heat transfer in micro channels
TRANSCRIPT
This article was downloaded by: [Universiti Teknologi Malaysia]On: 01 October 2011, At: 10:27Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number:1072954 Registered office: Mortimer House, 37-41 Mortimer Street,London W1T 3JH, UK
Microscale ThermophysicalEngineeringPublication details, including instructions forauthors and subscription information:http://www.tandfonline.com/loi/umte19
HEAT TRANSFER INMICROCHANNELSBjörn Palm
Available online: 29 Oct 2010
To cite this article: Björn Palm (2001): HEAT TRANSFER IN MICROCHANNELS,Microscale Thermophysical Engineering, 5:3, 155-175
To link to this article: http://dx.doi.org/10.1080/108939501753222850
PLEASE SCROLL DOWN FOR ARTICLE
Full terms and conditions of use: http://www.tandfonline.com/page/terms-and-conditions
This article may be used for research, teaching, and private studypurposes. Any substantial or systematic reproduction, redistribution,reselling, loan, sub-licensing, systematic supply, or distribution in anyform to anyone is expressly forbidden.
The publisher does not give any warranty express or implied or make anyrepresentation that the contents will be complete or accurate or up todate. The accuracy of any instructions, formulae, and drug doses shouldbe independently verified with primary sources. The publisher shall notbe liable for any loss, actions, claims, proceedings, demand, or costs ordamages whatsoever or howsoever caused arising directly or indirectly inconnection with or arising out of the use of this material.
Microscale Thermophysical Engineering, 5:155–175, 2001Copyright © 2001 Taylor & Francis1089-3954/01 $12.00 + .00
REVIEW
HEAT TRANSFER IN MICROCHANNELS
Björn PalmDepartment of Energy Technology, Royal Institute of Technology,Stockholm, Sweden
In this article an attempt has been made to review the literature regarding heat transferand pressure drop in one- and two-phase � ow in microchannels. The emphasis has been onreports presented during the last few years. For single-phase � ow, channels with hydraulicdiameters less than 1 mm have been considered. For two-phase � ow, very little informationis available for such small channels. Also, for two-phase � ow, deviations from large-tube behavior start at diameters of a few millimeters. For these reasons a slightly largerdiameter range has been considered in this case. As a conclusion, it can be stated thatthe understanding of � ow in microchannels is increasing steadily, but that there are stillmany questions to be answered concerning the reasons for deviations from classical theorydeveloped for larger channels.
During the last decade there has been growing interest in heat transfer in microchan-nels. Several reasons for this may be mentioned: with developments within the electronicindustry, methods have been contrived for manufacturing complex geometries on a verysmall scale. These manufacturing techniques include etching, vapor depositioning, andbonding in silicon and other materials, but also precision machining and methods for theforming of polymers. In general, the materials technologies have taken a leap forward,making possible new manufacturing methods for microdesign, often at a low cost whenused in large-scale production.
However, the new manufacturing methods for microdesign would not have come touse in the area of heat exchange if there was not a market for miniature heat exchangers.Within the electronics industry, the need for micro heat exchangers is a result of theminiaturization of the electronics, which leads to denser packaging of components andthereby to higher heat � uxes. As the cooling limit of air cooling is reached, the � rstalternative is liquid cooling, with or without evaporation of the � uid. So far, there has notbeen a broad introduction to the market of liquid-cooled electronics, with the exceptionof heat pipes used in laptop computers. However, intense activities are going on in thisarea, and it could be expected that within � ve years the value of these types of coolingsystems will increase 10-fold.
Received 13 September 2000; accepted 29 March 2001.Address correspondence to Prof. Björn Palm, Department of Energy Technology, Royal Institute of
Technology, SE-100 44, Stockholm, Sweden. E-mail: [email protected]
155
Dow
nloa
ded
by [
Uni
vers
iti T
ekno
logi
Mal
aysi
a] a
t 10:
27 0
1 O
ctob
er 2
011
156 B. PALM
NOMENCLATURE
a thermal diffusivity, m2/sBo boiling number [5 q�(Gl · hfg)]Br Brinkman number [5 l · u2
m �(k · D t)]c speed of sound, m/sd diameter, mdh hydraulic diameter, mE enhancement factorF suppression factorf friction factorG mass � ux, kg/m2 sGeq equivalent all-liquid mass � ux
5 {G · [(1 xm ) 1 xm · ( q l � q v )0.5]},kg/m2 s
h heat transfer coef� cient, W/m2 Khfg latent heat of vaporization, J/kgH channel height, mk thermal conductivity, W/m KKn Knudsen number ( 5 �dh )L length, mM molar massn number of parallel channelsNu Nusselt number ( 5 h · dh � k)p pressure, Pap r reduced pressurePr Prandtl number ( 5 l · cp � k)ÇQ heat � ow, W
q heat � ux, W/m2
r radius of curvature, mRe Reynolds number
( 5 u · dh � t l 5 G · dh � l l)Reeq equivalent all liquid Reynolds number
( 5 Geq · dh � l l)
Rp surface roughness parameter, l mS gap width, mt temperature, ° Cu velocity, m/sÇV volume � ow, m3/sv 9 speci� c volume of liquid at saturation,
m3/kgv 9 9 speci� c volume of vapor at saturation,
m3/kgW channel width, mWc c/c distance between channels, mx vapor fraction
critical dimension for the microchannel, mD p pressure difference, PaD t temperature difference, K
mean free path, ml dynamic viscosity, N s/m2
t kinematic viscosity, m2/sq density, kg/m3
surface tension, N/ms time, s
Indicesm meannb nucleate boilingl liquids saturationsup superheatv vapor
Microchannel heat exchangers have also found other applications. In the automotiveindustry, the need for low weight and small overall volume has pushed developmenttoward smaller-diameter heat exchangers. Also, new manufacturing technologies havemade possible more compact designs. One good example of this is multichannel tubesof aluminum, which are now manufactured by several companies. These tubes may haveindividual channels with diameters well below 1 mm.
When discussing microchannel heat transfer, a de� nition of the term is necessary.One de� nition suggested is that microchannels are channels in which classical theory isno longer valid. However, since it is still not clear at what diameter this will occur, thisde� nition is dif� cult to apply. An alternative, simple de� nition is that a microchannel isany channel with a (hydraulic) diameter in the micrometer range, i.e., less than 1 mm.This de� nition seems to be in accordance with the use of the word in the literatureconcerning single-phase � ow. For two-phase � ow, however, there is very little reportedin the literature on � ow in channels less than 1 mm. More important, deviations fromclassical theory may start at diameters of several millimeters. For these reasons it has
Dow
nloa
ded
by [
Uni
vers
iti T
ekno
logi
Mal
aysi
a] a
t 10:
27 0
1 O
ctob
er 2
011
HEAT TRANSFER IN MICROCHANNELS 157
been considered appropriate for the purpose of this review to have a wider de� nition ofthe term “microchannel” in the case of two-phase � ow than that applied to single-phase� ow.
Almost all microchannels discussed in the literature have diameters larger than1 l m. It should be noted that the diameter range of microchannels thus is quite large,and different phenomena may occur in different parts of this range.
Looking through the literature, it is quite clear that the interest in the area ofmicrochannel � ow and heat transfer has increased substantially during the last decade. Ingeneral, there also seems to be a shift in the focus of published articles, from descriptionsof the manufacturing technology to discussions of the physical mechanisms of � ow andheat transfer.
