TRANSPORT IN MICROCHANNELS – A CRITICAL REVIEW

CHAPTER

ONE

TRANSPORT IN MICROCHANNELS –A CRITICAL REVIEW

S. V. Garimella and C. B. Sobhan

ABSTRACT

The tremendous enhancement in heat transport obtained by employing microchannelshas provided an effective alternative to conventional methods of heat dissipation, espe-cially in applications related to cooling of microelectronics. A number of theoreticaland experimental studies have been reported on the fluid flow and heat transfer mecha-nisms in mini and microchannels as well as microtubes. Anomalies and deviations fromthe behavior expected for conventional channels, both in terms of the frictional and heattransfer characteristics have been noticed in microchannels under specific flow conditionsand flow regimes. The present work compiles and analyzes the results of the importantinvestigations on fluid flow and heat transfer in microchannels and microtubes.

1-56700-190-4/2003/$00+ $0.50c© 2003 by Begell House, Inc. 1

2 ANNUAL REVIEW OF HEAT TRANSFER, VOL. 13

NOMENCLATURE

A Channel aspect ratio (Hc/2Wc)Ac Cross-sectional areaAs Surface areaB Width of the slot nozzle for liquid impingement, mC, Cp Coolant specific heat, J/kg Kca Acoustic velocityc0 Concentration, molD Inside diameter, mDe, Dh Hydraulic diameter, mCFOM Coolant Figure of MeritF C Re[1− (d/d0)2] in Eq. (8), with empirical constantC = 7.6 · 10−5 and

d0 = 1.164 mmf Friction factorG Mass velocity, kg/m2sec (≡ m, mass flux)H, Hc Microchannel height, mhf g Latent heat of vaporization, J/kgjH Colburn J-factor [hcPr2/3/VρCp]kc Coolant thermal conductivity, w/m KL Heated length of heat sink channel, m; also channel length in Eq. (15)Nu Nusselt numberNux Local Nusselt numberNuGn Nusselt number from Gnielinski correlationPr Prandtl numberP Channel pitchPT Pumping power, W∆Pexp Experimental pressure drop, N/m2

∆Ppred Predicted pressure drop, N/m2

qm,p critical heat flux based on heated channel inside area, W/m2

Q Volumetric flow rateR Thermal resistance of a cross section, K/WRe Reynolds numberRecri Transition Reynolds numberRth 1D Thermal resistance from one-dimensional analysis, K/WRth 3D Thermal resistance from three-dimensional analysis, K/WR∗ Overall allowable thermal resistance between the entrance and the exit,

K/Wr Non-dimensional thermal resistance of a cross section (WTkf LR/Hc)s Heat spread effectTi Inlet temperaturet Tube wall thicknessv Inlet velocityV Fluid velocity, m/sec

TRANSPORT IN MICROCHANNELS – A CRITICAL REVIEW 3

W Microchannel width, mWc Center to center distance of microchannel, mWe Weber number, [G2L(σρ f )]WT Chip width, mw Half distance between adjacent channels, non-dimensionalized with chan-

nel heightwc Half channel width, non-dimensionalized with channel heightX Mole fractionx Lateral distance from stagnation point, mxL Equilibrium quality at the end of the channel heated lengthZ min(H,W)/max(H,W) in Eq. (7)µ Dynamic viscosity, kg/m secν Kinematic viscosityΦ Enhancement ratioρ Density, kg/m3

ρ f Density of liquid, kg/m3

σ Surface tension, N/mθ Angular coordinate, deg.ξc Zeta potential, V

1 INTRODUCTION

The continued increase in the functionality and compactness of microelectronics hascalled for novel methods for effective removal of the high heat fluxes associated withthese devices. The small sizes of the heat-dissipating devices and the very stringentoperational temperature requirements make thermal management of microelectronicdevices a challenging problem. Various cooling techniques such as impinging jetsand heat pipes have been applied to achieve effective heat removal, at the device andsystem levels. The use of microchannel heat sinks is a promising alternative whichcan provide much higher heat removal rates and may also be integrated directly intothe heat-dissipating substrates. The two important objectives in electronics cooling,namely the reduction of the device maximum temperature and the minimization oftemperature gradients on the device surface, can be efficiently achieved by the use ofmicrochannel heat sinks.

It has been observed that microchannel heat sinks can dissipate heat loads as highas 1000 W/cm2 with maximum surface temperatures of less than 120◦ [1]. Thepossibility of achieving this level of heat dissipation has lead resulted in a number ofstudies on the application of microchannel flow to the cooling of high power densitysystems. Some of the investigations focussed on understanding the fundamentalsof microchannel flow, and on comparing and contrasting the flow and heat transfercharacteristics in microchannels with those in conventional channels. Theoreticalanalyses leading to optimization of microchannel heat sinks were carried out; so alsowere experimental investigations to obtain new correlations and to extend the range


of application of large-channel correlations to include microchannels. Single-phaseliquid and air flow, boiling, and multiphase flow in microchannels have all beeninvestigated. Other studies have addressed fluid flow and heat transfer

in very small tubes and mini channels.Theoretical and experimental investigations reported over the past decade in fluid

flow and heat transfer in microchannels are reviewed in this work. Application ofmicrochannel cooling to electronic devices and other heat exchange systems is ex-amined. Important correlations that were proposed from original research and ob-tained by modifying existing large-channel correlations are summarized. Studies inthe literature on design, testing and optimization of microchannel heat sinks are alsodiscussed.

2 MICROCHANNEL CONCEPTS AND EARLY WORK

Fluid flow through microchannels was first proposed and demonstrated as an effec-tive means of dissipating heat from silicon integrated circuits by Tuckerman andPease [2]. This novel idea led to a number of innovative designs and spawned ex-tensive research efforts in the area of microchannel cooling. The first demonstrationinvolved the design and testing of a very compact water-cooled integral heat sinkfabricated into silicon. Microscopic channels 50µm wide and 300µm deep wereetched on silicon, and deionized water was pumped through as the coolant. A powerdensity of 790 W/cm2 was achieved with a corresponding substrate temperature riseof 71◦ above the inlet water temperature. Thermal resistance values obtained in theseexperiments are shown in Figure 1 as a function of the water flow rate; the straight-line behavior of the data was thought to indicate fully developed temperature profiles

Water flow rate, cm3/s

234102030

Max

imum

ther

mal

resi

stan

ce,

o C/W

0

0.1

0.2

Figure 1 Variation of the maximum thermal resistance with the inverse of the flow rate for a microchan-neled heat sink in a silicon wafer [2]. The linear variation implies fully developed temperature profiles.


in the microchannels.In a sequel to this work, Tuckerman and Pease [3] discussed the problems as-

sociated with coolant selection, packaging and headering, microstructure selection,fabrication and bonding, and described some successful strategies for forced convec-tion cooling using microchannels. To optimize the heat transfer coefficient at a givencoolant pressure or at a constant pumping power, the following coolant figures ofmerit were proposed:

CFOM =

(kcρC/µ)0.25 for a given coolant pressure

(kcρ2C2/µ)0.25 for a constant pumping power

(1)

The results of fabricating the microchannels in silicon by etching and precisionsawing were compared by an examination of electron micrographs. Micropillars,fabricated by precision sawing in orthogonal directions, were recommended as analternative to microchannels for reducing the problems of debris accumulation andfor obtaining lower pressure drops.

Wu and Little [4, 5] reported measurements of friction factors and heat trans-fer in the flow of nitrogen gas through very fine channels used in miniature Joule –Thomson refrigerators. Channels formed by etching in silicon and glass substrateswere used, and the experiments were conducted in the laminar and turbulent regimes.Channel widths used were in the range 130 to 300µm, with depths of 30 to 60µm.The friction factor variation with Reynolds number for these channels was found todeviate from the conventional Moody’s chart for conventional channels, and the de-viation was attributed to the relative roughness being larger in the small channels.It was found that the friction factors for the glass channels were as much as 3 to 5times larger than those predicted for smooth pipes, for both laminar and turbulentflows; the transition from laminar to turbulent flow was found to occur at a Reynoldsnumber of approximately 400. Friction factor correlations were proposed for glasschannels as follows [4]:

f =

(110± 8)/Re (Re≤ 900),

0.165(3.48− log Re)0.24 + (0.081± 0.007) (900< Re< 3000),

(0.195± 0.017)/Re0.11 (3000< Re< 15000).

(2)

Nusselt numbers and thermal resistances were obtained from the heat transfer exper-iments, and the following correlation for the Nusselt number in the turbulent regimewas proposed [5]:

Nu = 0.00222 Pr0.4 Re1.09. (3)

A theoretical model for fully developed and developing flows in a microchannel heatsink was presented by Phillips et al. [1]. This thermal-resistance model was used tocalculate the thermal and fluid flow performance of heat sinks with moderate aspect-ratio channels in the laminar and turbulent regimes. Calculations were performedfor a water-cooled silicon microchannel heat sink with an aspect ratio (defined inthis paper unless otherwise specified as the ratio of the microchannel depth to width)


Dimensionless entrance length x*=(L De)/(Re Pr)

0 0.01 0.02 0.03 0.04

Tot

alth

erm

alre

sist

ance

,o C

/(W

/cm

2 )

0

0.05

0.10

0.15

0.20

Surface

temperature

rise,oC

0

5

10

15

20

Curve Data Flow

2.450 (cm3s)/cm2

4.457 (cm3s)/cm2

6.260 (cm3s)/cm2

EXPERIMENTAL DATA POINTSOBTAINED FROM TUCKERMAN (1984)

Figure 2 Comparison of theoretical results with experimental data for laminar flow cooling of a siliconchip with water-cooled microchannels [1].

of 4, and the results were found to show very good agreement with experimentaldata [6] for various flow rates in the laminar regime, as shown in Figure 2. Thenumerical results indicated that turbulent flow designs could have equivalent or betterperformance than comparable laminar flow designs.

Mahalingam and Andrews [7] investigated a high-performance air cooling tech-nique for electronic devices and packages that involved high-velocity air flowthrough micro-structured compact heat sinks of large surface area. The heat transfercalculations performed for the air-cooled narrow channels were described in detail.The channels considered were 0.13 to 0.25 mm wide with an aspect ratio of 10, re-sulting in heat transfer surface areas of 47 to 63 cm2 per m3 of heat sink volume.Experiments and predictions showed that these heat sinks were an attractive alterna-tive to conventional forced air circulation heat sinks in terms of improved electricalperformance.

Pfahler et al. [8] experimentally studied the flow of N-propanol through micro-channels of different cross-sectional areas in an effort to identify the channel sizeat which conventional predictions of the friction coefficient no longer hold. It wasfound that for the smaller channel, which was 0.8 µm deep and 100µm wide, theconventional predictions (i. e.,f Re= const) deviated from the experimental resultssignificantly, with friction factor-Reynolds number products being as large as threetimes the predictions. The trend of variation in thef Re product with Reynoldsnumber was also quite different for this channel, as shown in Figure 3. For a deeperchannel (depth of 1.7µm) of the same width, the agreement was better; unfortunatelyno results were presented for the deepest channel (depth of 135µm) considered.Although it was suggested based on these results that a critical channel size existsbelow which the theory for conventional channels fails, the data presented were toosparse (only two channel depths and comparisons of friction factor only for laminar


Re

0 0.001 0.002 0.003 0.004 0.005 0.006

C=

f*

Re

0

100

200

300

400

500

depth=0.8 micronsdepth=1.7 micronstheory

Figure 3 The product of friction factor and Reynolds number shown as a function of Reynolds number,for 100µm wide channels of two different depths [8].

flow) to support a conclusive hypothesis.Choi et al. [9] measured the inner wall surface roughness, friction factors and con-

vective heat transfer coefficients for flow of nitrogen gas in microtubes with insidediameters ranging from 3 to 81µm. The experimentally determined values of frictionfactor and heat transfer coefficient deviated significantly from those predicted fromcorrelations for conventional-sized tubes. In the laminar regime, the friction factorfollowed f = 53/Re instead of the expected 64/Re dependence. In the turbulentregime, the measured friction factors were lower by 10 to 30% when compared topredictions from conventional correlations. The following correlations for the fric-tion factor were proposed (and may be compared to expressions for conventionaltubes off = 64/Re andf = 0.316 Re−0.25 respectively):

f =

64Re

[1 + 30

(ν

D Ca

)]−1

for laminar flow,

0.140 Re−0.182 for turbulent flow.

(4)

The heat transfer measurements from this study did not agree with the Colburnanalogy for turbulent flow in conventional-size channels. The measured values for(8 jH/ f ) were as high as 7, whereas the Colburn analogy dictates a value of 1 for thisparameter. The Petukhov analogy for turbulent heat transfer, given by (8jH/ f ) =

Pr2/3/[1.07 + 12.7( f /8)1/2(Pr1/2 − 1)], also did not satisfy the experimental data,which were instead correlated as:

Nu =

0.000972 Re1.17 Pr1/3 laminar flow (Re< 2000),

3.82 · 10−6 Re1.96 Pr1/3 turbulent flow (2500< Re< 20000).(5)

The experimental data in the turbulent regime fell above the predictions from the


Dittus – Boelter correlation for conventional tubes.Flow and heat transfer measurements in microchannels etched into silicon in a

series or parallel pattern were obtained by Rahman and Gui [10]. Six heat sinks eachwith microchannels of different aspect ratios were studied with water as the coolant.Measurements were obtained in the inlet and exit regions and included the substrateand coolant temperatures, pressure drop, input power and flow rate. Local and aver-age Nusselt numbers and friction factors were plotted against Reynolds number. Thelocal Nusselt number values were found to be higher than the corresponding valuespredicted from analytical solutions for developing laminar flow. It was concludedthat microchannels provided significant performance and operational advantages interms of higher heat fluxes compared to other cooling methods such as jet impinge-ment and forced convection.

Fabrication processes for microchannel structures were described byHoopman [11]. Various types of microchannel structures and their relative meritsand demerits were discussed, in addition to applications such as electronics cooling,compact heat exchangers, heat shields and fluid distribution systems. A review ofthe literature related to optimum design of microchannel heat sinks was presented byGoodling and Knight [12].

Investigations reported in the past decade on the fundamentals and applications offluid flow and heat transfer through microchannels are discussed in the sections thatfollow.

3 SINGLE-PHASE FLOW

Single-phase flow and heat transfer in microchannels has been studied extensivelythrough experimental and theoretical investigations. Most of this work has been di-rected at quantifying the effects of flow parameters and channel dimensions on theoverall frictional and heat transfer characteristics. In some cases, numerical mod-eling has been used to arrive at configurations and flow parameters which provideoptimum heat transfer rates.

3.1 Experimental Investigations

Water, methanol and Refrigerant-124 have been used as coolants, both as pure fluidsand in the form of binary mixtures. While flow regimes and transition were ad-dressed in some of the studies, others involved a study of the departure of the flowand heat transfer characteristics in microchannels from conventional channel flows.Predictive correlations for heat transfer and friction factors in microchannels havebeen proposed based on these experiments.

