flow characteristics of water in straight and serpentine

7/27/2019 Flow Characteristics of Water in Straight and Serpentine

1/8

Flow characteristics of water in straight and serpentinemicro-channels with miter bends

Renqiang Xiong *, Jacob N. Chung

Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611, USA

Received 1 March 2006; received in revised form 13 June 2006; accepted 23 August 2006

Abstract

Flow characteristics of pressure-driven de-ionized water were investigated experimentally in straight and serpentine micro-channelswith miter bends. The micro-channels had rectangular cross-sections with hydraulic diameters of 0.209 mm, 0.395 mm and 0.549 mm.To evaluate bend loss coefficient in the serpentine micro-channel and micro-scale size effect on it, the additional pressure drop due tothe miter bend must be obtained. This additional pressure drop can be achieved by subtracting the frictional pressure drop in the straightmicro-channel from the total pressure drop in the serpentine micro-channel. Since currently there still has a debate on the relationshipbetween the friction factor andRe number in the straight micro-channel, the frictional pressure drop had to be obtained experimentallyhere. Three groups of micro-channels were fabricated to remove the inlet and outlet losses. The experimental results show that after con-sidering the measurement uncertainties the experimental Poiseuille number can be well predicted by the conventional laminar incom-pressible flow theory when Re number is less than some value around 1500, the discrepancy observed by the former researchers canbe attributed to not accounting for the additional pressure drop in the entrance region. The onset of transition to turbulence mightbe at 15001700. For serpentine micro-channels, the additional pressure drop can be divided into two regions. One is Re< 100. It is verysmall since no circulation exists. The other one isRelarger than some value in 100200. At this time the circulation appears and developsat the inner and outer wall of the bend. The additional pressure drop increases sharply with Re number. The bend loss coefficient wasobserved to decrease and tend to be a constant with decreasing Re number. It is found to be larger than the predicted value for macro-channel turbulent flow and related with the channel size when flow separation appears, namely Re > 100200. 2006 Elsevier Inc. All rights reserved.

Keywords: Straight and serpentine micro-channels; Miter bends; Poiseuille number; Additional pressure drop; Bend loss coefficient

1. Introduction

Recently, there has been a growing interest to developmicroscale devices that can manipulate and transport rela-

tively small volumes of fluids. These devices have applica-tions in many areas of engineering, including propulsionand power generation of micro air vehicles and micro sat-ellites[1]. The recent surge of microfluidic devices requiresa good knowledge of flow characteristics in micro-channelsincluding straight and serpentine micro-channels for opti-mal design.

Flow characteristics in circular and non-circular macro-ducts with curved bends have been extensively studied[24]in the past years. However, there were limited literatureson single phase flow characteristics in the channels with miter

bends in the past. Streeter[5] reported the bend loss coeffi-cient for miter bend was taken to be around 1.1 for engineer-ing applications, which was usually for turbulent flow.Yamashita et al.[6,7]and Kushida et al.[8]studied three-dimensional flow and heat transfer in miter-bend experimen-tally and numerically. They found a decreasing trend of thebend loss coefficient with Re number in laminar and turbu-lent flow region and analyzed the effects ofRe number andaspect ratio on the flow structures. Though significant atten-tion has been paid to the flow in macro-systems with bends,research on flow characteristics in micro-systems with bends

0894-1777/$ - see front matter 2006 Elsevier Inc. All rights reserved.

doi:10.1016/j.expthermflusci.2006.08.006

* Corresponding author. Tel.: +1 3528703978.E-mail address:[email protected](R. Xiong).

www.elsevier.com/locate/etfs

Experimental Thermal and Fluid Science 31 (2007) 805812
mailto:[email protected]:[email protected]


2/8

has recently been started. In most practical applicationsthe micro-channels are not straight due to required turnsand sometimes it is complicated and expensive to keepthe micro-channel straight. Lee et al. [9] researched onthe gas flow in micro-channels having the dimensions20 1 5810lm3 with bends of miter, curved and double-

turn. They found the flow rate through the channel withthe miter bend was the lowest at a certain inlet pressureand the largest drop was found in the miter bend with thelowest flow rate. They also found the secondary flow coulddevelop in micro-channels, contrary to expectations. Afterliterature review, it can be seen that the experimental workof liquid flow in serpentine micro-channels with miter bendsand the micro-scale size effect on flow characteristics havenever been reported before.

As we know, the additional pressure loss due to themiter bend in serpentine channels was usually related withthe flow separation and reattachment around the bend. Toevaluate the bend loss coefficient, the additional pressuredrop must be achieved. It can be calculated by subtractingthe frictional pressure drop of straight micro-channels fromthe total serpentine micro-channel pressure drop. Hence,the issue of frictional pressure drop in straight micro-chan-nels was involved in this work too.