A MOTIVATING EXERCISE
For single-phase � ow, it is easy to show the advantages of going toward smallerchannel diameter using the classical correlations derived for macroscopic channels. Infully developed laminar � ow, the Nusselt number is constant, which means that the heattransfer coef� cient is inversely proportional to the diameter:
Nu 5h · d
k5 const Þ h a
1
d(1)
To transfer a certain amount of heat at a given logarithmic mean temperaturedifference (LMTD), the product of the surface area and the heat transfer coef� cient mustbe constant. Assuming circular tubes, and allowing any number n of parallel channels,this leads to the conclusion that the product of the tube length L and the number ofchannels should be constant:
ÇQ 5 h · A · D t 5 h · ( · d · L · n) · D t Þ L · n 5 const (2)
The friction factor in fully developed laminar � ow is inversely proportional to theReynolds number, which means that the pressure drop is inversely proportional to thediameter to the power of 4:
D p 5C
Re· q · u2 ·
L
d5
C · t
u · d· q · u ·
ÇV· d2 �4
·L
d
Þ D p a1
d4(3)
This also shows that, to keep the pressure drop constant, at a given mass � ow,while changing the tube diameter and the number of parallel tubes, the ratio L �(n · d4)must be kept constant
D p 5C 9 · t · q · ( ÇV tot � n) · L
d4Þ
L
n · d45 const (4)
However, as L · n also should be constant to maintain the mean temperature differ-ence, the product (n · d2) should be constant.
Dow
nloa
ded
by [
Uni
vers
iti T
ekno
logi
Mal
aysi
a] a
t 10:
27 0
1 O
ctob
er 2
011
158 B. PALM
In conclusion, to maintain the pressure drop and the mean temperature differenceat a given mass � ow and heat � ow, while changing the tube diameter and the numberof channels, the product n · d2 should be kept constant. The tube length is then givenby the condition (L · n 5 const) above. Applying these simple relations gives the resultsshown in Figure 1. As an example, decreasing the diameter by half would double theheat transfer coef� cient and reduce the necessary surface area to one-half of the original.The tube length would be reduced to one-fourth of the original, and the number ofparallel channels would increase by a factor of 4. In addition, the internal volume (n ·
· d2 �4 · L ), would decrease by a factor of 4. As an additional bene� t, the thickness ofthe tube wall necessary to withstand a certain pressure would decrease. In conclusion,a decrease of the tube diameter in the laminar-� ow region leads to much more compactdesigns.
A similar analysis could be made also for the turbulent-� ow region. The results aresimilar, although the advantage of reducing the tube diameter is not as large in this case.
Figure 1. Dependence of tube length, number of parallel tubes, heat transfer area, and heat transfercoef� cient on tube diameter for equal mass � ow, heat � ow, and LMTD. Laminar � ow.
Dow
nloa
ded
by [
Uni
vers
iti T
ekno
logi
Mal
aysi
a] a
t 10:
27 0
1 O
ctob
er 2
011
HEAT TRANSFER IN MICROCHANNELS 159
Figure 2. Example of dependence of tube length, heat transfer area, heat transfer coef� cient, internalvolume, � ow area, and number of parallel tubes on tube diameter for equal mass � ow, heat � ow, andLMTD. Laminar and turbulet � ow.
To get the complete picture, the turbulent and the laminar regions may be combined,looking at a speci� c case. The result of such a comparison is shown in Figure 2. Thereference case is a single 10-m tube of 16-mm inner diameter, with water � owing at arate of 6 kg/min. The heat exchange rate is 20 kW. As the tube diameter is decreased tobelow 3 mm the � ow will turn laminar, leading to a sudden change in the parameters.The range of diameters between 3 and 1 mm would obviously not be the best choice, asthe total surface area is even larger than that of the original single tube. However, thediameter does not have to be decreased much further to give a considerable advantage incompactness. As an example, this analysis shows that the original tube (16 mm diameter,10 m length) could be exchanged for a bundle of 0.5-mm tubes, 10 cm in length, havinga total internal cross-sectional area less than twice that of the single tube.
In � ow boiling and condensation a similar analysis would be more complex, as theheat transfer coef� cients depend on the � ow regime. Also, there are no generally acceptedcorrelations for calculation of heat transfer and pressure drop even if the � ow regimesare known. For larger-diameter tubes (>5 mm) it is generally recognized that the � owboiling heat transfer coef� cients increase with decreasing diameter. However, for smaller-diameter tubes new phenomena become important which prohibit the extrapolation ofthis trend.
ONE-PHASE FLOW
Introduction
For the practical application of microchannel heat exchangers in one-phase � ow, thetwo parameters of prime interest are the friction factor and the heat transfer coef� cient.Most of the work described in the literature is concerned with these two parameters,their possible deviations from classical theory, and the reasons for these deviations. Un-
Dow
nloa
ded
by [
Uni
vers
iti T
ekno
logi
Mal
aysi
a] a
t 10:
27 0
1 O
ctob
er 2
011
160 B. PALM
fortunately, the literature is not conclusive concerning the dependence of any of theseparameters on the channel diameter.
Reviews of heat transfer in microchannels have been presented by a number ofauthors [1–5]. Duncan and Peterson [2] provided a wide review of both one-phase andtwo-phase microscale convective heat transfer as well as micro-heat pipes, microscaleconduction, and radiation. Peng and Wang [3, 4] gave a short review of one- and two-phase � ow, but concentrated on presenting their own extensive research. Bailey et al.[5] gave a thorough treatment of one-phase forced convection and concluded that theliterature is inconclusive as to the effect of miniaturization on heat transfer and pressuredrop. They end, however, by stating that there seem to be indications that friction factorsin laminar � ow are lower, and turbulent � ow heat transfer coef� cients are higher thanexpected for larger-diameter channels.
Previous Work in One-Phase Flow
One of the � rst reports concerning heat transfer and pressure drop in microchannelswas presented by Tuckerman and Pease [6]. They designed and tested a multichannel heatexchanger for cooling of electronic components. The channel width was about 50 l mand the depth about 300 l m. Deionized water was used as test � uid. The � ow was foundto obey classical laminar-� ow theory, and the total thermal resistance was independentof the mass � ux, as would be expected for fully developed laminar � ow.
Another early investigation of microchannel pressure drop was done by Wu andLittle [7], who designed a microminiature Joule-Thompson refrigerator. The hydraulicdiameters of their rectangular test species ranged from 50 to 80 l m. The measuredfriction factors were found to be much higher than expected from classical theory (Moodydiagram), even though the Reynolds number dependence had about the same shape asexpected. The same authors also investigated the heat transfer [8]. In this case, they usednitrogen gas passing through rectangular channels with hydraulic diameters close to 150l m. The authors de� ned the ranges of the three � ow regimes as laminar (Re < 1,000),transition (1,000 < Re < 3,000), and turbulent (Re > 3,000). This indicates transitionfrom laminar � ow at lower Reynolds number than expected for larger tubes. For mostReynolds numbers, the heat transfer coef� cients were found to be higher than expectedfrom classical theory. For the turbulent regime, they proposed the following correlation:
Nu 5 0.00222 · Re1.09 · Pr0.4 (5)
In the laminar regime, the Nusselt number was found to be a function of theReynolds number with an exponent slightly higher than that in the turbulent regime. Atthe lowest Re the results were lower than expected.
The relative roughness of the channel walls was fairly high and unsymmetric, whichmight have in� uenced the results and could explain, at least partly, why both pressuredrop and heat transfer were higher than expected.
Peng and Peterson published several reports on single-phase as well as two-phase� ow in microchannels. In one article [9] they investigated heat transfer and pressure dropof water � owing through arrays of rectangular microchannels having different aspectratios and hydraulic diameters in the range 0.15–0.34 mm. The range of Reynolds num-
Dow
nloa
ded
by [
Uni
vers
iti T
ekno
logi
Mal
aysi
a] a
t 10:
27 0
1 O
ctob
er 2
011
HEAT TRANSFER IN MICROCHANNELS 161
bers was from 50 to 4,000. For both the laminar and the turbulent regimes, the Nusseltnumber was found to be a function not only of the Reynolds and Prandtl numbers butalso of different geometric parameters. For laminar � ow they suggested the followingcorrelation:
Nu 5 0.1165 ·dh
Wc
0.81
·H
W
0.79
· Re0.62 · Pr1�3 (6)
where Wc is the center-to-center distance between channels.For turbulent � ow the suggested correlation is similar to the Dittus-Boelter corre-
lation but with the constant being dependent on the geometry.The friction factors corresponding to the measured pressure drops deviated con-
siderably from the classical values and were more strongly dependent on the Reynoldsnumber than expected. Both higher and lower friction factors were measured. They alsonoted that transition from laminar to transition and turbulent � ow started at much lowerReynolds number than for larger-diameter tubes. Similar results were reported earlier byPeng and Wang [10] and Wang and Peng [11].