Peng et al. [13, 14] experimentally investigated the forced convection of waterthrough single rectangular microchannels with a range of hydraulic diameters (0.133to 0.367 mm) and aspect ratios (0.33 to 1). The microchannels were fabricated in astainless steel substrate. Measurements of the liquid flow rates, liquid temperatures,


inlet and outlet pressures, wall surface temperatures and heat input to the substratewere obtained under steady-state conditions. Results were plotted as friction factor-Reynolds number graphs, and were found to deviate from the values predicted byclassical correlations. The friction factor was found to be proportional to Re−1.98 un-der laminar conditions and Re−1.72 for turbulent flow, compared to Re−1 and Re−0.25

(Blasius) for conventional channels. The flow was found to be most strongly affectedby the hydraulic diameter and the aspect ratio of the channel. The flow was foundto undergo transition in the Reynolds number range of 200 to 700, with the criticalReynolds number increasing with increasing channel hydraulic diameter as shownin Figure 4. The occurrence of transition was identified from a plot of the frictionfactor versus Reynolds number. The corresponding heat transfer characteristics [14]showed that the Nusselt number was proportional to Re0.62 in the laminar regime,and Re0.8 in the turbulent regime. These results were further analyzed by Peng andPeterson [15], who proposed the following empirical correlations for heat transfer:

Nu = 0.1165

(Dh

Wc

)0.81 ( HW

)−0.79

Re0.62 Pr1/3 for laminar flow, (6)

Nu = 0.072

(Dh

Wc

)1.15

(1− 2.421(Z − 0.5)2)Re0.8 Pr1/3 for fully developedturbulent flow.

(7)

Experiments with water and methanol in microchannels of rectangular cross sectionfabricated into a stainless steel substrate were reported by Wang and Peng [16]. Thechannels were fabricated into test plates of 18 mm width and 125 mm length. Allthe channels had a depth of 0.7 mm, while the channel widths were varied through0.2, 0.4, 0.6 and 0.8 mm; the channel pitch was also varied from 0.24 to 4 mm.

Dh, mm

0.12 0.16 0.2 0.24 0.28 0.32 0.36

Re c

r

200

300

400

500

600

700

Figure 4 Variation of the critical Reynolds number with the hydraulic diameter in a rectangular chan-nel [13]. The critical Reynolds number is found to increase with the hydraulic diameter.


Heat transfer coefficients and Nusselt numbers were plotted against the measuredwall temperatures and Reynolds numbers respectively, for various flow velocities.As would be expected, the heat transfer was greater at lower liquid temperaturesand higher liquid velocities. It was inferred from the Nu-Re variations that fullydeveloped turbulent convection conditions were established in the microchannels atReynolds numbers of 1000 to 1500; transition to turbulence was found to be stronglyinfluenced by liquid temperature, velocity and microchannel size. The turbulent heattransfer coefficients obtained from the experiments (computed from the applied heatflux divided by the difference between the local surface temperature and the inletfluid temperature) were found to be well represented by modifying the constant inthe Dittus – Boelter correlation from 0.023 to 0.00805. Typical results from this workare shown in Figure 5 with methanol as the coolant.

The effects of thermofluid properties and geometrical parameters on convectiveheat transfer in microchannels were further discussed by Peng and Peterson [17].Compared to conventional-size channels, transition was found to be initiated at muchlower Reynolds numbers in the microchannels, with the transition range as well asthe heat transfer characteristics in laminar and turbulent flow, being influenced notonly by the Reynolds number but also by the liquid temperature, velocity and mi-crochannel size.

Peng and Wang [18] studied both single-phase convection and boiling character-istics of subcooled water in rectangular microchannels of cross section 0.6×0.7 mm,machined into stainless steel. In single phase convection, a steep increase of the wallheat flux was observed when plotted against the wall temperature, beyond whichthe heat flux for the microchannel was higher than for a conventional (9 mm diam-eter) tube. The results also indicated that the laminar or transition convection heat

Re

100 200 1000 2000

Nu

0.5

1

2

3

45

10

test section No.3test section No.4test section No.5test section No.6

METHANOL

Eq.(10)

Figure 5 Variation of the average Nusselt number with Reynolds number, for single phase forced con-vection flow of methanol in a rectangular microchannel [16]. The reduction in Nusselt number with anincrease in the Reynolds number may be noticed in the low Reynolds number regime.


transfer rates in microchannels could reach or exceed those in the turbulent regimein conventional tubes. The nucleate boiling heat flux was found to be intensified inmicrochannels, and the wall superheat required for flow boiling was much smallercompared to conventional channels for an identical wall heat flux. Moreover, thetransition between single phase convection and nucleate boiling was observed to becharacterized by an absence of partial nucleate boiling.

Single phase forced convection with binary mixtures of water and methanol inmicrochannels (hydraulic diameter of 0.133 to 0.367 mm) was investigated experi-mentally by Peng and Peterson [19]. The laminar regime extended up to Reynoldsnumbers of 70 to 400 depending on the flow conditions, and fully developed turbu-lent heat transfer was achieved in the Reynolds number range of 200 to 700. Thetransition Reynolds number decreased as the microchannel hydraulic diameter wasreduced. The channel hydraulic diameter and aspect ratio were discussed as distinctsignificant variables. The results indicated that the influence of the aspect ratio onheat transfer was further affected by the concentration of the mixture, and varied as afunction of the mole fraction of the mixture. As shown in Figure 6, the heat transfercoefficient was greater for the smaller mole fractions of the more volatile component,reaching a maximum at a characteristic mole fraction; the heat transfer enhancementalso occurred over a larger mole fraction range as the mass flow rate was increased.

Harms et al. [20] studied the heat transfer and pressure drop characteristics of“deep” rectangular microchannels, which had a width of 251µm and a depth of1030µm, at deionized water flow rates of 5.47 to 118 cm3/s. A critical Reynoldsnumber of 1500 was identified for the onset of turbulence. This lower value, relativeto conventional channels, was attributed to the inlet manifold conditions and chan-nel roughness. The experimental results were found to be in good agreement with

x

0 0.2 0.4 0.6 0.8 1

Hea

ttra

nsfe

rco

effi

cien

t,W

/(m

2 K)

1000

2000

3000

4000

5000

6000mass flux 190 kg/(m2s)mass flux 782 kg/(m2s)

Figure 6 The effect of the concentration of the more volatile component, and the mass flux of a binarymixture of water and methanol, on the heat transfer coefficient, in single phase forced convection flowthrough a rectangular microchannel [19].


those from a one-dimensional thermal resistance model, indicating that classical heattransfer analyses were applicable to the geometry investigated. The volumetric flowrate, pressure drop and pumping power were found to be inversely related to the ther-mal resistance; for a given pressure drop and pumping power, the thermal resistancewas found to be smaller for deeper channels.

Based on a dimensional analysis of the variables influencing laminar forced con-vection, Tso and Mahulikar [21] proposed that the Brinkman number be used as theparameter for correlating convective heat transfer in microchannels. Previous re-searchers had observed that the Nusselt number could decrease with an increase inReynolds number in the laminar regime, and remain unaffected by Reynolds num-ber in the transition regime [15–17]; Tso and Mahulikar offered possible reasons forsuch behavior and proposed a dimensionless geometric parameter for the analysis ofmicrochannels. It was proposed that the increase or decrease in the Nusselt numberas the Reynolds number increases in the laminar regime depends on whether the in-crease in Reynolds number is brought about by an increase in velocity or a reductionin fluid viscosity due to heating. An increase in Reynolds number caused by an in-crease in velocity would increase the Nusselt number; however, when this increasein Reynolds number is due to a reduction in viscosity, it is claimed that the Nusseltnumber would decrease. This work for laminar flow was extended by Tso and Mahu-likar [22] to cover flow transition in microchannels. Experimental results were alsopresented in [23] and found to correlate well in terms of the Brinkman number forlaminar flow.

Adams et al. [24] investigated turbulent forced convection of distilled water in mi-crochannels of 0.76 and 1.09 mm diameter fabricated in a copper substrate by elec-trode discharge machining. The Nusselt numbers obtained were found to be higherthan those predicted by traditional large-channel correlations. The experimental datawere compared with predictions from correlations for small-diameter channels [25];the divergence in the comparison increased with an increase in Reynolds number,with the experimental data being higher than the predictions. Figure 7 shows aplot of an enhancement ratio (experimental to predicted values) as a function of theReynolds number for three channel diameters. The enhancement factor was seen toincrease as the channel diameter decreased, and as the Reynolds number increased.A correlation for the Nusselt number in turbulent forced convection was proposed forcircular microchannels of diameters 0.102 to 1.09 mm (data for smaller tubes fromthe literature were included in their database to extend the diameter range), Reynoldsnumbers from 2600 to 23000 and Prandtl numbers of 1.53 to 6.43. The correlationproposed, which gathered the data to within±18.6%, was

Nu = NuGn(1 + F), (8)

in which NuGn is calculated from the correlation proposed by Gnielinski [25],

NuGn =( f /8) (Re− 1000) Pr

1 + 12.7( f /8)1/2(Pr2/3 − 1).


Re

0 5000 10000 15000 20000 25000

Enh

acem

ent

rati

o

0.5

1.0

1.5

2.0

2.5

3.0

D=0.102 mmD=0.760 mmD=0.190 mm

Figure 7 Variation of the “enhancement ratio” for the experimental Nusselt number over the Gnielinskicorrelation with Reynolds number [24].

The friction factor correlation to be used with this expression [26] is given by

f =[1.82 log(Re) − 1.64

]−2 . (9)

Adams et al. [27] extended the experiments to a non-circular microchannel of hy-draulic diameter 1.13 mm. The experimental Nusselt numbers for this case werefound to be well predicted by the Gnielinski correlation; based on this comparison, ahydraulic diameter of approximately 1.2 mm was suggested as a lower limit for theapplicability of standard turbulent convection correlations.

A somewhat unusual experimental configuration in the literature on microchan-nels was considered by Zhuang et al. [28], who obtained the heat transfer charac-teristics under the impingement of transformer oil and FC-72 on two-dimensionalmicrochannels. Local heat transfer coefficients were obtained in stagnation and par-allel flows for a range of Reynolds number from 70 to 170 for oil and 911 to 4807for FC-72. The influence of the liquid velocity, channel size and the Prandtl numberon the heat transfer behavior were studied. An empirical correlation was developedby analyzing the data for the two liquids used:

Nux = 0.429 Re0.583 Pr1/3( x2H

)0.349 ( B2H

)−0.494

. (10)

Yu et al. [29] reported experimental investigations on an air-cooled microchannelheat sink. The microchannels considered were of large aspect ratio (62.5) with theexpectation that the pressure drop would be lower. The experimentally determinedtotal thermal resistance was found to be in good agreement with that determinedfrom a thermal resistance model, with the assumption of a Nusselt number of 6.5in the model. The pressure drop was found to have a large discrepancy, up to 18%,


from the predicted values, especially at high air flow rates; this was attributed to theentrance and exit losses in the heat sink which were ignored in the pressure dropcalculations. The cooling capacity of the heat sink was approximately 1700 W witha heat flux of approximately 15 W/cm2. With a volumetric flow rate of 140 m3/hr,the pressure drop encountered was found to be as low as 400 Pa.

In summary, experimental investigations on single-phase flow in microchannelshave focussed mainly on three aspects. The effect of the channel dimensions andgeometry on flow and heat transfer was one of the primary concerns. An understand-ing of flow transitions has been sought and critical Reynolds numbers have beenproposed for transition in microchannel flows. A third area of research has led tocorrelations being proposed based on experimental measurements for various flowregimes, in terms of fluid properties and microchannel geometry.

3.2 Models and Optimization Studies

A number of numerical and analytical solutions have been reported for single-phaseconvective flow and heat transfer in microchannels. Optimization of the dimensionsand geometry of microchannels has also been attempted based on theoretical models.

A theoretical model for heat transfer and fluid flow in the microchannels formedbetween two parallel plates, incorporating the effects of the electric double layer(EDL) at the interface between the solid surface and liquid was presented by Malaet al. [30]. The effects of the EDL field and the channel size on the flow and heattransfer were studied. The EDL field was obtained by a linear approximate solutionof the Poisson – Boltzmann equation. In order to accommodate for the retardation ofthe fluid due to the EDL field, an apparent viscosity was introduced to modify thegoverning energy equation, and numerical solutions were obtained. Comparisonswere also presented, with very good agreement, of the predicted volume flow ratesfrom the mathematical model considering EDL effects with results from experimen-tal investigations on the flow of aqueous solutions of potassium chloride throughmicrochannels [31].

In further work by Yang et al. [32], the EDL field in rectangular microchan-nels was determined by solving the non-linear two-dimensional Poisson – Boltzmannequation. The effects of the flow-induced electrokinetic field were also consideredin the equation of motion. The flow and heat transfer characteristics in steady, fullydeveloped laminar flow with and without the electrokinetic effects included werecompared. For aqueous solutions of low ionic concentration and a solid surface ofhigh electrical potential, the liquid flow and heat transfer in the microchannels weresignificantly influenced by the presence of the electric field and the induced elec-trokinetic flow, as shown in Figures 8 and 9.

A forced convection cooling scheme with microchannels formed between platefins was investigated by Kleiner et al. [33]. A thermal resistance model was devel-oped incorporating the pressure drop and pumping power, using which optimizationstudies were performed. Experiments were conducted on heat sinks fabricated from


Non-dimensional pressure difference

0 500 1000 1500 2000Non

-dim

ensi

onal

volu

met

ric

flow

rate

0

1

2

3

4

51 no EDL effects2 c=150 mV, c0=10-6 M3 c=200 mV, c0=10-8 M

12

3

Figure 8 Variation of the non-dimensional flow rate with the non-dimensional pressure difference fordifferent concentrations and zeta (electrical) potentials, calculated from a computational model for mi-crochannel flow considering the electric double layer effect [32].

Non-dimensional channel length

10-2 10-1 100

Loc

alN

usse

ltnu

mbe

r

2

3

4

5

1 no EDL effects

2 with EDL effects

c=200 mV, c0=10-8 M

1

2

Figure 9 Comparison of the local Nusselt number variation along the channel length, from computationalsolutions with and without electric double layer effect incorporated in the formulation [32].

copper and aluminum foils, with channel widths of 200 and 500µm. Thermal resis-tance values (defined based on the maximum temperature rise of the heat exchangersurface above the coolant inlet temperature) as low as 0.2 K/W were measured, andfound to agree with model predictions to within 15 to 27%. The measured thermalresistance of the microchannel heat sink was lower than direct air cooled heat sinksby a factor of more than 3.

