rectangular and trapezoidal
having different aspect ratios are usually fabricated in
silicon wafers.
• Also, various surface roughness can be obtained depending on
the concentration and temperature of etching solutions.
•The surface hydrophilic property can easily be changed by
decreasing or increasing the thickness of oxide layer on a
silicon surface.
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EXPERIMENTAL INVESTIGATIONS,
ANALYTICAL AND NUMERICAL
CONTRIBUTIONS
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Wu and Little* measured friction factors and Nusselt numbers
of gases flowing (both laminar and turbulent) in trapezoidal
silicon/glass microchannels of widths 130 to 200 m and depths
of 30 to 60 m.
*Wu, P.Y. and Little, W.A., Cryogenics, 1983, V. 23(5), 273-277.
*Wu, P.Y. and Little, W.A., Cryogenics, 1984, V. 24(8), 415-420.
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Wu and Little reported,
• a transition from
laminar to turbulent
flow at Re ~ 400-900
• the surface roughness
affected the values of
friction factors even
in the laminar flow
regime, and
• the frictional pressure
drop for laminar flow
was higher than the
classical prediction.
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Wu and Little* also reported that
Reduction
in
transition
Re number
Improved
heat transfer
*Wu, P.Y. and Little, W.A., Cryogenics, 1983, V. 23(5), 273-277.
*Wu, P.Y. and Little, W.A., Cryogenics, 1984, V. 24(8), 415-420.
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Qu et al.* performed an
experimental
investigation on pressure
drop and heat transfer of
water in trapezoidal
silicon microchannels
with a hydraulic
diameter ranging from
62 to 169 mm
*Qu, G.W., Mal, M. and Li, D.Q., Int. J. Heat Mass Transfer, 43 (2000), 353-3656.
Qu, G.W., Mal, M. and Li, D.Q., Int. J. Heat Mass Transfer, 43 (2000), 3925-3936.
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Qu et al.* found that
the experimentally
determined Nu
number was much
lower than that
predicted by their
numerical analysis.
*Qu, G.W., Mal, M. and Li, D.Q., Int. J. Heat Mass Transfer, 43 (2000), 353-3656.
Qu, G.W., Mal, M. and Li, D.Q., Int. J. Heat Mass Transfer, 43 (2000), 3925-3936.
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Qu et al* attributed
the measured higher
pressure drops and
lower Nu numbers to
the wall roughness,
and proposed a
roughness-viscosity
model to interpret
their experimental
data.
*Qu, G.W., Mal, M. and Li, D.Q., Int. J. Heat Mass Transfer, 43 (2000), 353-3656.
Qu, G.W., Mal, M. and Li, D.Q., Int. J. Heat Mass Transfer, 43 (2000), 3925-3936.
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According to the roughness-viscosity
model of Qu et al*, the increase in
wall roughness causes
the decrease in Nu number
Contradictory
to
common
sense
*Qu, G.W., Mal, M. and Li, D.Q., Int. J. Heat Mass Transfer, 43 (2000), 353-3656.
Qu, G.W., Mal, M. and Li, D.Q., Int. J. Heat Mass Transfer, 43 (2000), 3925-3936.
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In addition to surface roughness effects, the
cross-sectional shape
of the channel can have great influence on the
fluid flow and heat transfer
inside the non-circular microchannels
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Peng and Peterson* investigated PD and HT of water in
rectangular microchannels of Dh = 0.133 - 0.367 and different
geometric configurations.
*Peng, X.F. and Peterson, G.P., Int. J. Heat Mass Transfer, 39 (1996), 2599-2608.
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The measurements of Peng and Peterson* indicated that
 the geometric configuration of the microchannel
plate and individual microchannels had a great
effect on the flow friction and the single-phase
convective heat transfer, and
 that the effect on the laminar and turbulent
convection was quite different.
 They also concluded that the shape of the channel
plays a negligible role for both laminar and
turbulent flow conditions.
*Peng, X.F. and Peterson, G.P., Int. J. Heat Mass Transfer, 39 (1996), 2599-2608.
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Peng and Peterson*
found that the
laminar heat
transfer does depend
on the aspect ratio
and the ratio of the
hydraulic diameter to
the center-to-center
distance of the
microchannels.
*Peng, X.F. and Peterson, G.P., Int. J. Heat Mass Transfer, 39 (1996), 2599-2608.
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*Peng, X.F. and Peterson, G.P., Int. J. Heat Mass Transfer, 39 (1996), 2599-2608.
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Peng and Peterson*
found that the
turbulent heat
transfer was further
a function of a new
dimensionless
variable, Z, such that
Z=0.5 is the optimum
configuration for
turbulent heat
transfer regardless
of the aspect ratio.
*Peng, X.F. and Peterson, G.P., Int. J. Heat Mass Transfer, 39 (1996), 2599-2608.
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*Peng, X.F. and Peterson, G.P., Int. J. Heat Mass Transfer, 39 (1996), 2599-2608.
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More recently, Wu and Cheng*
carried out an experimental
investigation on the laminar
convective heat transfer and
pressure drop of water in
trapezoidal silicon microchannels
having different
• surface roughness, and
• different geometric parameters,
• surface hydrophilic properties.
Cross-section of microchannels
*Wu, H.Y. and Cheng, P., Int. J. Heat Mass Transfer, 46 (2003) 2547-2556
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Wu and Cheng* found that
the values of the laminar
Nu number and apparent
friction constant depend
greatly on different
geometric parameters:
• Bottom-to-top width
ratio, Wb/Wt
• Height-to-top width
ratio, H/Wt
• Length-to-diameter
ratio, L/Dh
Cross-section of microchannels
*Wu, H.Y. and Cheng, P., Int. J. Heat Mass Transfer, 46 (2003) 2547-2556
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*Wu, H.Y. and Cheng, P., Int. J. Heat Mass Transfer, 46 (2003) 2547-2556
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The Nu number and
the apparent friction
constant in trapezoidal
microchannels having
strong hydrophilic
surfaces (thermal oxide
surfaces) are larger
than those having
weak hydrophilic
surfaces (silicon
surfaces).