Cuta et al. [12] tested a heat exchanger consisting of 54 parallel channels withrectangular cross section (1.0 mm ´ 0.27 mm), corresponding to a hydraulic diameterof 0.425 mm. The length of the channels was 20.52 mm, and R-124 was used as test� uid. The range of Reynolds number was from 100 to 570. The authors report thatthe friction factors were considerably smaller than expected from classical theory. TheNusselt number, on the other hand, was found to be substantially larger than expectedfrom laminar-� ow theory. In addition, the Nusselt number increased with increasingReynolds number, but at a lower rate than would be expected for turbulent � ow (Nu a
Re0.6).Harms et al. [13] investigated the � ow of deionized water through 68 parallel
rectangular microchannels, each being 0.251 mm wide and 1.000 mm deep, having alength of approximately 25 mm. The Reynolds number range covered was from 173 to12,900. The channels were etched from a silicon wafer and covered by a glass plate.The friction factor was found to be reasonably well predicted by classical theory, bothin the laminar and in the turbulent regimes. However, the critical Reynolds number wasfound to be lower, about 1,500, but the authors attributed this to the severity of the inletcondition.
The experimentally determined Nusselt numbers were compared to the theoreticalvalues for developing laminar � ow at low Reynolds number and for fully developedturbulent � ow at the higher Reynolds number. The agreement was reasonably good atthe higher Reynolds numbers, but at low Re the results were signi� cantly lower thanexpected. This deviation was thought to be due to � ow bypass in the manifold, and theauthors conclude that the classical relations for the local Nusselt number should also bevalid for microchannels.
Mala and Li [14] studied the � ow of water through microtubes with diametersranging from 50 to 254 l m. Tubes were manufactured from two different materials,stainless steel (SS) and fused silica (FS). Friction factors were generally higher thanexpected from classical theory. For Reynolds numbers below 1,000 and for the largerdiameters tested, the friction factors were approximately in agreement with classical
Dow
nloa
ded
by [
Uni
vers
iti T
ekno
logi
Mal
aysi
a] a
t 10:
27 0
1 O
ctob
er 2
011
162 B. PALM
theory. The deviations increased with decreasing diameter and with increasing Reynoldsnumber. The authors conclude that in microtubes, for Re 1,500, the Blasius equation is
f Blasius 5 0.3164 · Re 0.25 (7)
This is an indication of an earlier transition from laminar to turbulent � ow inmicrotubes as compared to larger-diameter tubes. A diameter dependence of this transitionis also discernible from the experimental data. However, the authors suggest that the earlytransition may also be a result of surface roughness effects.
Flockhart and Dhariwal [15], tested the � ow of water in trapezoidal channels havinghydraulic diameters in the range 50–120 l m. The Reynolds numbers were kept below600 to give laminar � ow. The experimentally determined friction factors were in goodagreement with results of a numerical calculation based on classical theory.
Qu et al. [16] recently presented an investigation of water � ow through trapezoidalsilicon microchannels with hydraulic diameters ranging from 51 to 169 l m. The investi-gated Re numbers were below 1,500. They found the friction factors to be 10% to 40%higher than expected from classical theory.
Possible Explanations for Deviations from Classical Theory
As seen above, the data reported in the literature are inconclusive. Some investiga-tors have reported increased heat transfer and/or pressure drop, while others reported theopposite. To some degree these deviations may be caused by the dif� culties in measuringthe parameters necessary for the theoretical calculation. As noted above, the pressuredrop in laminar � ow is inversely proportional to the diameter to the power of 4, meaningthat a very precise value of the diameter is necessary for determining the friction factor.Also, it could be dif� cult to measure the tube wall temperatures, which are necessary fordetermining the logarithmic mean temperature difference (LMTD) correctly. It should benoted that the Nusselt number in laminar � ow should only be expected to be constantfor “Long” tubes, at isothermal conditions, and if the heat transfer coef� cient is referredto the LMTD.
A second cause for deviations could be entrance effects, i.e., that the experimentalresults are compared to solutions for fully developed � ow, which is not always a goodapproximation. Pressure drop at tube entrances and exits may also have been neglectedin some cases.
A third possible source of deviations, mentioned by some authors, is the relativesurface roughness of the tube surfaces.
Even though some of the deviations may be explained by the rather trivial causesmentioned above, there are also new phenomena which may be of importance due to thesmall scale in microtubes.
Papautsky et al. [17] used a numerical model including micropolar � uid theory tocalculate the normalized friction coef� cient for � ow-in microchannels. The model tookinto account microrotational effects of the molecules and the variation in the apparentviscosity of the � uid close to the wall. It was then compared to experimental results usingwater as the test � uid in the Reynolds number range 1–20. The tested microchannels hadrectangular cross sections with widths ranging from 50 to 600 l m and heights from 20 to30 l m. The friction coef� cients were found to be around 12% higher than expected from
Dow
nloa
ded
by [
Uni
vers
iti T
ekno
logi
Mal
aysi
a] a
t 10:
27 0
1 O
ctob
er 2
011
HEAT TRANSFER IN MICROCHANNELS 163
classical macroscopic theory. However, when the results were compared to the numericalmodel the deviations were much smaller. It was also shown that experimental data fromother authors [18, 19] were well correlated by the numerical model.
Tso and Mahulikar have presented several articles advocating the inclusion of theBrinkman number in the heat transfer correlation for laminar � ow in microchannels[20–23].
Br 5l · u2
m
k · D t(8)
This number re� ects the relative importance of viscous heating to � uid conduction. Asviscous heating is not important in normal � ow through conventional size channels, theBrinkman number is not included in the classical heat transfer correlations. However,the authors point to the fact that the velocity gradients in laminar � ow in microchannelsare extremely high, and that the length-to-diameter ratios may be large in these cases.Through a conventional dimensional analysis [20] they arrive at a correlation of the form
Nu 5 A · Rea · Prb ·dh
c
· Brd (9)
where is a critical dimension for the microchannel. The exponent d is positive forheating of the � uid and negative for cooling. In a later article [23] they report on newexperimental data supporting their earlier proposition. In both studies, they use the ex-ponents of Re and Pr given by Peng and Peterson [9].
Another phenomenon, which has been proposed as responsible for deviations frommacroscopic behavior in liquid � ow, is the electric double-layer (EDL) effect. Yang et al.[24] investigated the effects of the electric double layer and the in� uence of this effect onpressure drop and heat transfer. Based on their model they estimated the friction factorand the Nusselt number for an aqueous solution of low ionic concentration and a wallsurface of high zeta potential. For rectangular channels with the shortest side around20–40 l m it was found that the electrokinetic effects could have signi� cant in� uenceon the friction factor and the Nusselt number. However, it was also noted that for theconditions used in the evaluation of the model, EDL effects should not be important forpressure drop or heat transfer in channels larger than 40 l m.
When considering gas � ow in microchannels it must be recognized that the contin-uum assumption is invalid when the mean free path of the molecules is of the same orderof magnitude as the hydraulic diameter of the channel. This relation could be expressedby the Knudsen number,
Kn 5dh
(10)
At high Knudsen numbers, the assumption of zero velocity at the wall will not bevalid, as there is little interaction between the molecules close to the surface. Slip � owwill then lead to a lower friction factor than expected for larger channels. Beskok andKarniadakis [25] suggested a range of the Knudsen number between 10 3 and 0.1 inwhich slip � ow could be expected, while at lower Knudsen number the � uid could betreated as a continuum and the zero-wall velocity assumption thus should apply.