Takamatsu et al. [34] performed a numerical study of the flow of superfluid he-


lium in capillary channels of small diameters. Two sets of channels with large(8.1 – 96µm) and small (0.76 – 4.7 µm) diameter ranges were analyzed represent-ing a “superleak” (a porous element with microchannels in a fountain effect pumpused under reduced gravity in space applications). The dynamics of superfluid flowwere incorporated in the governing equations through a “two-fluid model” in whichsuperfluid helium is represented through two components: a superfluid componentwith no entropy and viscosity, and a normal fluid component possessing all the en-tropy and viscosity. It was assumed that the two fluid components can flow througheach other without friction. Comparisons were presented for the predicted veloc-ity fields calculated with the assumption of only the normal fluid component beingpresent, to those from the two-fluid model. The results of the study indicated theexistence of an optimum channel diameter for maximizing the mass flow rate.

Bau [35] conducted an investigation to optimize the axial variation of the cross-sectional area of rectangular microchannels in a flat-plate micro heat exchanger, tominimize thermal resistance. An optimization problem was formulated under theassumption of fully developed incompressible flow and solved to achieve minimaltemperature gradients.

The relative performance of jet impingement and microchannel cooling was com-pared by Lee and Vafai [36] for high heat flux applications. Flow and heat transfercharacteristics of multiple-jet impingement were discussed, with reference to the ef-fect of the spent flow on the optimal cooling configuration. Friction and heat transferin microchannel cooling were also discussed, and a procedure for optimizing thechannel geometry was introduced. Based on a comparison of the maximum attain-able heat flux, microchannel cooling was found to be preferable for targets smallerthan 7× 7 cm, while impingement cooling, with proper treatment of the spent flow,was comparable to, or better than, microchannel cooling for larger target dimensions.

Theoretical models developed for the analysis of microchannel flows are seen togenerally fall into two categories – models which incorporate a detailed accountingof the governing equations for flow and heat transfer, and thermal resistance modelswhich deal with overall temperature drops. Fluid flow models have been augmentedfor special flow situations, and considerations such as the effect of an electric doublelayer have been included. One of the objectives common to many of the modelingstudies has been to optimize channel geometry in order to minimize thermal resis-tance.

4 BOILING AND TWO-PHASE FLOW

Boiling and two-phase flow in microchannels has been studied in a number of in-vestigations in the literature. Both mini and microchannels fabricated as part of heatsinks as well as small-diameter tubes and channels have been considered. Two-phaseflow of air-water mixtures in microchannels has been investigated, including a com-parison of the heat transfer performance in single-phase and two-phase flows. Flowpatterns in microchannels and small diameter tubes have also observed.


4.1 Boiling in Mini and Microchannels

Two-phase flow in the cooling of electronic equipment using mini and microchan-nel heat sinks was investigated by Bowers and Mudawar [37–39]. Circular channelsof diameter 2.54 and 0.51 mm (arbitrarily classified as mini and microchannels, re-spectively) were studied, with R113 used as the coolant. Critical heat flux valuesof the order of 200 W/cm2 were experimentally obtained for a range of inlet sub-cooling from 10 to 32◦C, for flow rates less than 95 ml/min. A heat sink thickness-to-channel diameter ratio of 1.2 was found to provide a good compromise betweenminimizing the overall thermal resistance and obtaining structural integrity; a valuefor this ratio of less than 2 provided negligible surface temperature gradients even atheat fluxes of 200 W/cm2 [37]. A pressure drop model was also developed to aid indetermining the channel diameter for a specific cooling application [38]. This modelaccounted for the pressure drop in the single-phase inlet region, the single and two-phase heated region and the two-phase unheated outlet region. The homogeneousequilibrium two-phase flow model was found to predict the heat sink pressure dropwith good accuracy.

A comparison of the theoretical predictions of pressure drop with experimentaldata was presented in Bowers and Mudawar [39], as shown in Figure 10. The majorcontributor to the pressure drop in both mini and micro channels was the accelerationresulting from evaporation; the compressibility effect was also important for the mi-crochannel in high flux applications when the Mach number exceeded 0.22. Channelerosion due to flow boiling in the mini channel geometry was found to be at accept-able levels but the erosion effects in the microchannel at high heat fluxes exceeded“allowable limits”. A single correlation for the critical heat flux was developed from

Ppred , bar

10-3 10-2 10-1

P exp

,ba

r

10-3

10-2

10-1

Plot includes 73 data pointswith +/- 30% error band

All data pointsfor xl <1

Heat sink L / D Ltot / D

mini 3.94 11.3micro 19.6 56.0

Figure 10 Comparison of theoretical predictions of pressure drop in mini and microchannels with exper-imental data [39].


experimental results for both the channels [39]:

qm,p

G hf g= 0.16 We−0.19

( LD

)0.54

. (11)

The influence of liquid velocity, subcooling, property variations and microchannelconfiguration (width, pitch and number of channels) on the heat transfer behavior,cooling performance and heat transfer and liquid flow mode transition (point beyondwhich the heat transfer coefficient is nearly independent of the wall temperature)in flow boiling in rectangular microchannels was studied by Peng et al. [40]. Ex-periments on nucleate flow boiling indicated that the liquid velocity and subcoolingdid not affect fully developed nucleate boiling, but greater subcooling increased thevelocity and suppressed the initiation of flow boiling.

Peng et al. [41] extended this work to experiments on the flow boiling of bi-nary water/methanol mixtures in microchannels. Eight rectangular microchannelconfigurations, each of length 50 mm with hydraulic diameter varying from 0.15 to0.267 mm, were tested at nine different mixture mole fractions. The liquid subcool-ing ranged from 38 to 82◦C, and the liquid velocity was varied from 0.1 to 4.0 m/sec.The results were presented as boiling curves (heat flux versus wall superheat) andheat transfer coefficients. The heat transfer coefficient at the onset of flow boilingand in the partial nucleate boiling region was greatly influenced by liquid concentra-tion, microchannel and plate configuration, flow velocity and subcooling. However,these parameters had little effect in the fully nucleate boiling regime. In general,mixtures with small concentrations of methanol augmented heat transfer relative tothat obtained with pure methanol whereas for large methanol concentrations, the heattransfer was lower.

A further extension of this study of flow boiling to V-shaped microchannels wasreported by Peng et al. [42]. Microchannel hydraulic diameters of 0.2 to 0.6 mm atgroove angles from 30 to 60 deg. were tested experimentally, and an optimum valuefor both these parameters was found to exist which resulted in a maximum in flowboiling heat transfer. In contrast to conventional channels, no bubbles were observedto form in the V-shaped microchannels during flow boiling even with heat fluxes ashigh as 106 W/m2.

Ha and Peterson [43] performed an analytical investigation of the heat transferin evaporating thin liquid films in V-shaped micro grooves with non-uniform inputheat flux. Liquid conduction and interfacial vaporization were both considered indetermining the local interfacial mass flux, and hence in defining a local heat trans-fer coefficient. An expression was developed for the evaporating film profile (axialvariation of film thickness). The axial flow of the evaporating film was further in-vestigated by Ha and Peterson [44], taking into account a gravity term to incorporatethe effect of small tilt angles. The resulting nonlinear equation was solved using aperturbation method.

Both single and two-phase flow of refrigerant 124 in a microchannel heat ex-changer were experimentally investigated by Cuta et al. [45]. The heat exchangerconsisted of 54 microchannels of rectangular cross section (1 mm deep by 0.27 mm


wide), with a hydraulic diameter of 425µm. The experiments were carried out inthe Reynolds-number range of 100 to 750 at a uniform heat flux of up to 40 W/cm2

with wall superheat ranging from 0 to 65◦C. The average heat transfer coefficienton the liquid side showed a significant increase over the expected value in lami-nar macroscopic flow at the same Reynolds numbers. The Nusselt number (rangingfrom 5 to 12) increased with increasing Reynolds number in single-phase flow, andappeared to be approximately constant (around 20) in two-phase flow. It was inferredfrom the experiments that a substantial improvement in thermal performance couldbe achieved in microscale heat exchangers without a large increase in pressure drop,but no explanations were offered.

Ravigururajan [46] investigated microchannels fabricated in a copper substrate,to study the effect of channel geometry on the two-phase heat transfer characteristicsof refrigerant 124. Two microchannel array patterns (parallel and diamond) of hy-draulic diameter 0.425 mm were studied. For the diamond pattern, the heat transfercoefficient was found to decrease from 12000 to 9000 W/m2K corresponding to anincrease in wall superheat from 10 to 80◦C. An increase in exit vapor quality from0.01 to 0.65 was accompanied by a decrease in the heat transfer coefficient of 30%.The heat exchanger with the diamond pattern yielded heat transfer coefficients thatwere 20% lower at corresponding conditions of inlet subcooling and wall superheat.

Roach et al. [47] experimentally investigated the critical heat flux (CHF) asso-ciated with the flow of subcooled water in heated microchannels. Two channels ofdiameter 1.17 and 1.45 mm were uniformly heated, while two others were formedby a micro rod bundle in a triangular array, with a hydraulic diameter of 1.13 mm.One of these latter channels was uniformly heated while the other was heated onlyover the surfaces of the surrounding rods. The CHF was found to increase mono-tonically with increasing mass flux or pressure; the CHF also changed with channelcross section geometry, increasing with an increase in channel diameter. The effectof dissolved air on CHF was to slightly increase the CHF for the smaller circularchannel and reduce it for the other cross sections. The experimental results werefound to be reasonably well predicted by various empirical correlations, particularlythat proposed by Bowring [48].

4.2 Boiling in Small-Diameter Tubes and Channels

Celata et al. [49] performed experimental studies on subcooled flow boiling of waterin small diameter tubes, under the application of very high heat fluxes of the order of60 MW/m2. The experiments were carried out with water at pressures ranging from0.1 to 2.5 MPa and velocities from 10 – 40 m/sec, through stainless steel channelsof diameter 2.5 mm and wall thickness 0.25 mm. The experimental data on criticalheat flux were compared with existing correlations and theoretical models, and thepossibility of upgrading some of the correlations to give acceptable predictions ofthe high heat flux data was discussed.

Mertz et al. [50] performed experimental studies on flow boiling in narrow rect-angular channels of planar heat exchanger elements of 1 to 3 mm width and aspect


ratios of up to 3, fabricated in copper. Saturated flow boiling in a vertical orienta-tion was studied, with water and R-141b as the working fluids. Boiling curves andthe variations of the heat transfer coefficient with local and average heat fluxes wereobtained.

Sturgis and Mudawar [51, 52] studied flow boiling of FC-72 in long rectangularmini-channels of cross section 5.0×2.5 mm, to explore the conditions leading to crit-ical heat flux. Flow visualization studies revealed that at the CHF, vapor coalescedinto a series of patches resembling a wavy vapor layer which propagated along theheated wall, and allowed the liquid to contact the wall only at discrete locations. Thelength and height of the vapor patch was found to increase along the flow direction,but decreased with increasing subcooling and velocity [51]. A model to predict criti-cal heat flux was also presented [52], incorporating the observed periodic distributionof increasingly larger vapor patches along the surface, by idealizing the effect as asinusoidal interface with amplitude and wavelength increasing in the flow direction.The critical interfacial wavelength was predicted through a stability analysis, whichutilized the velocities and average thickness obtained from a separate flow model.The model predicted the near-saturated CHF data in long channels within a meanabsolute error of 10%.

4.3 Two-Phase Flow

Flow visualization studies on two-phase flow of air-water mixtures in tubes withsmall hydraulic diameters were performed by Coleman and Garimella [53]. Tubes ofcircular and rectangular cross section were studied. Flow patterns were observed andflow regime maps obtained for superficial velocities in the range of 0.1 to 100 m/secfor the gas and 0.01 to 10 m/sec for the liquid. The effects of tube diameter andshape on the flow patterns for a range of hydraulic diameters from 1.3 to 5.5 mmwere presented. Flow transition observed in the experiments was contrasted to thatpredicted by correlations for flow in large tubes. It was concluded that the tubediameter influences the superficial gas and liquid velocities at which flow transitionstake place, due to combined effects of surface tension and the tube hydraulic diameterand aspect ratio.

An experimental study on two-phase air-water flow in circular and triangular mi-crochannels of hydraulic diameters 1.1 and 1.45 mm was conducted by Triplett etal. [54, 55]. Flow pattern maps were obtained based on visual observation, andconsisted of bubbly, churn, slug, slug-annular and annular flows. The data werecompared with flow regime transition models and correlations but with poor agree-ment [54]. Void fractions were estimated by analyzing photographs and were com-pared with predictions which assumed a homogeneous model and used various corre-lations. Frictional pressure drops in the microchannel were measured and comparedwith two-phase friction models. The void fraction and channel pressure drop werefound to be best predicted by the homogeneous mixture assumption. The modelsand correlations over-predicted the channel void fraction and pressure drop in annu-lar flow, suggesting that in this regime the liquid-gas interfacial momentum transfer


and wall friction in microchannels may be significantly different from those in largerchannels [55].

Ma et al. [56] presented a mathematical model for the liquid pressure drop inliquid-vapor flow in triangular microgrooves. They used a fluid flow model whichconsidered the interfacial shear stresses due to liquid-vapor frictional interaction,with a combination of analytical and finite-difference methods. Results were re-ported for channel angles ranging from 20 to 60 deg, and contact angles (angle be-tween the liquid-vapor meniscus and the groove wall) from 0 to 60 deg. A dimen-sionless vapor-liquid interface flow number was introduced to incorporate interfacialshear stress into the formulation, and calculations were performed with this numberas a parameter. Preditions for the product of the friction factor and Reynolds numberwere found to be strongly dependent upon the channel angle, the contact angle andthe dimensionless interface flow number. A comparison of these predictions with ex-perimental data [57,58] was found to be satisfactory. The dependence of the frictionfactor-Reynolds number product on the contact angle and the groove angle from thisstudy is shown in Figure 11.

Most of the work reported in the literature on boiling and heat transfer in mi-crochannels has been related to the cooling of electronic equipment. Attention wasfocussed on determining (and minimizing) the overall thermal resistance, as well ason obtaining and correlating critical heat flux data. Friction models have been devel-oped to describe the frictional effects in two-phase liquid-vapor flow. Visualizationof flow regimes and comparisons between single-phase and two-phase cooling meth-ods have also been presented.

Contact angle, degrees

0 10 20 30 40 50 60

f*

Re

9

10

11

12

13

14

152 =60o

2 =40o

2 =20o

by this paper

Ayyaswamy et al.

Figure 11Variation of the friction factor – Reynolds number product with the interfacial contact angle forflow in a triangular microgroove [56].


5 GAS FLOW

Experimental studies as well as theoretical models incorporating slip flow bound-ary conditions and compressibility effects of gas flow through microchannels andmicrotubes have been reported. Theoretical results obtained with and without the as-sumption of slip boundary conditions have been compared, and the effects of channeldimensions and operational parameters on friction and heat transfer have been exper-imentally investigated.