*Wu, H.Y. and Cheng, P., Int. J. Heat Mass Transfer, 46 (2003) 2547-2556
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Trapezoidal
Wu and Cheng found
that the Nu number
and
the apparent friction
constant
both increase
with the increase
in surface roughness.
Triangular
*Wu, H.Y. and Cheng, P., Int. J. Heat Mass Transfer, 46 (2003) 2547-2556
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Surf.
Geo.
Hydphlc.
Pars. Effect
Effect
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Surf. Rough. Effect
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Although significant amount of experimental data
is now available in the literature, momentum and
heat transport phenomena in gas and liquid flows
in the basic components of microdevices are still
not well understood.
The main difficulty in predicting the momentum and
heat transport in micro-scales lies in formulating the
appropriate governing equations.
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There are basically two distinct ways of modeling a flow field.
Fluid is continuous and
indefinitely divisible - Velocity,
Fluid is collection of
temperature, pressure, density,
molecules – Deterministic
etc. are all defined at every point
or probabilistic modeling Fluid Modeling
in space and time
Molecular Models
Continuum Models
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In considering the process of momentum exchange
and heat transfer between a gas and a solid surface in
microdomains (of characteristic length varying from
100 to 0.1 m), both macroscopic or continuum model,
as well as the molecular or microscopic model should
be considered.
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The distinction among the various regimes and
corresponding describing models can be obtained
by the so-called the Knudsen number.
Kn 

L
 Mean free molecular path
L = A characteristic flow dimension
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The limit Kn << 1 corresponds to the continuum limit.
 In the continuum limit, values of parameters at different
points in the domain essentially represent averages of the
microscopic behavior in the neighborhood of the point.
 This assumption eventually leads to the formulation of the
Navier-Stokes and energy equations, which express the
conservation of mass, momentum, and energy.
 However, these equations break down for finite values of
the Kn number.
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Beskok and Karniadakis* proposed four flow regimes for gases.
Kn 
Continuum flow
Slip-flow
regime
(slightly
rarefied)
Transition
regime
(moderately
rarefied)
Free-molecular
flow
*Beskok, A. and Karniadakis, G.E., J. Thermo. & Heat Transfer, 8 (1994), 647-655.
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For Kn > 10, the fluid is considered a free-molecular flow.
• In this regime, the only closed equation that is strictly
applicable is the Boltzmann equation that involves the
molecular velocities as the dependent parameters,
instead of the macroscopic quantities.
When 10-3 <Kn < 10, the gas is considered a rarefied.
• A rarefied gas can neither be considered an absolutely
continuous medium nor a free-molecular flow.
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The range 10-3 <Kn < 10 is further classified as,
• Slip flow, 10-3 <Kn < 0.1
• Transition flow, 0.1 <Kn < 10
The local value of Kn number determines the degree
of rarefaction and the degree of validity of the
Continuum model
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In the slip flow regime, the gas adjacent to the surface no
longer reaches the velocity and temperature of the surface.
• The gas at the surface has a tangential velocity and it
slips along the surface.
• The temperature of the gas at the surface is finitely
different from the temperature of the surface, and there
is a jump in temperature between the surface and the
adjacent gas.
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Experimental evidence indicates that in the slip-flow
regime, velocity and temperature distributions in the
flow field can be determined from the Navier-Stokes
and the energy equations if velocity-slip and
temperature-jump at the wall are taken into account
via the slip boundary conditions.
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In the analytical and numerical studies reported in the
literature, four important effects in microflows were
considered. These are:
• Compressibility effects,
• Rarefaction effects,
• Viscous heating effects, and
• Thermal creep effects.
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• The thermal creep phenomenon is a rarefaction effect.
For a rarefied gas flow it is possible to start the flow with
tangential temperature gradients along the channel
surface. In such a case, the gas molecules start creeping
from cold to hot direction.
• The viscous heating effects are due to the work done by
viscous stresses, and they are important for microflows,
especially in creating temperature gradients within the
domain.
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Tunc and Bayazitoglu* studied convection for steady-state and
hydrodynamically-developed laminar flow in microtubes with
Barron et al. [4]
uniform temperature and uniform heat flux boundary conditions.
Velocity slip and
temperature jump
conditions at the
tube wall and
Ameel et al. [1]
qw= Cont.
viscous heating
within the flow
Tw= Cont.
were included in
their study.
The effect of temperature jump.
*Tunc, G. and Bayazitoglu, Y., Int. J. Heat Mass Transfer, 44 (2001), 2395-2403.
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The Brinkman number is defined by
u m2
Br 
kT
,
where ΔT is the wall-fluid temperature difference.
Br measures the importance of viscous heating
relative to heat conduction
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Variation of
NU number
with
Kn number,
Tw=Const.*
*Tunc, G. and Bayazitoglu, Y., Heat transfer in microtubes with viscous dissipation,
Int. J. Heat Mass Transfer, 2001, 44, 2395-2403.
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Tw = Const.
The effect of viscous heating*
*Tunc, G. and Bayazitoglu, Y., Heat transfer in microtubes with viscous dissipation,
Int. J. Heat Mass Transfer, 2001, 44, 2395-2403.
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END
June 22-24, 2005, Budapest, Hungary