Other effects may also be present in gas � ow in microchannels. A theoreticalanalysis of the thermal conductivity of the gas in the “wall-adjacent layer” was presented
Dow
nloa
ded
by [
Uni
vers
iti T
ekno
logi
Mal
aysi
a] a
t 10:
27 0
1 O
ctob
er 2
011
164 B. PALM
recently by Li et al. [26]. The analysis is based on a simpli� ed kinetic gas theory assumingrigid-sphere molecules. The result of this analysis is that the thermal conductivity in alayer close to the wall is considerably lower than in the bulk region. Within this regionthe ratio k� kbulk varies from 0.5 at the surface to 1 at a distance of three to � ve times themean free path of the molecules. A similar analysis was presented by the same authorsin an earlier article concerning the viscosity close to the wall [27]. From theses analysesthe Nusselt number in fully developed laminar � ow was deduced. This showed that forcircular tubes a slight reduction in the Nusselt number should be expected at Kn 0.005.Also, the friction factor should be smaller than expected according to classical theory.
Conclusions, One-Phase Flow
In conclusion, there seem to be no general agreement as to what diameters classicaltheory can be applied for determining friction factors and heat transfer coef� cients inmicrochannels. Several authors have concluded that transition from laminar to transitionand turbulent � ow starts at lower Reynolds numbers than expected for larger hydraulicdiameters and that the critical Reynolds number decreases with decreasing hydraulicdiameter. The reported friction factors are both above and below predictions of classicallaminar theory. The friction coef� cient has also been reported to be dependent on theReynolds number. It seems, though, that the deviations are in most cases smaller than6 30%, although deviations of more than 100% have been reported.
For the heat transfer there are several reports indicating slightly higher Nusseltnumbers in turbulent � ow than expected. In laminar � ow both higher and lower Nusseltnumbers have been reported.
Suggested reasons for these deviations are surface roughness effects, entranceeffects, electric double-layer effects, nonconstant � uid properties, two- and three-dimensional transport effects, and slip � ow (for gases). Finally, the deviations in the ex-perimental results may be caused by the dif� culties in accurately determining hydraulicdiameters and � uid and surface temperatures in microchannels. Considering these dif� -culties, the scatter in the results is not surprising.
TWO-PHASE FLOW
Introduction
Heat transfer in two-phase � ow in microchannels has not been studied as extensivelyas single-phase � ow. Especially, the size range below 1 mm has been investigated byonly a few researchers. Most of what has been presented concerns evaporation, and onlyfour reports are known to the author about � ow condensation inside tubes of diametersless than 3 mm.
As noted above, even at these relatively large diameters deviations from largediameter behavior should be expected. The main reasons for this is that surface tensionforces are more dominant and gravity forces less dominant in small-diameter tubes.
Evaporation
Flow boiling heat transfer is often assumed to be the result of two different mech-anisms, nucleate boiling and convective boiling. In general, nucleate boiling is dominant
Dow
nloa
ded
by [
Uni
vers
iti T
ekno
logi
Mal
aysi
a] a
t 10:
27 0
1 O
ctob
er 2
011
HEAT TRANSFER IN MICROCHANNELS 165
at high heat � ux and low vapor quality, while convective boiling is important at highmass � ux and high vapor quality, where nucleate boiling is suppressed. The local heattransfer coef� cient is then calculated as a sum of the two contributions:
hntp 5 (E · hl)
n 1 (F · hnb)n (11)
where hl and hnb are the heat transfer coef� cients for one-phase liquid � ow and for poolboiling respectively. E and F are enhancement and suppression factors. hl in the aboveequation is calculated by, e.g., the Dittus-Boelter equation, while hnb is calculated by apool boiling correlation, e.g., the Cooper [28] correlation.
hnb 5 55 · p0.12 0.2·log10 Rpr · ( log10 p r)
0.55 · M 0.5 · q0.67 (12)
In the nucleate boiling regime the heat transfer coef� cient is thus dependent on theheat � ux and the saturation pressure. In the convective boiling regime heat transfer ismainly in� uenced by the mass � ux and the vapor quality.
The in� uence of channel diameter on the heat transfer coef� cient is not obviousfrom the above correlation. The Pierre correlation for complete evaporation in horizontaltubes [29], which has proved reasonably accurate for conditions common in refrigerationapplications, indicate that, at constant mass � ux, the heat transfer coef� cient is inverselyproportional to the diameter to the power of 0.2, i.e., a slight increase with decreasingdiameter. However, this correlation has not been tested against microchannel data.
When choosing working � uid for two-phase cooling systems it should be recog-nized from the Cooper correlation that � uids with low molar mass and high (reduced)pressure are expected to give the highest heat transfer coef� cients. Such � uids couldalso be expected to have high critical heat � ux [30]. The � uid’s in� uence on the globalenvironment must also be considered.
One of the � rst reports on boiling in narrow tubes was presented by Lazarek andBlack [31]. In their tests, R-113 was evaporated in vertical tubes with a diameter of 3.1mm. Pressure drop, critical heat � ux, and heat transfer coef� cients were measured. It wasfound that heat transfer was relatively independent of vapor fraction but highly dependenton heat � ux, indicating a dominant in� uence of nucleate boiling. They suggested thefollowing correlation for the heat transfer coef� cient:
Nul 5 30 · Re0.857l · Bo0.714 (13)
It should be noted that as Re is proportional, and Bo inversely proportional to the mass� ux, this means that the heat transfer coef� cient is only a weak function of this parameterand mainly dependent on the heat � ux.
Another early report on boiling in narrow channels in between one heated plateand an adiabatic glass plate was given by Fujita et al. [32]. The gap sizes tested were5, 2, 0.6, and 0.15 mm. The channel widths were 30 mm and the heights 30 and 120mm. The test � uid was water at atmospheric pressure. Tests were run with the sides ofthe channel either closed or open. With the sides open it was found that the data for thethree widest channels were well predicted by the equation
Nu 5 16 · (Re1�2)2�3 (14)
Dow
nloa
ded
by [
Uni
vers
iti T
ekno
logi
Mal
aysi
a] a
t 10:
27 0
1 O
ctob
er 2
011
166 B. PALM
where Nu is calculated using the gap width as characteristic length and the liquid thermalconductivity, and Re is de� ned by
Re 5q
D hf g · q t·
S
t·
q
q0(15)
and q0 5 1.6 ´ 106 W/m2. With closed sides this correlation often underpredicted theexperimental results.
For the 0.15-mm channel, most of the surface area was found to be dry and onlythe edges were wetted by liquid.
Aligoodarz and Kenning [33] investigated the behavior of water vapor bubblesduring evaporation in single channels having a cross section of 2 ´ 1 mm. Three sides ofthe channels were heated, while the fourth side was a glass window through which thebubbles could be monitored. The surface temperature at the bottom wall was measuredfrom the color (hue) of a thin layer of thermochromic liquid crystals. Three types of � owregimes were noted: saturated nucleating bubbles, sliding bubbles, and slightly subcooledbubbles. They stated that part of the bubble growth had similarities to the process in poolboiling when a thin liquid � lm evaporates underneath a growing bubble.
Cornwell and Kew [34] used high-speed video to investigate forced convectiveboiling of R-141b inside single tubes of diameters from 1.39 to 3.69 mm. Relating toprevious publications, they stated that there were very few reports in the literature of� ow boiling in channels where the con� nement number, de� ned as
Co 5{ �[g · ( q l q g )]}1�2
dh(16)
is in the range 0.5–10. For this range, they show experimentally that four different � owregimes may occur: isolated bubble (IB), con� ned bubble (CB), annular slug � ow (ASF),and partial dryout (PD). According to the authors, the heat transfer coef� cient calculatedby a traditional pool boiling correlation such as Cooper’s [28] gives the lower limit for allthese regions except for partial dryout. They suggest that the heat transfer coef� cients inthe CB and ASF regimes may be calculated by a fairly simple model, where all thermalresistance is concentrated to the liquid � lm in between the bubble and the channel wall.They also suggest methods of predicting this � lm thickness. Finally, they show that theirmodel is in reasonable agreement with experimental data.