Arkilic et al. [59, 60] measured the rate of flow of helium gas through rectan-gular microchannels at different inlet pressures with the outlet held at atmosphericpressure. The experimental results were compared with the mass flow predicted forgiven inlet and outlet pressures utilizing the solution of the Navier – Stokes equa-tions, assuming both no-slip and slip boundary conditions. It was found that theassumption of no-slip underestimated the mass flow, while the inclusion of the slipflow boundary condition at the wall, derived from a momentum balance, modeled themass flow-pressure relationship in a very satisfactory manner, as shown in Figure 12.Details of the nondimensional formulation and a perturbation solution of the govern-ing equations to obtain the mass flow-pressure drop relationship are available in [60];the experimental setup is also described in detail.

Yu et al. [61] conducted experiments on the flow of dry nitrogen gas and water inmicrotubes of diameters 19, 52 and 102µm, with Reynolds numbers ranging from250 to 20000. A theoretical scaling analysis indicated that turbulent momentum andenergy transport in the radial direction was significant in the near-wall zone of amicrotube. In the laminar regime, the flow friction was lower than that predictedfor conventional channels. The relation between the measured friction factor and

Pressure ratio

1.5 2 2.5 3 3.5 4 4.5

Mas

sfl

ow,k

g/s

x10

-11

0

0.2

0.4

0.6

0.8

1.0

1.2

1.4Slip-flow model, full accomodationNo-slip modelData

Figure 12 Variation of the mass flow rate of helium with the pressure ratio for a microchannel of depth1.33 µm, compared with prediction from models with and without the assumption of slip boundary con-ditions [60].


Reynolds number was found to be linear, and was correlated based on the experi-ments as:

f = 50.13/Re (Re< 2000). (12)

The friction factor was lower than predictions for conventional tubes in the turbulentregime as well, and was correlated as

f = 0.302/Re0.25 (6000< Re< 20000). (13)

In the turbulent regime, heat transfer was enhanced and the Nusselt number wasmuch higher than that predicted by conventional correlations for large tubes. Therecommended correlation was:

Nu = 0.007 Re1.2Pr0.2 (6000< Re< 20000). (14)

Flows in two dimensional microchannels were investigated using a direct simulationMonte Carlo technique by Mavriplis et al. [62]. Supersonic, subsonic and pressure-driven low speed flows were simulated in microchannels of different aspect ratiosfor a range of continuum to transitional-regime rarefied flows. The channel surfaceheat flux was found to depend on the Knudsen number and channel length. As theKnudsen number increased, the heat flux decreased monotonically along the channelwall, and the flow became fully subsonic in the channel. These effects were ex-plained in light of the shock-boundary interaction and the broadening of the shockwith increases in Knudsen number and channel length.

Kavehpour and Faghri [63] analyzed gas flow in microchannels assuming a slip-flow regime, in order to study the effect of gas compressibility and rarefaction on flowand heat transfer. Compressible forms of the momentum and energy equations weresolved using finite differences with a slip velocity and temperature jump boundaryconditions expressed in terms of the Knudsen number. The mass flow rates, frictioncoefficients and the axial pressure distribution were compared with experimental re-sults [59, 64] for nitrogen and helium, and found to be in very good agreement.The Nusselt number and friction coefficient were substantially reduced for slip flowscompared to continuum flows. It was also shown that the effect of compressibilitywas important at high Reynolds numbers, and that the effect of rarefaction was sig-nificant for lower Reynolds numbers in supersonic flow, leading to a reduced wallheat flux.

Guo and Wu [65] investigated gas flow in a smooth microtube, to examine theeffect of compressibility on the friction coefficient and Nusselt number. The two-dimensional axial and radial momentum equations and the energy equation weresolved along with the equation of state for an ideal gas written in terms of the in-let Mach number, using a finite difference forward marching technique. The varia-tions of pressure, density and temperature, the local friction coefficients and the localNusselt number were calculated from the analysis, with the inlet Mach number as aparameter. The local Nusselt number was found to increase with the dimensionlesslength due to compressibility effects. It was found that the product of the frictionfactor and Reynolds number was not a constant, but depended instead on the value


of the Reynolds number. This was attributed to the variation of the velocity profilealong the tube as a result of compressibility and the consequent absence of fullydeveloped flow.

Chen et al. [66] studied the flow of nitrogen and helium gas in microchannels withlarge (width to height) aspect ratios, for which a two-dimensional flow was assumed.Compressibility effects and a slip boundary condition were included in the numericalcomputations. The numerical results agreed with experimental data [59] to within1.15% for pressure and 3.13% for mass flow rate. Gas flow in microchannels wasfound to be characterized by small velocities but high pressure gradients due to thelarge wall shear stresses.

An analysis of slip flow in long microgrooves was presented by Niu [67], usingwhich flow in two-dimensional microchannels and three-dimensional straight andspiral grooves (in turbomolecular pumps) was studied numerically. The non-linearpressure gradient obtained along the microchannels was attributed to variations indensity.

The major geometric parameters that have been investigated in the analysis ofgas flow through microchannels are the diameters of microtubes and aspect ratiosof channels. Slip boundary conditions and compressibility effects have been in-corporated into models. Experimental studies on gas flow in microchannels haveconsidered flow rates, Reynolds numbers, pressure ratios and channel dimensions asparameters.

6 DESIGN AND TESTING FOR ELECTRONICS COOLING

Some of the investigations into microchannels in the literature have specifically dealtwith optimal design of heat sinks for specific electronics cooling applications. Per-formance characterization and testing of electronic devices with microchanneled heatsinks has also been reported.

Weisberg et al. [68] reported an analysis aimed at developing an optimal designalgorithm for heat exchangers with integrally fabricated microchannels for coolingelectronic chips. Numerical analysis of the two-dimensional conjugate heat transferproblem in the solid substrate and fluid was presented. A design algorithm for theselection of heat exchanger dimensions was developed, resulting in an expressionfor the minimum pumping power specified as a function of the channel geometry, asfollows:

PT =

L µ

8ρ2f C

2pWT H3

c

wwc

(1 + A)2C(A)(R∗ − R)2

, (15)

whereC(A) is a constant which depends on the channel geometry. The values ofRforuse in the above expression were presented in dimensionless form (r = WTkf LR/Hc)as in Figure 13, as a function of channel geometry.

Design and testing of microchannel heat exchangers for cooling semiconduc-tor laser diode arrays capable of dissipating very high heat fluxes of the order of


h

1 1.5 2 2.5 3 3.5

r

0.01

0.02

0.1

A=3 (0.3) A=3 (0.5) A=3 (0.7)

A=6 (0.3) A=6 (0.5) A=6 (0.7)

A=9 (0.3) A=9 (0.5) A=9 (0.7)

Figure 13 Dimensionless thermal resistance of a microchannel heat sink as a function of channel heightand aspect ratio [68].

1000 W/cm2 was reported by Roy and Avanic [69]. These heat exchangers con-sisted of microchannels of almost rectangular cross section, with dimensions of0.5 × 12 mm. The overall thermal resistance of the heat exchangers was less than0.03 W/◦C, which was stated to be an improvement of 2 to 3 times over other state-of-the-art heat sinks. Another design with dimensions of 0.125× 12 mm was alsotested and found capable of dissipating 200-300 W from a solder-bonded resistor ofarea 0.5 mm2, while limiting the surface temperature rise to 20 – 30◦C.

Aranyosi et al. [70] reported a parametric analysis and experiments on compactheat sinks for power packages, which utilized air impingement cooling in microchan-nels. A thermal resistance model was developed and used to determine the influenceof the operational (static pressure and pumping power) and geometric parameterson thermal resistance. Measured thermal resistances and pressure drops agreed withmodel predictions to within 20%. Heat dissipation rates as high as 10 W/cm2 weremeasured.

Gillot et al. [71] presented a three-dimensional analysis of a high-performancemicro heat sink for a power multichip module. Thermal resistance values obtainedfrom the simulation were compared with experimental results, and the agreementwas found to be within 10%. Comparing one-dimensional and three-dimensionalapproaches of analysis, a parameter s was defined to represent the “heat spread ef-fect” ass = (Rth 1D−Rth 3D)/Rth 1D. The heat spread effect was found to decrease withan increase in the heat transfer coefficient.

Perret et al. [72] investigated the use of water-cooled microchannel heat sinks in-tegrated into a silicon substrate. Using a finite-element analysis the optimum value


of the total thermal resistance was obtained. Thermal resistances were calculated forhexagonal, diamond-shaped and rectangular channel geometries, and the rectangulargeometry was shown to cause the lowest thermal resistance. Experiments on singleand two-phase micro heat exchangers for cooling insulated gate bipolar transistors(IGBT) were performed by Gillot et al. [73]. The heat exchangers were fabricatedby brazing the copper microchannel heat sinks on to silicon chips. Water and FC-72were used as the cooling fluids. As expected, the two-phase heat exchanger resultedin lower thermal resistances compared to single-phase operation. Further, the re-quired flow rates and pressure drops were also lower for the two-phase exchangerfor the same dissipated power. The experimental measurements agreed with predic-tions of the thermal resistance to within 13%.

7 MEASUREMENT TECHNIQUES

A bulk of the experimental work on microchannel flows has utilized conventionalmeasurement techniques such as thermocouples for local temperatures, and the mea-surement of overall flow rates and pressure drops. More recently, new techniques arebeing utilized for obtaining localized measurements, helped in large part by advancesin microfabrication technologies.

Optical flow measurements using microscopic observation in different microchan-nel geometries, with flow rates in the range 0.01 – 1000µl/min, were reported byRichter et al. [74]. The application of concern was liquid dosing, involving verysmall discharge and precise flow control, for which the microchannels were fabri-cated as etched V grooves in silicon, covered with pyrex glass by anodic bonding.The maximum channel width ranged from 28 to 182µm. The measured flow rateswere found to be in good agreement with theoretical values for laminar flow througha straight channel with a triangular cross section.

Meinhart et al. [75] described the use of Particle Image Velocimetry for the mea-surement of local velocities in microchannel flow. The accuracy of the measurementtechnique was demonstrated by measuring known flow fields in a 30× 300µm mi-crochannel. The results agreed well with analytical solutions for Newtonian flow inrectangular channels.

Measurement of the local flow and temperature fields in liquid and gas flowsin microchannels is an area with room for extensive research. Sophisticated, non-intrusive visualization techniques and microfabricated temperature sensors can pro-vide insight into the fundamental mechanisms of flow and heat transfer at the smallphysical dimensions of microchannels, and help to explain or correct reported de-viations in the overall friction and heat transfer characteristics from conventionalmodels and correlations.


8 CLOSURE

As discussed in this review, flow and heat transfer in microchannels have been thefocus of attention of many investigators in the past decade. The attractiveness ofusing microchannels in the cooling of electronic systems has led to studies on thecharacteristics of liquid and gas flow in microchannels, both experimental and the-oretical. These studies have attempted to delineate the flow regimes in single-phaseflow, characterize flow patterns in two-phase flow, determine the critical heat fluxcondition in boiling, and analyze gas flow with slip boundary conditions and com-pressibility effects. A large number of investigations have dealt with determiningthe dependence of the flow and heat transfer characteristics in microchannels fordifferent channel geometries, operating conditions and fluid-substrate combinations.However, success in generalizing the results and observations of specific studies toa broad range of microchannels has been limited as demonstrated quantitatively ina recent study by Sobhan and Garimella [76]. Anomalies and deviations observedin microchannel flow in comparison to the behavior in conventional channels haveneither been demonstrated beyond doubt, nor adequately explained. Most of the ex-perimental results have been limited to global measurements of pressure drops andtemperatures. Sophisticated local measurements of the flow and thermal fields inmicrochannels are only recently being attempted. Studies discussed in this revieware summarized for convenience in a tabular format in Table 1.

The information in the literature thus far does not provide unequivocal predictivecorrelations or design information for microchannels. There is no evidence that con-tinuum assumptions are violated for the microchannels considered in past studies,most of which have hydraulic diameters of 50µm or more. As such, analyses basedon Navier – Stokes and energy equations would be expected to adequately modelthe phenomena observed, as long as the experimental conditions and measurementsare correctly identified and simulated. The discrepancies between the results fromvarious studies in the literature may very well be due to entrance and exit effects,differences in surface roughness in the different microchannels investigated, nonuni-formity of channel dimensions, thermophysical property variations, nature of thethermal and flow boundary conditions, and uncertainties and errors in instrumenta-tion, measurement and measurement locations. Given the diversity in the results inthe literature, a reliable prediction of the heat transfer rates and pressure drops inmicrochannels is not currently possible for design applications such as microchannelheat sinks. There is a clear need for additional systematic studies which carefullyconsider each parameter influencing transport in microchannels.

9 ACKNOWLEDGEMENT

Support for this work provided by members of the Purdue Cooling Technologies Re-search Consortium (http://widget.ecn.purdue.edu/˜CTRC) directed by SVGis gratefully acknowledged.


Tabl

e1

Sum

mar

yof

Mic

roch

anne

lStu

dies

inth

eLi

tera

ture

Con

figur

atio

n/P

aram

eter

sN

atur

eof

Wor

kO

bser

vatio

ns/C

oncl

usio

nsR

efer

ence

MIC

RO

CH

AN

NE

LC

ON

CE

PT

SA

ND

EA

RLY

WO

RK

Rec

tang

ular

cros

sse

ctio

n;w

ater

insi

licon

W=

50µm

,H

=30

0µm

,Q

=4.

7,6.

5,8.

6cm

3/s

Exp

erim

ents

onin

tegr

alhe

atsi

nkfo

rsi

licon

inte

grat

edci

rcui

ts

•D

emon

stra

ted

use

ofm

icro

chan

nels

for

very

high

conv

ectiv

ehe

attr

ansf

erin

cool

ing

inte

grat

edci

rcui

ts(7

90W/cm

2

ata

subs

trat

e-to

-coo

lant

tem

pera

ture

diff

eren

ceof

71◦C

)

Tuc

kerm

an&

Pea

se[2

]

Mic

roch

anne

lsin

cool

ing

ofin

tegr

ated

circ

uits

Mic

roch

anne

lfa

bric

atio

nan

dim

plem

enta

tion

deta

ilsdi

scus

sed

•C

oola

ntse

lect

ion,

pack

agin

g/h

eade

ring,

mic

rost

ruct

ure

sele

ctio

n,fa

bric

atio

nan

dbo

ndin

gdi

scus

sed

•E

tchi

ngan

dpr

ecis

ion-

saw

ing

com

pare

d;fa

bric

atio

nan

dad

vant

ages

of’m

icro

pilla

rs’u

sing

prec

isio

n-sa

win

gdi

scus

sed

•E

xpre

ssio

nsfo

rC

oola

ntF

igur

eof

Mer

itpr

ovid

ed:

CF

OM

=(k

cρC/µ

)0.25

)fo

rgi

ven

cool

antp

ress

ure,

and

(k cρ

2 C2/µ

)0.25

)fo

rgi

ven

pum

ping

pow

er

Tuc

kerm

an&

Pea

se[3

]

Tra

pezo

idal

;ni

trog

enin

silic

onan

dgl

ass

W=

130

–30

0µm

,H

=30

–60µm

,D

h=

55–

76µm

Fric

tion

fact

ors

mea

sure

dan

dco

mpa

red

with

Moo

dy’s

char

tva

lues

for

com

mer

cial

chan

nels

•F

rictio

nfa

ctor

for

glas

sch

anne

ls3

–5

times

larg

erth

ansm

ooth

-pip

epr

edic

tions

•F

low

tran

sitio

noc

curr

edat

Re≈

400

•C

orre

latio

nsfo

rfr

ictio

nfa

ctor

f:

(110±8

)/R

eR

e≤90

00.