A clear difference is seen in the test results between the larger- and the smaller-diameter tubes. In the larger tubes, the heat transfer coef� cient increases with increasingvapor fraction, whereas with the smaller-diameter tubes, the heat transfer coef� cientdecreases with increasing vapor fraction. This last behavior is thought to be caused bypartial dryout in the smaller tubes.
Tran et al. [35] published a very interesting report on boiling of R-12 and R-113in circular and rectangular channels with hydraulic diameters of 2.4, 2.46, and 2.92 mm.Even though this is at the upper limit of what could be called microtubes, it was found thatthe heat transfer mechanisms deviate substantially from those in larger-diameter tubes.The authors found that at all but the lowest heat � uxes, the heat transfer coef� cientwas independent of vapor quality and of mass � ux. On the other hand, it was heavilydependent on heat � ux and also on the pressure level. This showed clearly that nucleate
Dow
nloa
ded
by [
Uni
vers
iti T
ekno
logi
Mal
aysi
a] a
t 10:
27 0
1 O
ctob
er 2
011
HEAT TRANSFER IN MICROCHANNELS 167
boiling was the dominant heat transfer mechanism. At the lowest heat � uxes (<6–8kW/m2), corresponding to temperature differences less than 2.75° C, there was a cleardependence on the mass � ux but not on heat � ux. The authors concluded that below thistemperature difference forced convection was dominant. The transition between the tworegions was more obvious than expected for larger-diameter tubes and, more important,appeared at lower temperature differences than for larger tubes.
Comparing the circular tube (diameter 2.46 mm) and the rectangular channel (1.7mm ´ 4.06 mm, dh 5 2.4 mm), it was found that the differences in heat transfercoef� cients were very small.
A correlation for the average heat transfer coef� cient (in W/(m2 K) in the nucleateboiling regime ( D t > 2.75° C) was also presented:
h 5 8.4 ´ 10 5 · (Bo2 · Wel)0.3 ·
q l
q v
0.4
(17)
Compared to correlations for larger-diameter tubes, the heat transfer coef� cients wereconsiderably higher.
Xia et al. [36] measured the heat transfer as R-113 boiled at atmospheric pressurebetween two plates forming a vertical narrow channel. The heat � ux, the gap width,and the channel height were varied and the in� uence on heat transfer and critical heat� ux were studied. It was found that there exists an optimum gap size resulting in thehighest heat transfer coef� cients. However, this optimum also depends on the heightof the channel. It was also found that the critical heat � ux is reduced with decreasingchannel size, and that the smaller the gap size, the lower the incipient heat � ux.
Bonjour and Lallemand [37] reported on tests of boiling in between one heatedand one adiabatic surface. The channel height was 120 mm and the gap size ranged from0.5 to 2 mm. Hot-wire anemometry was used to detect the phases. Three � ow regimeswere detected: nucleate boiling with isolated deformed bubbles, nucleate boiling withcoalesced bubbles, and partial dryout. A new � ow regime map was also suggested basedon the Bond number and the ratio between heat � ux and critical heat � ux.
Lin and Kew [38] used a 1-mm vertical tube for tests with R-141b as refrigerant.They found that, for the lower heat � uxes (18–40 kW/m2), the heat transfer coef� cientsincreased with increasing vapor fraction, while for the higher heat � uxes (>60 kW/m2),the trend was opposite. At vapor fractions between 40% and 80% the heat transfercoef� cients were more or less independent of vapor fraction at all but the highest heat� ux (72 kW/m2). In general, the levels of h were in the range 2,000–6,000 W/(m2 K).
Yan and Lin [39] measured heat transfer and pressure drop during evaporationof R-134a in circular tubes of inside diameter 2 mm. They reported that heat transferwas generally higher (30–80%) than expected for an 8-mm-diameter tube (as calculatedby correlations from the literature). At low vapor qualities, the heat transfer coef� cientincreased with increasing heat � ux, while at higher vapor qualities it seemed to be moredependent of mass � ux. The friction factor was found to be fairly constant, varying inthe range 0.03–0.08, decreasing only slightly with increasing Re.
Hapke et al. [40] used infrared thermography to determine the surface temperaturesof a vertical heated tube with 1.5-mm inside diameter in which water was boiling atatmospheric pressure. From these measurements, they were able to calculate the localsurface temperatures on the inside of the tube. These temperatures decreased at the
Dow
nloa
ded
by [
Uni
vers
iti T
ekno
logi
Mal
aysi
a] a
t 10:
27 0
1 O
ctob
er 2
011
168 B. PALM
location of bubble nucleation. They also suggested a correlation for determining thelocation of and the temperature difference at the onset of boiling.
Bao et al. [41] tested R-11 and R-123 boiling in a smooth copper tube with aninternal diameter of 1.95 mm. Heat � uxes were varied from 5 to 200 kW/m2 and mass� uxes from 50 to 1,800 kg/(m2 s). The in� uence of mass � ux, vapor quality, heat � ux,and system pressure on the heat transfer coef� cient was investigated for the two � uids.It was found that the in� uence of mass � ux and vapor quality was very small, whilethat of heat � ux and system pressure was large. These results suggest that the dominantheat transfer mechanism was nucleate boiling. The experimental results were comparedto several � ow boiling correlations, but none of them predicted the experimental data forall conditions. The authors conclude by stating that Cooper’s [28] correlation for poolboiling is in quite good agreement with the experimental data.
Flow patterns, pressure drop, and void fractions in adiabatic two-phase � ow ofwater and air have been studied by Triplett et al. [42, 43]. The tubular test sections haddiameters of 1.09 and 1.49 mm. New � ow pattern maps for microtubes are suggested, andrecommendations for the calculation of void fraction and pressure drop are given. How-ever, it should be noted that the results from these adiabatic tests may not be applicableto the highly dynamic and unstable situation in � ow boiling.
Zhao et al. [44], investigated the � ow boiling of CO2 and R-134a in microchannels(diameter not stated). The heat transfer coef� cient was found to be independent of boththe mass � ux and the heat � ux. This was interpreted as indicating a dominant in� uenceof nucleate boiling, but, simultaneously, a suppression of nucleation at increased vaporfraction. Compared to R-134a, CO2 was found to give twice as high heat transfer coef� -cients at less than half the pressure drop. These differences were attributed to the lowersurface tension and liquid viscosity of CO2. It should be noted that the use of CO2 as aboiling coolant is restricted to low temperatures, as the critical temperature of this � uidis 1 31° C.
Phenomena in Small-Diameter Channels
Peng, with different co-workers, has made extensive studies of one- and two-phase� ow phenomena in very small microchannels, reported in numerous publications. Thesestudies have revealed some extremely interesting phenomena concerning boiling in mi-crochannels.
Peng and Wang [10, 45] and Peng et al. [46] used rectangular ducts with sides0.6 ´ 0.7, 0.4 ´ 0.7, and 0.2 ´ 0.7 mm2, which were heated from three sides while thefourth had a Pyrex glass cover. Deionized water and methanol were used as test � uids.An interesting phenomenon was that no bubbles were seen inside the microchannelseven at high heat � uxes. However, in the manifold, streams of bubbles were seen by theoutlet from the microchannels. Although no bubbles were formed inside the channels, theauthors still found the temperature–heat � ux relation (boiling curve) indicating that theprocess was in the nucleate boiling regime. From these experiments they concluded thatfor bubble nucleation there is a critical minimum space, which they called evaporatingspace. The boiling without visible bubble nucleation was called � ctitious boiling. Theheat transfer coef� cients in this boiling regime seemed to be independent of the � owvelocity and of the subcooling.
Peng et al. [47] reported on continued studies of subcooled boiling in 12 dif-ferent rectangular cannel con� gurations with hydraulic diameters ranging from 0.15 to
Dow
nloa
ded
by [
Uni
vers
iti T
ekno
logi
Mal
aysi
a] a
t 10:
27 0
1 O
ctob
er 2
011
HEAT TRANSFER IN MICROCHANNELS 169
0.343 mm (0.1 ´ 0.3 mm2 to 0.4 ´ 0.3 mm2) using water, methanol, and mixtures ofthese as working � uids. A direct comparison of the in� uence of the channel diameter wasdif� cult to make as the authors used the area of the base plates containing the channelswhen de� ning the heat � ux. The pure � uids were found to give the highest heat transfercoef� cients.
Peng et al. [48] presented an analytical model explaining the phenomenon of � c-titious boiling reported in previous articles. They started by stating that if the channelsize is smaller than the evaporating space, then � ctitious boiling may be induced. Thephysical explanation to this may be that “internal evaporation and bubble growth havenot yet been realized or there may exist countless microbubbles within the liquid thatcannot be visualized by ordinary means.” The authors then presented their analysis, basedon thermodynamic phase stability theory, and arrived at a dimensionless parameter, Nmb,which gives a condition for nucleation in microchannels:
Nmb 5hf g · av
c · · (v 9 9 v 9 ) · q · dh(18)
(c is an empirical constant)
If Nmb 1 nucleation should be expected, while at larger values of Nmb � ctitiousboiling will occur. The � uid is then in a “highly non-equilibrium state with an exceptionalcapability to absorb, transfer and transport thermal energy.” A correlation for the superheatnecessary for nucleation is also presented:
D tsup4 · A · ts · (v 9 9 v 9 ) ·
h f g · dh(19)
[A ( 280) is an empirical constant]
Fictitious boiling has also been explained in terms of an interphase propagationand superposition model by Hu et al. [49].
Recently, Peng et al. [50] reported on an investigation of the in� uence of pressureperturbations on the development of high-energy clusters in a superheated liquid. Theyproposed that the pressure wave from the initial growth of a cluster could be re� ected inthe walls of a microchannel and thereby suppress the growth of the emerging bubble. Acriterion for the development of � ctitious boiling would then be
L < 0.5 · c · s c (20)
where L is the scale of the microchannel, c is the speed of sound, and s c is the timerequired for the initial development phase of the bubble embryo ( 10 l s).
Conclusions, Evaporation
From the information above, it may be concluded that � ow boiling is governedmainly by nucleate boiling mechanisms in the diameter range below ~ 4 mm. A poolboiling correlation such as Cooper’s could be expected to give reasonable but conservativevalues for the heat transfer coef� cient as long as the critical heat � ux is not reached.
Dow
nloa
ded
by [
Uni
vers
iti T
ekno
logi
Mal
aysi
a] a
t 10:
27 0
1 O
ctob
er 2
011
170 B. PALM
At diameters below ~ 1 mm the data of Peng and co-workers show that a newphenomenon, � ctitious boiling, could be expected. In this boiling mode no bubbles aredetected, but the heat exchange and temperature differences are as in nucleate boiling.
CONDENSATION
Very little information is found in the literature on condensation in microtubes.A reason for the lower interest for condensation as compared to evaporation is that themain application for two-phase micro heat exchangers is for cooling of electronics. Forthis application the evaporator is placed in contact with the electronic components andis therefore the more critical part.
Condensation heat transfer is governed by the thickness of the liquid � lm at thecooled wall. In two-phase � ow condensation there are two mechanisms acting to decreasethe � lm thickness: gravity and shear stress. In general, gravity should be expected tohave less in� uence as the channel diameter is reduced. Shear stress could be expected toincrease with decreasing diameter. Also, surface tension forces could be of importance.This is clearly seen from the Laplace equation for a cylindrical interphase,
p v p l 5r
(21)
If the tube radius is small there will be a noticeable pressure difference betweenthe vapor and the liquid phases, which will in� uence the saturation temperature and alsomight tend to increase the � lm thickness.
Yang and Webb [51, 52] investigated heat transfer and pressure drop as R-12condensed in two different � at extruded aluminum tubes. These tubes had external di-mensions 16 ´ 3 mm and a wall thickness of 0.5 mm. At the inside the tubes were dividedinto four channels by thin longitudinal walls. The difference between the two tubes wasthat one had smooth internal surfaces while the other had longitudinal micro� ns, 0.2 mmin height.
The tubes were � rst tested in one-phase � ow and the results were compared topredictions of the Petukhov equation using the total surface area as a base for the heattransfer coef� cient. The agreement was very good, especially for the plain tube.
In condensation it was found that the heat transfer coef� cient increased with in-creasing vapor quality, increasing mass � ux, and with increasing heat � ux. The resultswere compared to predictions by the following correlation by Akers et al. [53]:
h · d
kl5 0.0265 · Re0.8
eq · Pr1.3l Reeq > 50,000 (22)
The agreement was good for the plain tube at low mass � ux (400 kg/m2 s) but10–20% lower than predicted at higher mass � ux (1,000 kg/m2 s). There was also aslight dependence on heat � ux not accounted for in the correlation. For the micro� ntube, the enhancement ratio hmicro� n � hplain was found to be higher than the surfacearea ratio Amicro� n �A plain . The additional enhancement was thought to be due to surfacetension acting to pull the liquid into the valleys in between the � ns, thereby reducing� lm thickness on the � n tips.
Dow
nloa
ded
by [
Uni
vers
iti T
ekno
logi
Mal
aysi
a] a
t 10:
27 0
1 O
ctob
er 2
011
HEAT TRANSFER IN MICROCHANNELS 171
The friction factors in one-phase � ow were compared to the Blasius equation andfound to be 14% higher (plain tube) and 36% higher (micro� n tube) than predicted. Fortwo-phase � ow, the pressure drops were compared to the Martinelli two-phase multipliermodel and to a correlation proposed by Akers et al. [53]. The Martinelli method did notcorrelate the data well, while the comparison with Akers et al. correlation was very good.Akers et al. de� ned the friction factor by
f 5D p
G2eq �2 q l
·dh
4 · L5
D p
Re2eq · l 2
l �2 q l·
d3h
4 · L(23)
where
G eq 5 G ·
"(1 xm) 1 xm ·
q l
q v
0.5#
(24)
The two-phase friction factor is then calculated from the single-phase friction factorby the relation
f
f l5 0.435 · Re0.12
eq (25)
Yan and Lin [58] measured heat transfer and pressure drop of R-134a condensingin an array of 28 tubes with 2-mm inner diameter connected in parallel. The results werecompared to correlations from the literature and new correlations for the heat transfercoef� cient and the friction factor were proposed.
The heat transfer coef� cients were compared to average values for a long, 8-mmtube according to Eckels and Pate [54] and were found to be lower than expected at vaporfractions below about 0.4 and higher than expected above this value. When averaged overthe complete range of vapor fractions, the values were about 10% higher than expectedfrom the correlation. The following equation was proposed based on the authors’ results:
h · d
kl· Pr 0.33
l · Bo0.3 · Re 5 6.48 · Re1.04eq (26)
The friction factor, de� ned as by Akers [Eq. (23)], was correlated by the equation
f tp 5 498.3 · Re 1.074eq (27)
Wang and Du [55] recently proposed an analytical model of condensation in tubes.They compared the results of the model with measurements conducted with four coppertubes with inside diameters 1.94, 2.8, 3.95, and 4.98 mm at different inclination anglesusing water as test � uid. It was found that the inclination angle had very little in� uence onheat transfer in the smallest diameter tube, but that this in� uence became more obviousin the larger tubes. The Reynolds numbers had opposing effects on the Nusselt number,depending on the size of the tube. In the two smallest tubes Nu increased with Re, whilethe lowest Re gave the highest Nu in the two larger tubes. This shows that gravity ismore important in large-diameter tubes, where strati� cation may lead to increased heattransfer.
Dow
nloa
ded
by [
Uni
vers
iti T
ekno
logi
Mal
aysi
a] a
t 10:
27 0
1 O
ctob
er 2
011
172 B. PALM
In general, the Nusselt numbers were approximately the same at equal vapor qualityand equal Reynolds number in all tubes, ranging from about 150 at the tube intlet to 50at the outlet.