165(

3.48−l

ogR

e)0.

24+

(0.0

81±0.0

07)

900<

Re<

3000

(0.1

95±0.0

17)/

Re0.

1130

00<

Re<

1500

0

Wu

&Li

ttle

[4]


As

in[4

]H

eatt

rans

fer

expe

rimen

ts•

Cor

rela

tion

for

Nus

selt

num

ber

inth

etu

rbul

entr

egim

e:N

u=

0.00

22P

r0.4

Re1.

09fo

rR

e>

3000

Wu

&Li

ttle

[5]

Rec

tang

ular

;ai

rin

silic

onW

=0.

13–

0.25

mm

,H/W

=10

,A

s=

47–

63cm

2/c

m3

Com

paris

onof

perf

orm

ance

with

conv

entio

nal

heat

sink

s,ba

sed

onco

rrel

atio

ns

•M

icro

-str

uctu

red

com

pact

heat

sink

sat

trac

tive

com

pare

dto

conv

entio

nala

irci

rcul

atio

nhe

atsi

nks

Ma-

halin

gam

&A

n-dr

ews

[7]

Rec

tang

ular

;w

ater

insi

licon

W=

50–

600µ

m

The

oret

ical

mod

elfo

rfu

llyde

velo

ped,

deve

lopi

ngflo

ws

•T

urbu

lent

flow

desi

gns

show

edeq

uiva

lent

orbe

tter

perf

orm

ance

com

pare

dto

lam

inar

flow

desi

gns

Phi

llips

etal

.[1]

Rec

tang

ular

;N

-pro

pano

lin

silic

onA

c=

80–

7200

sq.µm

Exp

erim

ents

•C

hann

els

with

larg

ercr

oss-

sect

iona

lare

assh

owed

bette

rag

reem

entw

ithth

eore

tical

pred

ictio

nsfo

rth

efr

ictio

nfa

ctor

•P

ropo

sedf

=C/R

ew

ithC

give

nas

Cvs

Re

grap

hs(la

min

ar)

Pfa

hler

etal

.[8]

Mic

roch

anne

lstr

uctu

res

for

cool

ing

appl

icat

ions

Mic

roch

anne

lap

plic

atio

nsdi

scus

sed

•A

pplic

atio

nsof

mic

roch

anne

lsto

elec

tron

ics

cool

ing,

com

pact

heat

exch

ange

rs,h

eats

hiel

dsan

dflu

iddi

strib

utio

nsy

stem

sdi

scus

sedH

oopm

an[1

1]


Tabl

e1

(con

tinue

d)M

icro

tube

s;ni

trog

enin

silic

aD

=3,

7,10

,53,

81µm

,L

=24

–52

mm

Exp

erim

ents

onfr

ictio

nan

dhe

attr

ansf

er•

Cor

rela

tions

for

fric

tion

fact

oran

dN

usse

ltnu

mbe

r:

Lam

inar

(Re<

2000

)f=

64/

Re[

1+30

(ν/D

c a)]−1

Nu

=0.

0009

72R

e1.17

Pr1/

3;

Tur

bule

nt(2

500<

Re<

2000

0)f=

0.14

0Re−

0.18

2

Nu

=3.

82·1

0−6

Re1.

96P

r1/3

Cho

iet

al.[

9]

Rec

tang

ular

;w

ater

inet

ched

silic

onW

=1

mm

,H

=17

6–

325µ

m,

L=

46m

m,

P=

2m

m

Exp

erim

ents

•N

usse

ltnu

mbe

rshi

gher

than

thos

epr

edic

ted

from

anal

ytic

also

lutio

nsfo

rde

velo

ping

lam

inar

flow

Rah

man

&G

ui[1

0]

SIN

GLE

-PH

AS

E(L

IQU

ID)

EX

PE

RIM

EN

TS

Rec

tang

ular

;de

ioni

zed

wat

erin

stai

nles

sst

eel

W=

0.6

mm

,H=

0.7

mm

,T

i=

30–

60◦ C

,v

=0.

2–

2.1

m/s

Exp

erim

ents

onsi

ngle

-pha

sefo

rced

conv

ectio

n

•In

sing

le-p

hase

conv

ectio

n,a

stee

pin

crea

sein

wal

lhea

tflux

with

the

wal

ltem

pera

ture

•H

eatfl

uxfo

rm

icro

chan

nels

high

erth

anfo

rno

rmal

-siz

etu

be

Pen

g&

Wan

g[1

8]

Rec

tang

ular

;w

ater

,met

hano

lin

stai

nles

sst

eel

W=

0.2,

0.4,

0.6,

0.8

mm

,H

=0.

7m

m,

Ti=

10–

35◦ C

(wat

er),

14–

19◦ C

(met

hano

l),v

=0.

2–

2.1

m/s

Exp

erim

ents

onfo

rced

conv

ectio

nflo

wan

dhe

attr

ansf

er

•H

eatt

rans

fer

augm

ente

das

liqui

dte

mpe

ratu

rew

asre

duce

dan

das

liqui

dve

loci

tyw

asin

crea

sed

•F

ully

deve

lope

dtu

rbul

entc

onve

ctio

nre

gim

est

arts

atR

e=

1000

–15

00

•C

orre

latio

nfo

rtu

rbul

enth

eatt

rans

fer

Nu=0.

0080

5R

e4/5

Pr1/

3

Wan

g&

Pen

g[1

6]


Rec

tang

ular

;w

ater

inst

ainl

ess

stee

lD

h=

0.13

3–

0.367

mm

,L

=50

mm

,H/W

=0.

333

–1,

Ti=

22–

44◦ C

,v

=0.

25–

12m/

s,R

e=

50–

4000

Exp

erim

ents

onfr

ictio

nal

beha

vior

inla

min

aran

dtu

rbul

entfl

ow

•F

low

tran

sitio

noc

curr

edfo

rR

e=20

0−

700

•C

orre

latio

nspr

opos

ed(v

alue

sfo

rC

f,l,

Cf,

tpr

ovid

edin

[13,

Tabl

e2]

) f=

Cf,

l/R

e1.98

Lam

inar

flow

f=

Cf,

t/R

e1.72

Tur

bule

ntflo

w

Pen

get

al.[

13]

As

in[1

3]E

xper

imen

tson

forc

edco

nvec

tion

heat

tran

sfer

char

acte

ristic

s

•F

ully

turb

ulen

tcon

vect

ive

cond

ition

sre

ache

dat

Re

=40

0–

1500

•T

rans

ition

Re

dim

inis

hed

with

are

duct

ion

inm

icro

chan

nel

dim

ensi

on

Nu

=C

h,lR

e0.62

Pr1/

3La

min

arN

u=

Ch,

tR

e0.8

Pr1/

3T

urbu

lent

(val

ues

forC

h,l,

Ch,

t)av

aila

ble

in[1

4]

Pen

get

al.[

14]

As

in[1

6]ex

cept

Ti=

11–

28◦ C

(wat

er),

12–

20◦ C

(met

hano

l)v

=0.

2–

2.1

m/s

(wat

er),

0.2

–1.

5m

/s(m

etha

nol)

Exp

erim

ents

oneff

ecto

fth

erm

oflui

dpr

oper

ties

and

geom

etry

onco

nvec

tive

heat

tran

sfer

•C

hang

esin

flow

regi

mes

and

heat

tran

sfer

mod

esin

itiat

edat

low

erR

ein

mic

roch

anne

lsco

mpa

red

toco

nven

tiona

lcha

nnel

s

•T

rans

ition

zone

and

heat

tran

sfer

char

acte

ristic

sin

lam

inar

and

tran

sitio

nflo

win

fluen

ced

byliq

uid

tem

pera

ture

,vel

ocity

,Re

and

mic

roch

anne

lsiz

e

Pen

g&

Pet

erso

n[1

7]


Tabl

e1

(con

tinue

d)A

sin

[13]

Exp

erim

ents

onsi

ngle

-pha

seflo

wan

dhe

attr

ansf

er

•R

atio

ofex

perim

enta

lto

theo

retic

alfr

ictio

nfa

ctor

atcr

itica

lRe

plot

ted

asa

func

tion

ofZ=

min

[H,W

]/m

ax[H,W

]

•C

orre

latio

nspr

opos

ed

Nu

=0.

1165

( Dh/P

)0.81

( H/W

)−0.

79R

e0.62

Pr0.

33La

min

arN

u=

0.07

2(D

h/P

)1.15

[ 1−

2.42

1(Z−

0.5)

2] ×

Re0.

8P

r0.33

Tur

bule

nt

Pen

g&

Pet

erso

n[1

5]

Rec

tang

ular

;w

ater

-met

hano

lmix

ture

inst

ainl

ess

stee

lD

h=

0.13

3–

0.367

mm

,L

=50

mm

W=

0.1,

0.2,

0.3,

0.4

mm

,H

=0.

2,0.

3m

m,

Ti=

14–

36◦ C

,v

=0.

04–

3.8

m/s

,R

e=

6–

3500

Exp

erim

ents

•La

min

arhe

attr

ansf

erce

ased

for

Re≈70

–40

0de

pend

ing

onflo

wco

nditi

ons;

fully

deve

lope

dtu

rbul

enth

eatt

rans

fer

achi

eved

atR

e=

200

–70

0,de

pend

ing

onDh

•T

rans

ition

Re

redu

ced

with

are

duct

ion

inm

icro

chan

nels

ize

•D

h,H

/Wan

dm

ixtu

rem

ole

frac

tion

influ

ence

dhe

attr

ansf

er

•H

eatt

rans

fer

incr

ease

dfo

rsm

alle

rm

ole

frac

tions

ofth

em

ore

vola

tile

com

pone

nt

Pen

g&

Pet

erso

n[1

9]

Rec

tang

ular

;de

ioni

zed

wat

erin

silic

onW

=25

1µm

,H=

1030µm

,D

h=

404µm

,L

=2.

5cm

,Q

=5.

47–

118

cm3/s

Exp

erim

enta

l&th

eore

tical

stud

y•

Crit

ical

Re

of15

00id

entifi

edfo

ron

seto

ftur

bule

nce

•A

naly

sis

show

edth

atflo

wan

dhe

attr

ansf

erpe

rfor

man

ceco

uld

beim

prov

edby

incr

easi

ngH

,and

that

for

the

sam

epr

essu

redr

opan

dpu

mpi

ngpo

wer

,the

rmal

resi

stan

cew

assm

alle

rfo

rde

eper

chan

nels

Har

ms

etal

.[20

]


Rec

tang

ular

;F

C-7

2an

dtr

ansf

orm

eroi

lin

stai

nles

sst

eel

H=

0.10

–0.

58m

m;

nozz

ledi

men

sion

s(m

m):

Leng

th=

35,

B=

0.14

6,0.

210,

0.23

4,H

eigh

t=12

,v

=0.

54–

8.45

m/s

,R

e=

70–

170

(oil)

,91

1-48

07(F

C72

)

Exp

erim

ents

inim

ping

emen

ton

2D mic

roch

anne

ls

•E

mpi

rical

corr

elat

ion

for

Nus

selt

num

ber

for

the

two

liqui

ds

Nu x

=0.

429

Re0.

583P

r1/3(x/2

H)0.

349 (B

/2H

)−0.

494

Zhu

ang

etal

.[28

]

Circ

ular

;dis

tille

dw

ater

inco

pper

D=

0.10

2–

1.09

mm

,v<

18.9

m/s

,R

e=

2.6·

103

–2.

3·10

4,

Pr=

1.53

–6.

43,

q′′ <

3.0

MW

/m2

Exp

erim

ents

ontu

rbul

ent

sing

le-p

hase

flow

•N

usse

ltnu

mbe

rshi

gher

than

thos

epr

edic

ted

byla

rge-

chan

nel

corr

elat

ions

•G

niel

insk

i[71

]cor

rela

tion

mod

ified

for

Nus

selt

num

ber

for

turb

ulen

tflow

inci

rcul

arm

icro

chan

nels

(f

from

Filo

nenk

o,19

54):

Nu

=N

u Gn( 1

+F

)w

here

F=

CR

e[ 1−

(D/D

0)2]

Nu G

n=

( f/8

)(R

e−

1000

)P

r/[ l+

12.7

( f/8

)1/2( P

r2/3−

1)]

C=

7.6×

10−5

;D

0=

1.16

4m

m,f

=[ 1.

82lo

g(R

e)−

1.64

] −2

Ada

ms

etal

.[24

]

Non

-circ

ular

;wat

erin

copp

erD

h=

1.13

mm

,R

e=

3.9·

103

–2.

14·1

04,

Pr=

1.22

–3.

02

Exp

erim

ents

ontu

rbul

ent

conv

ectio

n•

Exp

erim

enta

lNus

selt

num

ber

wel

l-pre

dict

edby

Nu

Gn

•D

h≈

1.2

mm

prop

osed

asre

ason

able

low

erlim

itfo

rap

plic

abili

tyof

stan

dard

Nus

selt-

type

corr

elat

ions

tono

n-ci

rcul

arch

anne

ls

Ada

ms

etal

.[27

]


Tabl

e1

(con

tinue

d)R

ecta

ngul

ar;

lam

inar

and

tran

sitio

nflo

wD

imen

sion

alan

alys

isba

sed

onex

perim

enta

lda

tain

the

liter

atur

e

•A

ttem

pted

toex

plai

nth

eob

serv

atio

nth

atN

um

ayde

crea

sew

ithin

crea

sing

Re

inla

min

arre

gim

ean

dm

ayre

mai

nun

aff

ecte

din

tran

sitio

nre

gim

e

•P

ropo

sed

that

Brin

kman

num

ber

may

bette

rco

rrel

ate

conv

ectiv

ehe

attr

ansf

er

Tso

&M

ahul

ikar

[21,

22]

Alm

ostc

ircul

ar;

wat

erin

alum

inum

Dh

=0.

73m

m

Exp

erim

ents

•La

min

arflo

wda

tafo

und

toco

rrel

ate

wel

lusi

ngB

rinkm

annu

mbe

rTso

&M

ahul

ikar

[23]

SIN

GLE

-PH

AS

E(L

IQU

ID)

MO

DE

LSA

ND

OP

TIM

IZAT

ION

ST

UD

IES

Tria

ngul

arm

icro

groo

ves

chan

nela

ngle

20–

60de

g.A

naly

ti-ca

l/num

eric

alan

alys

is

Fric

tion

fact

or-R

eyno

lds

num

ber

prod

ucts

tron

gly

depe

nden

ton

chan

nel

angl

e,co

ntac

tang

le,a

nddi

men

sion

less

vapo

r-liq

uid

inte

rfac

eflo

wnu

mbe

r

Ma

etal

.[56

]

Mic

roch

anne

lpl

ate-

finhe

atsi

nk;

air

inco

pper

,alu

min

umW

=40

0,50

0µm

,H

=2.

5cm

,Q=

1–

6l/s

The

rmal

resi

stan

cem

odel

,ex

perim

ents

,op

timiz

atio

n

•T

herm

alre

sist

ance

ofm

icro

chan

nele

dhe

atsi

nklo

wer

than

for

heat

sink

sem

ploy

ing

dire

ctai

rco

olin

g,by

afa

ctor

ofm

ore

than

3Kle

iner

etal

.[33

]

Circ

ular

capi

llary

chan

nels

D=

8.1

–96µm

,0.

76–

4.7µm

Num

eric

alst

udy

onth

eflo

wof

supe

rflui

dH

eliu

mus

ing

atw

o-flu

idm

odel

•E

xist

ence

ofan

optim

umch

anne

ldia

met

erfo

rm

axim

umm

ass

flow

rate

indi

cate

d

Taka

mat

suet

al.[

34]


Par

alle

lpla

tes

at25µ

mse

para

tion

dilu

teaq

ueou

sel

ectr

olyt

eL=

10m

m

The

oret

ical

anal

ysis

inco

rpor

atin

geff

ects

ofel

ectr

icdo

uble

laye

rfie

ld

•E

DL

resu

lted

ina

redu

ced

flow

velo

city

than

inco

nven

tiona

lth

eory

,thu

saff

ectin

gte

mpe

ratu

redi

strib

utio

nan

dre

duci

ngR

e

•H

ighe

rhe

attr

ansf

erpr

edic

ted

with

outt

hedo

uble

laye

r

Mal

aet

al.[

30]

Par

alle

lpla

tes

(10×2

0m

m)

ofP

-typ

esi

licon

and

glas

sat

10–

280µ

mse

para

tion;

∆P

=0

–35

0m

bar

Exp

erim

enta

lst

udy

and

com

paris

onw

ithpr

edic

ted

volu

me

flow

rate

s

•F

orso

lutio

nsof

high

ioni

cco

ncen

trat

ion

asw

ella

sfo

rD

h>

few

hund

redµ

m,E

DL

effec

tneg

ligib

leE

DL

effec

tbec

omes

sign

ifica

ntfo

rdi

lute

solu

tions

Mal

aet

al.[

31]

Rec

tang

ular

;di

lute

aque

ous

elec

trol

yte

insi

licon

H=

20µm

,W=

30µm

,L

=10

mm

,∆

P=

2at

m,T

i=

298

K,

q′′ =

1.0×

105W

/m2

Num

eric

alan

alys

isw

itheff

ects

ofE

DL

and

flow

-indu

ced

elec

trok

inet

icfie

ld

•T

heE

DL

field

and

elec

trok

inet

icpo

tent

iala

ctag

ains

tthe

liqui

dflo

w,r

esul

ting

inhi

gher

fric

tion

coeffi

cien

t,re

duce

dflo

wra

tean

da

redu

ceN

usse

ltnu

mbe

r,fo

rdi

lute

solu

tions

Yan

get

al.[

32]

Rec

tang

ular

(flat

plat

em

icro

heat

exch

ange

rs)

Opt

imiz

atio

nst

udy

onm

icro

chan

nel

shap

e

•W

idth

ofhe

atex

chan

ger

cond

uits

may

beop

timiz

edto

redu

cem

axim

umte

mpe

ratu

reof

the

unifo

rmly

heat

edsu

rfac

e

Bau

[35]


Tabl

e1

(con

tinue

d)M

icro

chan

nelc

oolin

gan

dje

tim

ping

emen

tC

ompa

rativ

ean

alys

isof

jet

impi

ngem

ent

and

mic

roch

anne

lco

olin

g

•T

herm

alpe

rfor

man

ceof

jeti

mpi

ngem

entw

ithou

tany

trea

tmen

tof

spen

tflow

subs

tant

ially

low

erth

anm

icro

chan

nelc

oolin

g,re

gard

less

ofta

rget

dim

ensi

on

•M

icro

chan

nelc

oolin

gpr

efer

able

for

targ

etdi

men

sion

ssm

alle

rth

an7×

7cm

Lee

and

Vafa

i[36

]

GA

SF

LOW

Rec

tang

ular

;he

lium

insi

licon

W=

52.2

5µm

,H=

1.33

µm

,L

=75

00µm

;In

lett

oou

tlet

pres

sure

ratio

=1.

2–

2.5,

Re

=(0.5

–4)·1

0−3

Flo

wra

tes

mea

sure

dan

dco

mpa

red

with

theo

retic

alm

odel

•M

ass

flow

-pre

ssur

ere

latio

nshi

pac

cura

tely

mod

eled

byin

clud

ing

asl

ipflo

wbo

unda

ryco

nditi

onat

the

wal

l

Ark

ilic

etal

.[59

]

As

in[5

9]w

ithpr

essu

rera

tio=

1.6

–4.

2,R

e=

(1.4

–12

)·10−

3

Exp

erim

ents

and

com

paris

onof

mas

sflo

ww

ithre

sults

from

2Dan

alys

isw

ithsl

ipbo

unda

ryco

nditi

on

•D

iscu

ssio

nson

nond

imen

sion

alfo

rmul

atio

nan

dpe

rtur

batio

nso

lutio

n

Ark

ilic

etal

.[60

]


Mic

rotu

bes;

nitr

ogen

and

wat

erin

silic

aD

=19

,52,

102µ

m,

Pr=

0,7

–5,

Re

=25

0–

2000

0

Exp

erim

ents

;th

eore

tical

scal

ing

anal

ysis

•T

urbu

lent

mom

entu

man

den

ergy

tran

spor

tin

the

radi

aldi

rect

ion

sign

ifica

ntin

the

near

-wal

lzon

eof

am

icro

tube

•C

orre

latio

nspr

opos

ed:

f=

50.1

3/R

e(la

min

ar,R

e<

2000

)f

=0.

302/

Re0.

25(t

urbu

lent,

6000<

Re<

2000

0)N

u=

0.00

7R

e1.2

Pr0.

2(t

urbu

lent,

6000<

Re<

2000

0)

Yu etal

.[61

]

Rec

tang

ular

H=

0.5,

5µm

,H/W

=

2.5,

5,10,2

0(s

ubso

nic)

;5,

10,2

0(s

uper

soni

c)

Num

eric

alst

udy

usin

gdi

rect

sim

ulat

ion

Mon

teC

arlo

tech

niqu

e

•H

eatfl

uxon

the

chan

nels

urfa

cede

crea

ses

with

incr

ease

inK

nuds

ennu

mbe

ran

dch

anne

llen

gth

insu

pers

onic

flow

Mav

riplis

etal

.[62

]

Rec

tang

ular

;he

lium

(as

in[5

9]),

heliu

man

dni

trog

en,

Dh

=1.

01µm

,L=

10.9

mm

2Dnu

mer

ical

mod

el,

com

paris

onw

ithex

perim

ents

inlit

erat

ure

•N

usse

ltnu

mbe

ran

dfr

ictio

nco

effi

cien

tsub

stan

tially

redu

ced

for

slip

flow

sco

mpa

red

toco

ntin

uum

flow

s

•E

ffec

tofc

ompr

essi

bilit

ysi

gnifi

cant

athi

ghR

e

Kav

ehpo

ur& F

aghr

i[63

]

Sm

ooth

mic

rotu

bes

gas

flow

Num

eric

also

lutio

nof

gas

flow

inm

icro

tube

s

•Lo

calN

usse

ltnu

mbe

rin

crea

sed

with

dim

ensi

onle

ssle

ngth

,due

toco

mpr

essi

bilit

y

•f-

Re

prod

uctn

otco

nsta

nt;d

epen

dent

onR

e

Guo

&W

u[6

5]


Tabl

e1

(con

tinue

d)R

ecta

ngul

ar;

nitr

ogen

,hel

ium

insi

licon

W=

40µm

,H=

1.2µm

,L

=3

mm

(N2)

,W=

52µm

,H

=1.

33µm

,L=

7.5

mm

(He)

Num

eric

also

lutio

nw

ithsl

ipbo

unda

ryco

nditi

on

•S

mal

lvel

ociti

esan

dhi

ghpr

essu

regr

adie

nts

due

tola

rge

wal

lshe

arst

ress

es

•C

ompa

rison

sw

ithex

perim

ents

of[5

9]

Che

net

al.[

66]

3Dst

raig

htan

dsp

iralg

roov

esN

umer

ical

stud

yon

slip

flow

inlo

ngm

icro

chan

nels

•N

on-li

near

pres

sure

grad

ient

sal

ong

the

mic

roch

anne

lsdu

eto

dens

ityva

riatio

ns

Niu

[67]

BO

ILIN

GIN

MIC

RO

CH

AN

NE

LSC

ircul

ar;R

-113

inco

pper

D=

2.45

mm

(min

i),51

0µm

(mic

ro),

Q=

19−

95m

l/min

,∆

T=

10–

32◦ C

Exp

erim

ents

onbo

iling

&tw

o-φ

flow

;bo

iling

curv

es&

CH

Fva

lues

obta

ined

•M

icro

chan

nely

ield

edhi

gher

CH

F(2

8%gr

eate

ratQ=

64m

l/min

)th

anm

inic

hann

el,w

itha

larg

er∆P

(0.3

bar

for

mic

ro,0

.03

bar

for

min

i)

Bow

ers

&M

udaw

ar[3

7]

As

in[3

7]P

ress

ure

drop

mod

elde

velo

ped;

pred

ictio

nsco

mpa

red

toex

perim

ents

•M

ajor

cont

ribut

orto

pres

sure

drop

iden

tified

asth

eac

cele

ratio

nre

sulti

ngfr

omev

apor

atio

n

•C

ompr

essi

bilit

yeff

ecti

mpo

rtan

tfor

mic

roch

anne

lwhe

nM

ach

num

ber>

0.22

•C

hann

eler

osio

neffec

tsm

ore

pred

omin

anti

nm

icro

chan

nels

than

inm

inic

hann

els

Bow

ers

&M

udaw

ar[3

8]


As

in[3

7]E

xper

imen

tson

boili

ngan

dtw

o-ph

ase

flow

•S

ingl

eC

HF

corr

elat

ion

for

min

iand

mic

roch

anne

lsde

velo

ped:

q m,p/( G

h fg

) =0.

16W

e−0.

19( L/D

)0.54

Bow

ers

&M

udaw

ar[3

9]

Rec

tang

ular

;w

ater

inst

ainl

ess

stee

lW

=0.

6m

m,H

=0.

7m

m,

Ti=

30–

60◦ C

,v

=1.

5–

4.0

m/s

Exp

erim

ents

onsu

bcoo

led

boili

ngof

wat

er•

Nuc

leat

ebo

iling

inte

nsifi

edan

dw

alls

uper

heat

for

flow

boili

ngsm

alle

rin

mic

roch

anne

lsth

anin

norm

al-s

ized

chan

nels

for

the

sam

ew

allh

eatfl

ux

•N

opa

rtia

lnuc

leat

ebo

iling

obse

rved

inm

icro

chan

nels

Pen

g&

Wan

g[1

8]

Rec

tang

ular

;m

etha

noli

nst

ainl

ess

stee

lW

=0.

2,0.

4,0.

6m

m,

H=

0.7

mm

,L

=45

mm

,P=

2.4

–4

mm

;T

i=

14–

19◦ C

(Sub

cool

ing:

45–

50◦C

),v

=0.

2–

1.5

m/s

Exp

enm

ents

onbo

iling

•Li

quid

velo

city

and

subc

oolin

gdo

notaff

ectf

ully

deve

lope

dnu

clea

tebo

iling

•G

reat

ersu

bcoo

ling

incr

ease

dve

loci

tyan

dsu

ppre

ssed

initi

atio

nof

flow

boili

ng

Pen

get

al.[

40]


Tabl

e1

(con

tinue

d)R

ecta

ngul

ar;

met

hano

l-wat

erm

ixtu

rein

stai

nles

sst

eel

W=

0.1,

0.2,

0.3,

0.4

mm

,H

=0.

2,0.

3m

m,

L=

45m

m,

Dh

=0.

133

–0.3

43m

m,

v=

0.1

–4.

0m

/s,

Ti=

18–

27.5◦ C

(Sub

cool

ing:

38–

82◦C

)

Exp

erim

ents

onflo

wbo

iling

inbi

nary

mix

ture

s•

Hea

ttra

nsfe

rco

effici

enta

tons

etof

flow

boili

ngan

din

part

ial

nucl

eate

boili

nggr

eatly

influ

ence

dby

conc

entr

atio

n,m

icro

chan

nel/sub

stra

tedi

men

sion

s,flo

wve

loci

tyan

dsu

bcoo

ling

•T

hese

para

met

ers

had

nosi

gnifi

cant

eff

ecto

nhe

attr

ansf

erco

effici

enti

nth

efu

llynu

clea

tebo

iling

regi

me

•M

ixtu

res

with

smal

lcon

cent

ratio

nsof

met

hano

laug

men

ted

flow

boili

nghe

attr

ansf

er

Pen

get

al.[

41]

V-s

hape

d;w

ater

and

met

hano

lin

stai

nles

sst

eel

groo

vean

gle

30–

60de

g;D

h=

0.2

–0.

6m

mv

(wat

er)=

0.31

–1.

03m

/sv

(met

hano

l)=0.

12–

2.14

m/s

Exp

erim

ents

onflo

wbo

iling

•H

eatt

rans

fer

and

pres

sure

drop

wer

ea

ffec

ted

byflo

wve

loci

ty,

subc

oolin

g,D

han

dgr

oove

angl

e

•N

obu

bble

sob

serv

edin

mic

roch

anne

lsdu

ring

flow

boili

ng,u

nlik

ein

conv

entio

nalc

hann

els

•E

xper

imen

tsin

dica

ted

anop

timumD

han

dgr

oove

angl

e

Pen

get

al.[

42]

V-s

hape

dA

naly

sis

ofm

icro

groo

ves

with

non-

unifo

rmhe

atin

put

•A

naly

tical

expr

essi

onde

velo

ped

for

the

evap

orat

ing

film

profi

le

Ha

&P

eter

son

[43]

V-s

hape

dA

naly

sis

ofax

ialfl

owof

evap

orat

ing

thin

film

•U

sed

pert

urba

tion

met

hod

toso

lve

the

axia

lflow

ofan

evap

orat

ing

thin

film

thro

ugh

aV

-sha

ped

mic

roch

anne

lwith

tilt

Ha

&P

eter

son

[44]


Circ

ular

and

rod

bund

le;

wat

erin

copp

erD

=1.