That surface tension forces may have a large in� uence on condensation in mi-crochannels was also shown by Tengblad and Palm [56, 57]. In this test, vertical, square,2 ´ 2 mm channels, connected at the top and the bottom, without forced convection,were used for condensing different refrigerants in a closed-loop thermosyphon. The heattransfer coef� cients were compared to the Nusselt correlation for vertical plates. It wasfound that the measured heat transfer coef� cients were at least three times higher thanexpected from the Nusselt theory. The increase was thought to be the result of surfacetension forces attracting the liquid to the corners of the channel, thereby decreasing the� lm thickness on the main part of the walls and also facilitating the drainage of liquidthrough the streams forming in the corners.
Conclusions, Condensation
As a conclusion it may be stated that very little data are available in the literatureconcerning condensation inside microchannels. For forced-convection condensation thecorrelations of Akers et al. for heat transfer and pressure drop seem to be in goodagreement with experimental data for 2-mm channels. No information is available forsmaller channels at this time. Surface tension effects should be expected to be moredominant, while the in� uence of gravity is expected to be smaller than for larger tubes.
CONCLUDING REMARK
The literature concerning heat transfer and pressure drop in one- and two-phase� ow in microchannels has been reviewed. It can be concluded that there are still manyopen questions to be answered before reliable design tools are available in the formof correlating equations for heat transfer and pressure drop. More research is thereforeneeded in this relatively new and exciting � eld.
REFERENCES
1. J. Goodling, Microchannel Heat Exchangers, SPIE Vol 1997 High Heat Flux Enginering II,pp. 66–82, 1993.
2. A. B. Duncan and G. P. Peterson, Review of Microscale Heat Transfer, ASME Appl. Mech.Rev., vol. 47, no. 9, pp. 397–428, 1994.
3. X. F. Peng and B. X. Wang, Liquid Flow and Heat Transfer in Microchannels with/withoutPhase Change, Proc. 10th Int. Heat Transfer Conf., Brighton, England, 14–18 August 1994,in Heat Transfer 1994, Taylor & Francis, Washington, DC, vol. 1 (Sk-11), pp. 159–177, 1994.
4. X. F. Peng and B. X. Wang, Forced-Convection and Boiling Characteristics in Microchannels,Proc. 11th Int. Heat Transfer Conf., Kyongyu, Korea, vol. 1, pp. 371–390, 1998.
5. D. K. Bailey, T. A. Ammel, R. O. Warrington, and T. I. Savoie, Single Phase Forced Convec-tion Heat Transfer in Microgeometries—A Review, IECEC Conference, ES-396, Orlando, FL,ASME, 1995.
6. D. B. Tuckerman and R. F. W. Pease, High Performance Heat Sinking for VLSI, IEEE ElectronDev. Lett. EDL-2, pp. 126–129, 1981.
Dow
nloa
ded
by [
Uni
vers
iti T
ekno
logi
Mal
aysi
a] a
t 10:
27 0
1 O
ctob
er 2
011
HEAT TRANSFER IN MICROCHANNELS 173
7. P. Wu and W. A. Little, Measurement of Friction Factors for the Flow of Gases in Very FineChannels Used for Microminiature Joule-Thompson Refrigerators, Cryogenics, vol. 23, no. 5,pp. 273–277, 1983.
8. P. Wu and W. A. Little, Measurement of the Heat Transfer Characteristics of Gas Flow inFine Channel Heat Exchangers Used for Microminiature Refrigerators, Cryogenics, vol. 24,pp. 415–420, 1984.
9. X. F. Peng and G. P. Peterson, Forced Convection Heat Transfer of Single-Phase BinaryMixtures through Microchannels, Exp. Thermal Fluid Sci., vol. 12, pp. 98–104, 1996.
10. X. F. Peng and B. X. Wang, Forced Convection and Flow Boiling Heat Transfer for LiquidFlowing through Microchannels, Int. J. Heat Mass Transfer, vol. 36, no. 14, pp. 3421–3427,1993.
11. B. X. Wang and X. F. Peng, Experimental Investigation of Liquid Forced Convection HeatTransfer through Microchannels, Int. J. Heat Mass Transfer, vol. 37 (suppl. 1), pp. 73–82,1994.
12. J. M. Cuta, C. E. McDonald, and A. Shekarriz, Forced Convection Heat Transfer in ParallelChannel Array Microchannel Heat Exchanger, ASME PID-Vol. 2/HTD-Vol. 338, Advances inEnergy Ef� ciency, Heat/Mass Transfer Enhancement, pp. 17–23, 1996.
13. T. M. Harms, M. J. Kazmierczak, and F. M. Gerner, Developing Convective Heat Transfer inDeep Rectangular Microchannels, Int. J. Heat Fluid Flow, vol. 20, pp. 149–157, 1999.
14. G. M. Mala and D. Li, Flow Characteristics of Water in Microtubes, Int. J. Heat Fluid Flow,vol. 20, pp. 142–148, 1999.
15. S. M. Flockhart and R. S. Dhariwal, Experimental and Numerical Investigation into the FlowCharacteristics of Channels Etched in (100) Silicon, Trans. ASME: J. Fluids Eng., vol. 120,pp. 291–295, 1998.
16. W. Qu, G. M. Mala, and D. Li, Pressure-Driven Water Flows in Trapezoidal Silicon Microchan-nels, Int. J. Heat Mass Transfer, vol. 43, pp. 353–364, 2000.
17. I. Papautsky, J. Brazzle, T. Ammel, and A. B. Frazier, Laminar Fluid Behavior in MicrochannelsUsing Micropolar Fluid Theory, Sensors and Actuators, vol. 73, pp. 101–108, 1999.
18. X. N. Jiang, Z. Y. Zhou, J. Yao, Y. Li, and X. Y. Ye, Micro-� uid Flow in Microchannel, Proc.Transducers ’95, Stockholm, Sweden, pp. 317–320, 25–29 June 1995.
19. P. Wilding, M. A. Shoffner, and L. J. Kircka, Manipulation and Flow of Biological Fluids inStraight Channels Micromachined in Silicon, Clin. Chem., vol. 40, pp. 43–47, 1994.
20. C. P. Tso and S. P. Mahulikar, The Use of the Brinkman Number for Single Phase Forced Con-vective Heat Transfer in Microchannels, Int. J. Heat Mass Transfer, vol. 41, no. 12, pp. 1759–1769, 1998.
21. C. P. Tso and S. P. Mahulikar, Proc. 2nd IEEE Electronics Packaging Technology Conf.,Singapore, pp. 126–132, 1998.
22. C. P. Tso and S. P. Mahulikar, The Role of the Brinkman Number in Analysing Flow Transitionsin Microchannels, Int. J. Heat Mass Transfer, vol. 42, pp. 1813–1833, 1999.
23. C. P. Tso and S. P. Mahulikar, Experimental Veri� cation of the Role of Brinkman Number inMicrochannels Using Local Parameters, Int. J. Heat Mass Transfer, vol. 43, pp. 1837–1849,2000.
24. C. Yang, D. Li, and J. H. Hasliyah, Modeling Forced Liquid Convection in Rectangular Mi-crochannels with Electrokinetic Effects, Int. J. Heat Mass Transfer, vol. 41, pp. 4229–4249,1998.
25. A. Beskok and G. E. Karniadakis, Simulation of Slip-Flows in Complex Micro-geometries,ASME Proc. DSC, vol. 40, pp. 355–370, 1992.
26. J.-M. Li, B.-X. Wang, and X.-F. Peng, Wall-Adjacent Layer Analysis for Developed-FlowLaminar Heat Transfer of Gases in Microchannels, Int. J. Heat Mass Transfer, vol. 43, pp. 839–847, 2000.