17,1.4

5m

m,

Dh

=1.

131

mm

,m

=25

0–

1000

kg/m

2s

Exi

tpre

ssur

e=34

4–

1043

kPa

Inle

tpre

ssur

e=40

7–

1204

kPa,

Ti=

49–

72.5◦ C

Exp

erim

ents

onC

HF

inflo

wof

subc

oole

dw

ater

•C

HF

foun

dto

incr

ease

mon

oton

ical

lyw

ithin

crea

sing

mas

sflu

xor

pres

sure

•C

HF

depe

nds

onth

ech

anne

lcro

ssse

ctio

nge

omet

ry,a

ndin

crea

ses

with

incr

easi

ngD

Roa

chet

al.[

47]

BO

ILIN

GIN

SM

ALL

DIA

ME

TE

RT

UB

ES

AN

DC

HA

NN

ELS

Circ

ular

;w

ater

inst

ainl

ess

stee

lD

=2.

5m

m,t

=0.

25m

m,

v=

10–

40m/

s

Exp

erim

ents

onsu

bcoo

led

flow

boili

ngof

wat

erun

der

high

heat

fluxe

s

•E

xper

imen

tald

ata

did

notm

atch

pred

ictio

nsfr

omC

HF

corr

elat

ions

inth

elit

erat

ure

Cel

ata

etal

.[49

]

Rec

tang

ular

;w

ater

and

R14

1bin

copp

erW

=1,

2,3

mm

,H/W

<3,

m=

50,2

00,3

00kg/

m2s

Exp

erim

ents

onflo

wbo

iling

inna

rrow

chan

nels

ofpl

anar

heat

exch

ange

rel

emen

ts

•B

oilin

gcu

rves

and

varia

tions

ofhe

attr

ansf

erco

effi

cien

twith

loca

lan

dav

erag

ehe

atflu

xes

obta

ined

Mer

tzet

al.[

50]


Tabl

e1

(con

tinue

d)R

ecta

ngul

ar;

FC

-72

infib

ergl

ass

W=

5m

m,H

=2.

5m

m,

Hea

ted

leng

th=10

1.6

mm

,v

=0.

25–

10m/

s,R

e=

2000

–13

0000

Sub

cool

ing

atou

tlet=

3,16

,29◦ C

CH

Fex

perim

ents

onlo

ngch

anne

ls;

flow

visu

aliz

atio

n

•P

ropa

gatio

nof

vapo

rpa

tche

sre

sem

blin

ga

wav

yva

por

laye

ral

ong

the

heat

edw

alla

tthe

criti

calh

eatfl

ux

•Le

ngth

and

heig

htof

vapo

rpa

tch

foun

dto

incr

ease

alon

gflo

wdi

rect

ion,

and

decr

ease

dw

ithin

crea

sing

subc

oolin

gan

dve

loci

ty

Stu

rgis

&M

udaw

ar[5

1]

As

in[5

1]T

heor

etic

alm

odel

for

CH

F;

data

anal

ysis

•E

ffec

tofp

erio

dic

dist

ribut

ion

ofva

por

patc

hes

idea

lized

asa

sinu

soid

alin

terf

ace

with

ampl

itude

and

wav

elen

gth

incr

easi

ngin

flow

dire

ctio

n

Stu

rgis

&M

udaw

ar[5

1]

TW

O-P

HA

SE

FLO

WR

ecta

ngul

ar;

R12

4in

copp

erW

=0.

27m

m,H

=1.

0m

m,

Dh

=42

5m

m,

Re D

h=

100

–75

0;q′′ <

40W

/cm

2

Exp

erim

ents

onm

icro

chan

nel

heat

exch

ange

r•

Nus

selt

num

ber

(−5to

12)

show

edan

incr

ease

with

Rey

nold

snu

mbe

rin

sing

le-φ

flow

,but

was

appr

oxim

atel

yco

nsta

ntin

two-φ)

flow

Cut

aet

al.[

45]

Rec

tang

ular

;R

124

inco

pper

W=

270µm

,H=

1000µm

,L

=2.

052

cm,D

h=

425µm

;In

lets

ubco

olin

g:5

–15◦

C;

Q=

35–

300

ml/m

in

Exp

erim

ents

with

two

mic

roch

anne

lpa

ttern

s(p

aral

lela

nddi

amon

d)

•H

eatt

rans

fer

coeffi

cien

tand

pres

sure

drop

foun

dto

befu

nctio

nsof

flow

qual

ityan

dm

ass

flux,

inad

ditio

nto

the

heat

flux

and

surf

ace

supe

rhea

t

•H

eatt

rans

fer

coeffi

cien

tdec

reas

edby

20–

30%

for

anin

crea

sein

exit

vapo

rqu

ality

from

0.01

to0.

65

Rav

igur

u-ra

jan

[46]


Circ

ular

and

sem

i-tria

ngul

ar;

air-

wat

erm

ixtu

rein

glas

sD

=1.

1,1.

45m

m,

Dh

=1.

09,1.4

9m

m,v

(air)

:0.

02–

80m/

s,v

(wat

er):

0.02

–8

m/s

(sup

erfic

ial

velo

city

)

Vis

ual

obse

rvat

ion

offlo

wpa

ttern

san

dpa

ttern

map

s

•B

ubbl

y,ch

um,s

lug,

slug

-ann

ular

and

annu

lar

flow

patte

rns

obse

rved

Trip

lett

etal

.[54

]

As

in[5

4]F

rictio

nal

pres

sure

drop

sm

easu

red

and

com

pare

dw

ithva

rious

two-φ

fric

tion

mod

els

•M

odel

san

dco

rrel

atio

nsov

erpr

edic

ted

chan

nelv

oid

frac

tion

and

pres

sure

drop

inan

nula

rflo

wpa

ttern

•A

nnul

arflo

win

terf

ace

mom

entu

mtr

ansf

eran

dw

allf

rictio

nin

mic

roch

anne

lssi

gnifi

cant

lydiffer

entf

rom

thos

ein

larg

erch

anne

ls

Trip

lett

etal

.[55

]

Circ

ular

and

rect

angu

lar;

air-

wat

erm

ixtu

rein

glas

sD

h=

1.3

–5.

5m

m;

v=

0.1

–10

0m/

s(g

as);

v=

0.01

–10

m/s

(liqu

id)

Exp

erim

ents

,flo

wvi

sual

izat

ion

•T

ube

diam

eter

influ

ence

sth

esu

perfi

cial

gas

and

liqui

dve

loci

ties

atw

hich

flow

tran

sitio

nsta

kepl

ace,

due

toco

mbi

ned

eff

ecto

fsu

rfac

ete

nsio

n,hy

drau

licdi

amet

eran

das

pect

ratio

Col

eman

&G

arim

ella

[53]

DE

SIG

NA

ND

TE

ST

ING

Rec

tang

ular

;wat

erin

silic

onN

umer

ical

solu

tion

for

tem

pera

ture

field

;co

mpa

rison

with

expe

rimen

ts

•D

esig

nal

gorit

hmde

velo

ped

for

sele

ctio

nof

heat

exch

ange

rdi

men

sion

s

•E

xpre

ssio

nfo

rm

axim

umpu

mpi

ngpo

wer

obta

ined

asfu

nctio

nof

chan

nelg

eom

etry

Wei

sber

get

al.[

58]


Tabl

e1

(con

tinue

d)A

lmos

trec

tang

ular

;w

ater

inco

pper

0.5×

12m

m,0.1

25×1

2m

m,

Q=

0.47

–5

gpm

Des

ign

and

test

ing,

mic

roch

anne

lhe

atex

chan

ger

for

lase

rdi

ode

arra

ys

•T

herm

alre

sist

ance

due

toso

lder

bond

estim

ated

Roy

&A

vani

c[6

9]

Rec

tang

ular

and

alm

ostt

riang

ular

;ai

rin

copp

er,a

lum

inum

Par

amet

ricst

udie

san

dex

perim

ents

ofai

rim

ping

emen

tin m

icro

chan

nels

•T

herm

alre

sist

ance

mod

elde

velo

ped

•P

aram

etric

stud

ies

tode

term

ine

influ

ence

ofst

atic

pres

sure

,pu

mpi

ngpo

wer

and

geom

etric

para

met

ers

onth

erm

alre

sist

ance

Ara

nyos

iet

al.[

70]

Rec

tang

ular

,di

amon

d-sh

aped

and

hexa

gona

l;w

ater

insi

licon

3Dnu

mer

ical

mod

el;

optim

izat

ion

for

redu

cing

ther

mal

resi

stan

ce

•R

ecta

ngul

arge

omet

ryha

dth

elo

wes

tthe

rmal

resi

stan

ce

Per

ret

etal

.[72

]

Rec

tang

ular

;w

ater

,FC

72in

copp

erE

xper

imen

tson

mic

rohe

atsi

nkfo

rpo

wer

mul

tichi

pm

odul

e;3D

and

IDth

erm

alre

sist

ance

mod

els

•P

ower

dens

ities

of23

0–

350

W/cm

2di

ssip

ated

with

ate

mpe

ratu

reris

eof

35◦ C

,and

apu

mpi

ngpo

wer

ofab

out1

Wpe

rch

ip

•P

aram

eter

’hea

tspr

ead

eff

ect’

defin

edS

=( R

th1D−

Rth

3D) /

Rth

1D

Gill

otet

al.[

71]


Rec

tang

ular

;w

ater

,FC

72in

copp

erW

=23

0,31

1µm

,H

=73

0,30

40µm

,Q

(ml/

min

)=13

50(w

ater

,1-φ)

and

30(2−φ);

2000

(FC

721-φ

)an

d30

0(2

-φ)

Exp

erim

ents

onsi

ngle

and

two-

phas

em

icro

heat

exch

ange

rsfo

rco

olin

gtr

ansi

stor

s

•Tw

o-ph

ase

heat

exch

ange

rpr

ovid

edlo

wer

ther

mal

resi

stan

cean

dpr

essu

redr

opco

mpa

red

tosi

ngle

-pha

sehe

atex

chan

gers

Gill

otet

al.[

73]

Rec

tang

ular

;ai

rin

copp

erW

=80

0pm

,H

=50

mm

,Q=

140

m3/h

r

Exp

erim

ents

and

ther

mal

resi

stan

cem

odel

•P

ress

ure

drop

foun

dto

have

larg

ede

viat

ion

from

pred

icte

dva

lues

athi

ghai

rflo

wra

tes

•C

oolin

gca

paci

ty≈17

00W

athe

atflu

x≈15

W/c

m2

Yu etal

.[29

]

ME

AS

UR

EM

EN

TT

EC

HN

IQU

ES

Tria

ngul

ar;

wat

erin

silic

onW

=28−

182µm

,Q

=0.

01−

1000µl/m

in

Opt

ical

flow

mea

sure

men

tsus

ing

mic

rosc

ope

•M

easu

red

flow

rate

sin

good

agre

emen

twith

theo

retic

alva

lues

for

lam

inar

flow

thro

ugh

tria

ngul

arch

anne

ls

Ric

hter

etal

.[74

]

Rec

tang

ular

;w

ater

ingl

ass

W=

300,

H=

30,

L=

25m

m

Par

ticle

imag

eve

loci

met

ry•

Res

ults

agre

edw

ellw

ithan

alyt

ical

solu

tions

for

New

toni

anflo

win

rect

angu

lar

chan

nels

Mei

nhar

tet

al.[

75]


REFERENCES

1. R. J. Phillips, L. R. Glicksman, and R. Larson, Forced-Convection, Liquid Cooled,Microchannel Heat Sinks for High Power-Density Microelectronics, in:Proc.Int. Symp. on Cooling Technology for Electronic Equipment, Honolulu, Hawaii,pp. 295–316, 1987.

2. D. B. Tuckerman and R. F. W. Pease, High-Performance Heat Sinking for VLSI,IEEE Electron. Device Lett., Vol. EDL-2, pp. 126–129, 1981.

3. D. B. Tuckerman and R. F. W. Pease, Ultrahigh Thermal Conductance Microstruc-tures for Cooling Integrated Circuits, in:Procs. 32-nd Electronic ComponentsConf., IEEE, EIA, CHMT, pp. 145–149, 1982.

4. P. Y. Wu and W. A. Little, Measurement of Friction Factor for the Flow of Gasesin Very Fine Channels used for Micro Miniature Joule Thompson Refrigerators,Cryogenics, Vol. 23, pp. 273–277, 1983.

5. P. Y. Wu and W. A. Little, Measurement of the Heat Transfer Characteristics ofGas Flow in Fine Channel Heat Exchangers for Micro Miniature Refrigerators,Cryogenics, Vol. 24, pp. 415–420, 1984.

6. D. B. Tuckerman,Heat Transfer Microstructures for Integrated Circuits, Ph.D.Thesis, Stanford University, Stanford, CA, 1984.

7. M. Mahalingam and J. Andrews, High Performance Air Cooling for Microelectron-ics, in: Proc. Int. Symp. on Cooling Technology for Electronic Equipment, Hon-olulu, Hawaii, pp. 608–625, 1987.

8. J. Pfahler, J. Harley, H. H. Bau, and J. Zemel, Liquid Transport in Micron andSubmicron Channels,J. Sensors Actuators A, Vol. 21–23, pp. 431–434, 1990.

9. S. B. Choi, R. F. Barron, and R. O. Warrington, Fluid Flow and Heat Transferin Microtubes,Micromechanical Sensors, Actuators and Systems, ASME DSC-Vol. 32, pp. 123–134, 1991.

10. M. M. Rahman and F. Gui, Experimental Measurements of Fluid Flow and HeatTransfer in Microchannel Cooling Passages in a Chip Substrate,Advances in Elec-tronic Packaging, ASME EEP-Vol. 4–2, pp. 685–692, 1993.

11. T. L. Hoopman, Microchanneled Structures,Microstructures, Sensors and Actua-tors, ASME DSC-108, pp. 171–174, 1990.

12. J. S. Goodling and R. W. Knight, Optimal Design of Microchannel Heat Sinks – AReview, in:Optimal Design of Thermal Systems and Components, 65–78, pp. 1994,.

13. X. F. Peng, G. P. Peterson, and B. X. Wang, Frictional Flow Characteristics of WaterFlowing through Microchannels,Experiment. Heat Transfer, Vol. 7, pp. 249–264,1994.

14. X. F. Peng, G. P. Peterson, and B. X. Wang, Heat Transfer Characteristics of WaterFlowing through Microchannels,Experiment. Heat Transfer, Vol. 7, pp. 265–283,1994.

15. X. F. Peng and G. P. Peterson, Convective Heat Transfer and Flow Friction for Wa-ter Flow in Microchannel Structures,Int. J. Heat Mass Transfer, Vol. 39, pp. 2599–2608, 1996.

16. B. X. Wang and X. F. Peng, Experimental Investigation on Liquid Forced Con-vection Heat Transfer through Microchannels,Int. J. Heat Mass Transfer, Vol. 37,pp. 73–82, 1994.

17. X. F. Peng and G. P. Peterson, The Effect of Thermofluid and Geometrical Param-


eters on Convection of Liquids Through Rectangular Microchannels,Int. J. HeatMass Transfer, Vol. 38, pp. 755–758, 1995.

18. X. F. Peng and B. X. Wang, Forced Convection and Flow Boiling Heat transferfor liquid flowing through microchannels,Int. J. Heat Mass Transfer, Vol. 36,pp. 3421–3427, 1993.

19. X. F. Peng and G. P. Peterson, Forced Convection Heat Transfer of Single PhaseBinary Mixtures through Microchannels,Experiment. Thermal Fluid Sci., Vol. 12,pp. 98–104, 1996.

20. T. M. Harms, M. Kazmierczak, F. M. Gerner, A. Holke, H. T. Henderson, J. Pil-chowski, and K. Baker, Experimental Investigation of Heat Transfer and PressureDrop through Deep Microchannels in a (110) Silicon Substrate, in:Proc. ASMEHeat Transfer Div., ASME HTD-Vol. 351–1, pp. 347–357, 1997.

21. C. P. Tso and S. P. Mahulikar, Use of the Brinkman Number for Single PhaseForced Convective Heat Transfer in Microchannels,Int. J. Heat Mass Transfer,Vol. 41, pp. 1759–1769, 1998.

22. C. P. Tso and S. P. Mahulikar, Role of the Brinkman Number in Analyzing FlowTransitions in Microchannels,Int. J. Heat Mass Transfer, Vol. 42, pp. 1813–1833,1999.

23. C. P. Tso and S. P. Mahulikar, Experimental Verification of the Role of BrinkmanNumber in Microchannels using Local Parameters,Int. J. Heat Mass Transfer,Vol. 43, pp. 1837–1849, 2000.

24. T. M. Adams, S. I. Abdel-Khalik, S. M. Jeter, and Z. H. Qureshi, An ExperimentalInvestigation of Single-Phase Forced Convection in Microchannels,Int. J. HeatMass Transfer, Vol. 41, pp. 851–857, 1998.

25. V. Gnielinski, New Equations for Heat and Mass Transfer in Turbulent Pipe andChannel Flow,Int. Chem. Engng, Vol. 16, pp. 359–368, 1976.

26. G. Filonenko, Hydraulic Resistance in Pipes,Teploenergetika, Vol. 1, pp. 40–44,1954 [in Russian].

27. T. M. Adams, C. F. Dowling, S. I. Abdel-Khalik, and S. M. Jeter, Applicabil-ity of Traditional Turbulent Single Phase Forced Convection Correlations to Non-Circular Microchannels,Int. J. Heat Mass Transfer, Vol. 42, pp. 4411–4415, 1999.

28. Y. Zhuang, C. F. Ma, and M. Qin, Experimental Study on Local Heat Transfer withLiquid Impingement Flow in Two Dimensional Micro-Channels,Int. J. Heat MassTransfer, Vol. 40, pp. 4055–4059, 1997.

29. S. Yu, T. Ameel, and M. Xin, An Air-Cooled Microchannel Heat Sink with HighHeat Flux and Low Pressure Drop, in:Proc. 33-rd Nat. Heat Transfer Conf., Albu-querque, New Mexico, Paper No. NHTC 99-162, pp. 1–7, 1999.

30. G. M.Mala, D. Li, and J. D. Dale, Heat Transfer and Fluid Flow in Microchannels,Int. J. Heat Mass Transfer, Vol. 40, pp. 3079–3088, 1997.

31. G. M. Mala, D. Li, C. Werner, H. J. Jacobasch, and Y. B. Ning, Flow Characteristicsof Water through a Microchannel between Two Parallel Plates with ElectrokineticEffects,Int. J. Heat Fluid Flow, Vol. 18, pp. 489–496, 1997.

32. C. Yang, D. Li, and J. H. Masliyah, Modeling Forced Liquid Convection in Rect-angular Microchannels with Electrokinetic Effects, Int. J. Heat Mass Transfer,Vol. 41, pp. 4229–4249, 1998.

33. M. B. Kleiner, S. A. Kuehn, and K. Haberger, High Performance Forced Air Cool-ing Scheme employing Microchannel Heat Exchangers,IEEE Trans. Components,Pack. Manuf. Technol. Part A, Vol. 18, pp. 795–804, 1995.


34. K. Takamatsu, N. Fujimoto, Y. F. Rao, and K. Fukuda, Numerical Study of Flowand Heat Transfer of Superfluid Helium in Capillary Channels,Cryogenics, Vol. 37,pp. 829–835, 1997.

35. H. H. Bau, Optimization of Conduits’ Shape in Microscale Heat Exchangers,Int. J.Heat Mass Transfer, Vol. 41, pp. 2717–2723, 1998.

36. D. Y. Lee and K. Vafai, Comparative Analysis of Jet Impingement and Microchan-nel Cooling for High Heat Flux Applications,Int. J. Heat Mass Transfer, Vol. 42,pp. 1555–1568, 1999.

37. M. B. Bowers, and I. Mudawar, Two Phase Electronic Cooling using Mini-Channeland Micro-Channel Heat Sinks. Part 1: Design Criteria and Heat Diffusion Con-straints,ASME J. Electron. Pack., Vol. 116, pp. 290–297, 1994.

38. M. B. Bowers, and I. Mudawar, Two Phase Electronic Cooling using Mini-Channeland Micro-Channel Heat Sinks. Part 2: Flow Rate and Pressure Drop Constraints,ASME J. Electron. Pack., Vol. 116, pp. 298–305, 1994.

39. M. B. Bowers, and I. Mudawar, High Flux Boiling in Low Flow Rate, Low PressureDrop Mini-Channel and Micro-Channel Heat Sinks,Int. J. Heat Mass Transfer,Vol. 37, pp. 321–332, 1994.

40. X. F. Peng, B. X. Wang, G. P. Peterson, and H. B. Ma, Experimental Investigationof Heat Transfer in Flat Plates with Rectangular Microchannels,Int. J. Heat MassTransfer, Vol. 38, pp. 127–137, 1995.

41. X. F. Peng, G. P. Peterson, and B. X. Wang, Flow Boiling of Binary Mixtures inMicrochannel Plates,Int. J. Heat Mass Transfer, Vol. 39, pp. 1257–1264, 1996.

42. X. F. Peng, H. Y. Hu, and B. X. Wang, Flow Boiling through V-Shape Microchan-nels,Experiment. Heat Transfer, Vol. 11, pp. 87–90, 1998.

43. J. M. Ha and G. P. Peterson, The Interline Heat Transfer of Evaporating Thin FilmsAlong A Micro Grooved Surface,ASME J. Heat Transfer, Vol. 118, pp. 747–755,1996.

44. J. M. Ha and G. P. Peterson, Capillary Performance of Evaporating Flow in Mi-crogrooves – An Analytical Approach for Very Small Tilt Angles,ASME J. HeatTransfer, Vol. 120, pp. 452–457, 1998.

45. J. M. Cuta, C. E. McDonald, and A. Shekarriz, Forced Convection Heat Trans-fer in Parallel Channel Array Microchannel Heat Exchanger,Advances in EnergyEfficiency, Heat/Mass Transfer Enhancement, ASME PID-Vol. 2/HTD, Vol. 338,pp. 17–23, 1996.

46. T. S. Ravigururajan, Impact of Channel Geometry on Two Phase Flow Heat Trans-fer Characteristics of Refrigerants in Microchannel Heat Exchangers,ASME J.Heat Transfer, Vol. 120, pp. 485–491, 1998.

47. G. M. Roach Jr., S. I. Abdel-Khalik, S. M. Ghiaasiaan, M. F. Dowling, andS. M. Jeter, Low-Flow Critical Heat Flux in Heated Microchannels,Nuclear Sci-ence and Engineering, Vol. 131, pp. 411–425, 1999.

48. R. W. Bowring, A Simple but Accurate Round Tube, Uniform Heat Flux, DryoutCorrelation over the Pressure Range 0.7 – 17 MW/m2 (100 – 2500 psia),AEEW-R789, United Kingdom Atomic Energy Authority, 1972.

49. G. P. Celata, M. Cumo, and A. Mariani, Burnout in Highly Subcooled Water FlowBoiling in Small Diameter Tubes,Int. J. Heat Mass Transfer, Vol. 36, pp. 1269–1285, 1993.

50. R. Mertz., A. Wein, and M. Groll, Experimental Investigation of Flow Boiling HeatTransfer in Narrow Channels,Heat and Technology, Vol. 14, pp. 47–54, 1996.


51. J. C. Sturgis and I. Mudawar, Critical Heat Flux in a Long, Rectangular ChannelSubjected to One-Sided Heating – I. Flow Visualization,Int. J. Heat Mass Transfer,Vol. 42, pp. 1835–1847, 1999.

52. J. C. Sturgis and I. Mudawar, Critical Heat Flux in a Long, Rectangular ChannelSubjected to One-Sided Heating – II. Analysis of Critical Heat Flux Data,Int. J.Heat Mass Transfer, Vol. 42, pp. 1849–1862, 1999.

53. J. M. Coleman and S. Garimella, Characterization of Two-Phase Flow Patterns inSmall Diameter Round and Rectangular Tubes,Int. J. Heat Mass Transfer, Vol. 42,pp. 2869–2881, 1999.

54. K. A. Triplett, S. M. Ghiaasiaan, S. I. Abdel-Khalik, and D. L. Sadowski, Gas-Liquid Two Phase Flow in Microchannels. Part I: Two Phase Flow Patterns,Int. J.Multiphase Flow, Vol. 25, pp. 377–394, 1999.

55. K. A. Triplett, S. M. Ghiaasiaan, S. I. Abdel-Khalik, A. LeMouel, and B. N. Mc-Cord, Gas-Liquid Two Phase Flow in Microchannels. Part II: Void Fraction andPressure Drop,Int. J. Multiphase Flow, Vol. 25, pp. 395–410, 1999.

56. P. B. Ma, G. P. Peterson and X. J. Lu, Influence of Vapor-Liquid Interactions onthe Liquid Pressure Drop in Triangular Microgrooves,Int. J. Heat Mass Transfer,Vol. 37, pp. 2211–2219, 1994.

57. E. M. Sparrow, T. S. Chen, and V. K. Jonsson, Laminar Flow and Pressure Drop inInternally Finned Annular Ducts,Int. J. Heat Mass Transfer, Vol. 7, pp. 583–585,1964.

58. P. S. Ayyaswamy, I. Catton, and D. K. Edwards, Capillary Flow in TriangularGrooves,ASME J. Appl. Mech., Vol. 41, pp. 332–336, 1974.

59. E. B. Arkilic, K. S. Breuer, and M. A. Schmidt, Gaseous Flow in Microchannels,Application of Microfabrication to Fluid Mechanics, ASME FED, Vol. 197, pp. 57–66, 1994.

60. E. B. Arkilic, M. A. Schmidt, and K. S. Breuer, Gaseous Slip Flow in Long Mi-crochannels,IEEE J. Microelectromechanical Systems, Vol. 6, pp. 167–178, 1997.

61. D. Yu, R. Warrington, R. Barron, and T. Ameel, An Experimental and Theoreti-cal Investigation of Fluid Flow and Heat Transfer in Microtubes, in:ASME/JSMEThermal Engng Conf., Vol. 1, pp. 523–530, 1995.

62. C. Mavriplis, J. C. Ahn, and R. Goulard, Heat Transfer and Flow Fields in Short Mi-crochannels using Direct Simulation Monte Carlo,Thermophysics and Heat Trans-fer, Vol. 11, pp. 489–496, 1997.

63. H. P. Kavehpour, M. Faghri, and Y. Asako, Effects of Compressibility and Rar-efaction on Gaseous Flows in Microchannels,Numerical Heat Transfer, Vol. 32A,pp. 677–696, 1997.

64. J. Pfahler, J. Harley, H. H. Bau, and J. Zemel, Gas and Liquid Flow in Small Chan-nels,Micromechanical Sensors, Actuators and Systems, ASME DSC-32, pp. 49–60, 1991.

65. Z. Y. Guo and X. B. Wu, Compressibility Effect on the Gas Flow and Heat Transferin a Micro Tube,Int. J. Heat Mass Transfer, Vol. 40, pp. 3251–3254, 1997.

66. C. S. Chen, S. M. Lee,and J. D. Sheu, Numerical Analysis of Gas Flow in Mi-crochannels,Numerical Heat Transfer, Vol. 33A, pp. 749–762, 1998.

67. Y. Y. Niu, Navier – Stokes Analysis of Gaseous Slip Flow in Long Grooves,Nu-merical Heat Transfer, Vol. 36A, pp. 75–93, 1999.

68. A. Weisberg, H. H. Bau, and J. Zemel, Analysis of Microchannels for IntegratedCooling,Int. J. Heat Mass Transfer, Vol. 35, pp. 2465–2474, 1992.


69. S. K. Roy and B. L. Avanik, Very High Heat Flux Microchannel Heat Exchangerfor Cooling of Semiconductor Laser Diode Arrays,IEEE Trans. Components, Pack.Manuf. Technol. Part B: Advanced Packaging, Vol. 19, pp. 444–451, 1996.

70. A. Aranyosi, L. M. R. Bolle, and H. A. Buyse, Compact Air-Cooled Heat Sinks forPower Packages,IEEE Trans. Components, Pack. Manuf. Technol. Part A, Vol. 20,pp. 442–451, 1997.

71. C. Gillot, C. Schaeffer, and A. Bricard, Integrated Micro Heat Sink for Power Mul-tichip Module, in:IEEE Industry Applications Soc. Ann. Meet., Vol. 2, 98CH36242,pp. 1046–1050, 1998.

72. C. Perret, C. Schaeffer, and J. Boussey, Microchannel Integrated Heat Sinksin Silicon Technology, in:IEEE Industry Applications Soc. Ann. Meet., Vol. 2,98CH36242, pp. 1051–1055, 1998.

73. C. Gillot, L. Meysenc, and C. Schaeffer, Integrated single and two phase microheat sinks under IGBT chips,IEEE Transactions on Components and PackagingTechnology, Vol. 22, pp. 384–389, 1999.

74. M. Richter, P. Woias, and D. Wei, Microchannels for Applications in Liquid Dosingand Flow Rate Measurement,Sensors and Actuators A, Vol. 62, pp. 480–483, 1997.

75. C. D. Meinhart, S. T. Wereley, and J. G. Santiago, PIV Measurements of a Mi-crochannel Flow,Exp. Fluids, Vol. 27, pp. 414–419, 1999.

76. C. B. Sobhan and S. V. Garimella, A Comparative Analysis of Studies on HeatTransfer and Fluid Flow in Microchannels, in:Heat Transfer and Transport Phe-nomena in Microsystems, Banff, Canada, October 15-20, pp. 80–92, 2000.

Documents

TRANSPORT IN MICROCHANNELS – A CRITICAL REVIEW