Dow
nloa
ded
by [
Uni
vers
iti T
ekno
logi
Mal
aysi
a] a
t 10:
27 0
1 O
ctob
er 2
011
174 B. PALM
27. J.-M. Li, B.-X. Wang, and X.-F. Peng, The Wall Effect for Laminar Flow through Microtubes,Proc. Int. Centre for Heat and Mass Transfer (ICHMT) Symp. on Molecular and MicroscaleHeat Transfer in Material Processing and Other Applications, Yokohama, Japan, pp. 55–65,1–5 Dec. 1996.
28. M. G. Cooper, Saturation Nucleate Boiling—A Simple Model, Proc. 1st UK Natl. Conf. onHeat Transfer, vol. 2, pp. 785–793, 1984.
29. B. Pierre, Värmeövergången vid kokande köldmedier i horisontella rör, Kylteknisk tidskrift,no. 3, June 1957 (in Swedish). See also ASHRAE Handbook, Fundamentals, p. 4.7, 1997.
30. B. Palm and R. Khodabandeh, Optimum Design of Two Phase Thermosyphon Systems forCooling of Electronics, Proc. InterPack’99, Hawaii, June 1999. In ASME Advances in Elec-tronic Packaging 1999, EEP-Vol. 26-2, pp. 491–498, 1999.
31. G. M. Lazarek and S. H. Black, Evaporative Heat Transfer, Pressure Drop and Critical HeatFlux in a Small Vertical Tube, Int. J. Heat Mass Transfer, vol. 25, no. 7, pp. 945–960, 1982.
32. Y. Fujita, H. Ohta, S. Uchida, and K. Nishikawa, Nucleate Boiling Heat Transfer and CriticalHeat Flux in Narrow Space between Rectangular Surfaces, Int. J. Heat Transfer, vol. 31, no. 2,pp. 229–239, 1988.
33. M. R. Aligoodarz and D. B. R. Kenning, Vapour Bubble Behaviour in a Single Narrow Channel,IMechE, C510/076/95, pp. 273–276, 1995.
34. K. Cornwell and P. A. Kew, Evaporation in Microchannel Heat Exchangers, IMechE, C510/117/95, pp. 289–293, 1995.
35. T. N. Tran, M. W. Wambsganss, and D. M. France, Small Circular- and Rectangular-ChannelBoiling with Two Refrigerants, Int. J. Multiphase Flow, vol. 22, no. 3, pp. 485–498, 1996.
36. C. Xia, W. Hu, and Z. Guo, Natural Convection Boiling in Vertical Rectangular NarrowChannels, Exp. Thermal Fluid Sci., vol. 12, pp. 313–324, 1998.
37. J. Bonjour and M. Lallemand, Flow Patterns during Boiling in a Narrow Space between TwoVertical Surfaces, Int. J. Multiphase Flow, vol. 24, pp. 947–960, 1998.
38. S. Lin and P. A. Kew, Characteristics of Two-Phase Flow and Heat Transfer in Small Tubes,IMechE, C565/040/99, 1999.
39. Y.-Y. Yan and T.-F. Lin, Evaporation Heat Transfer and Pressure Drop of Refrigerant R134ain a Small Pipe, Int. J. Heat Mass Transfer, vol. 41, pp. 4183–4194, 1998.
40. I. Hapke, H. Boye, and J. Schmidt, Onset of Nucleate Boiling in Minichannels, Int. J. ThermalSci., vol. 39, pp. 505–513, 2000.
41. Z. Y. Bao, D. F. Fletcher, and B. S. Haynes, Flow Boiling Heat Transfer of Freon R11 andHCFC123 in Narrow Passages, Int. J. Heat Mass Transfer, vol. 43, pp. 3347–3358, 2000.
42. 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.
43. K. A. Triplett, S. M. Ghiaasiaan, S. I. Abdel-Khalik, and D. L. Sadowski, Gas-Liquid Two-Phase Flow in Microchannels, Part II: Void Fraction and Pressure Drop, Int. J. MultiphaseFlow, vol. 25, pp. 395–410, 1999.
44. Y. Zhao, M. Molki, M. M. Ohadi, and S. V. Dessiatoun, Flow Boiling of CO2 in Microchannels,ASHRAE Trans., vol. 106, pt. 1, DA-00-2-1, 2000.
45. X. F. Peng and B. X. Wang, Cooling Characteristics with Microchanneled Structures, J. En-hanced Heat Transfer, vol. 1, no. 4, pp. 315–326, 1994.
46. X. F. Peng, B. X. Wang, G. P. Peterson, and H. B. Ma, Experimental Investigation of HeatTransfer in Flat Plates with Rectangular Microchannels, Int. J. Heat Mass Transfer, vol. 38,no. 1, pp. 127–137, 1995.
47. X. F. Peng, G. P. Peterson, and B. X. Wang, Flow Boiling of Binary Mixtures in MicrochanneledPlates, Int. J. Heat Mass Transfer, vol. 39, no. 6, pp. 1257–1264, 1996.
48. X. F. Peng, H. Y. Hu, and B. X. Wang, Boiling Nucleation during Liquid Flow in Microchan-nels, Int. J. Heat Mass Transfer, vol. 41, no. 1, pp. 101–106, 1998.
Dow
nloa
ded
by [
Uni
vers
iti T
ekno
logi
Mal
aysi
a] a
t 10:
27 0
1 O
ctob
er 2
011
HEAT TRANSFER IN MICROCHANNELS 175
49. H. Y. Hu, G. B. Peterson, X. F. Peng, and B. X. Wang, Interphase Fluctuation Propagation andSuperposition Model for Boiling Nucleation, Int. J. Heat Mass Transfer, vol. 41, pp. 3483–3489, 1998.
50. X. F. Peng, D. Liu, D. J. Lee, Y. Yan, and B. X. Wang, Cluster Dynamics and FictitiousBoiling in Microchannels, Int. J. Heat Mass Transfer, vol. 43, pp. 4259–4265, 2000.
51. C.-Y. Yang and R. L. Webb, Condensation of R-12 in Small Hydraulic Diameter ExtrudedAluminum Tubes with and without Micro-� ns, Int. J. Heat Mass Transfer, vol. 39, no. 4,pp. 791–800, 1996a.
52. C.-Y. Yang and R. L. Webb, Friction Pressure Drop of R-12 in Small Hydraulic DiameterExtruded Aluminum Tubes with and without Micro-� ns, Int. J. Heat Mass Transfer, vol. 39,no. 4, pp. 801–809, 1996.
53. W. W. Akers, H. A. Deans, and O. K. Crosser, Condensation Heat Transfer within HorizontalTubes, Chem. Eng. Prog. Symp. Ser., vol. 55, no. 29, pp. 171–176, 1959.
54. S. J. Eckels and M. B. Pate, An Experimental Comparison of Evaporation and CondensationHeat Transfer Coef� cients for HFC-134a and CFC-12, Int. J. Refrig., vol. 14, pp. 70–77, 1991.
55. B.-X.Wang and X.-Z. Du, Study on Laminar Film-wise Condensation for Vapor Flow in anInclined Small/Mini-Diameter Tube, Int. J. Heat Mass Transfer, vol. 43, pp. 1859–1868, 2000.
56. N. Tengblad and B. Palm, Flow Boiling and Film Condensation Heat Transfer in NarrowChannels of Thermosiphons for Cooling of Electronic Components, Proc. Eurotherm, Sem.No. 45, Leuven, Belgium, September 1995.
57. N. Tengblad and B. Palm, External Two-Phase Thermosiphons for Cooling of Electronic Com-ponents, Int. J. Microcircuits Electronic Packaging, vol. 19, no. 1, pp. 22–29, 1996.
58. Y.-Y. Yan and T.-F. Lin, Condensation Heat Transfer and Pressure Drop of Refrigerant R-134ain a Small Pipe, Int. J. Heat Mass Transfer, vol. 42, pp. 697–708, 1999.
Dow
nloa
ded
by [
Uni
vers
iti T
ekno
logi
Mal
aysi
a] a
t 10:
27 0
1 O
ctob
er 2
011