For recently 15 years, many scientists have publishednumerous papers on the flow characteristics in straightmicro-channels. Some of them found flow characteristicsin the straight micro-channel were quite different withthose predicted by the conventional laminar flow theory.One of the important flow characteristics was the relation-ship between the friction factor and Re number. For liquid

flow in straight micro-channels, an increase of friction

factor withRenumber was found by the scientists includingWu and Little [10], Peng and Peterson[11], Mala and Li[12], Papautsky et al. [13], Qu et al.[14], Pfund et al.[15],and Li et al. [16]. Some of them attributed it to surfaceroughness effect or the early transition to turbulent flowin straight micro-channels[17,12,14,18,19]. However, there

were some other scientists finding general agreementwith theoretical macroscale prediction for friction factorincluding Wilding et al. [20], Xu et al. [21], Judy et al.[22], Wu and Cheng [23], Hetsroni et al. [24], and Kohlet al.[25]. They attributed the deviation from the theoreti-cal prediction in the previous literatures to the size andmeasurement uncertainties. Hence, the relationshipbetween the friction factor and Re number in straightmicro-channels is not clear yet. The frictional pressure dropin straight micro-channels cannot be calculated by auniversal formulation and need to be achieved experimentallyhere.

In this work, three groups of micro-channels were fabri-cated. Each group has three micro-channels with the samesize: straight long, straight short and single serpentine withmiter bends. The straight long and straight short micro-channels were used to achieve the reliable frictional pres-sure drop in straight micro-channels, and the serpentinemicro-channels were used to get the additional pressuredrop due to the miter bend. The main objective of thisstudy is to achieve this additional pressure drop and bendloss coefficient to evaluate flow characteristics in serpentinemicro-channels, and compare it with the bend loss coeffi-cient in macro-channels. The Poiseuille number for straightmicro-channels can also be achieved experimentally and

compared with the previous conclusions.

Nomenclature

A cross-section area [m2]C coefficient in Eq.(8)d distance between successive bends [mm]

Dh hydraulic diameter [mm]f fraction factorfapp apparent friction factorg gravitational acceleration [m/s2]K pressure drop defectKb bend loss coefficientL length of micro-channels [mm]Ld entrance lengthN number of miter bendsP pressure [Pa]Q flow rate [ml/min]Re Reynolds numberS depth of micro-channels [mm]

U mean velocity [m/s]W width of micro-channels [mm]x the distance to the channel beginningx+ dimensionless entrance length

Greek symbols

D variable differencea aspect ratiod

standard deviationl viscosity [kg/m s]q density [kg/m3]

Subscripts

b miter benddev developing and developed flowexp experimental resultfd fully developedio inlet and outletl long straight micro-channels serpentine micro-channelsh short straight micro-channel

806 R. Xiong, J.N. Chung / Experimental Thermal and Fluid Science 31 (2007) 805812
http://-/?-http://-/?-


3/8

2. Experimental apparatus

Fig. 1(a)(d) shows the photographs of straight and ser-pentine micro-channels and schematic of the straight andserpentine micro-channel used in this work. The micro-channel was laser etched in a silicon plate and then a Pyrex

thin cover glass plate was anodically bonded on the top ofthe plate. The micro-channel plates have two dimensions of30 12 2 mm3 (straight long and serpentine) and 1112 2 mm3 (straight short). Two small connection tubeswhich can be inserted into the inlet and outlet assembly

were connected with the small reservoirs. Each of the ser-pentine micro-channels had five straight micro-channelswith the same size and eight miter bends. A microscope(Olympus BX50), a 10 objective lens and a CCD camerawith pixel size 6.45lm were used to measure the dimen-sions of the micro-channels rectangular cross-sections,

which were listed inTable 1.Fig. 2shows schematic and 3-D assembly drawing of theexperimental apparatus used to investigate the pressure-driven de-ionized water flow in straight and serpentinemicro-channels. It includes a syringe infusion pump(Cole-Parmer Instrument), 60 ml syringe (Mcmaster),micro-filter (Swagelok), pressure transducers (Kavlico),straight and serpentine micro-channel test sections andcomputerized data acquisition system. The de-ionizedwater at the flow rate from 0.1 ml/min to 70 ml/min, whichcan be set on the panel of the infusion pump with an accu-racy of 0.5%, was driven to the micro-channel testsection. The 2lm micro-filter can remove any particles or

bubbles which may block the micro-channel before theflow enters into the test section. Owing to the unavailabilityof appropriate internal pressure sensors which would allowin situ measurements, two pressure transducers with 0.5% FS accuracy were installed at the inlet and outlet ofthe micro-channel to measure the upstream and down-stream pressure and then sent to the data acquisition sys-tem. To get the accurate pressure at the upstream, twopressure transducers with different measurement rangewere used. The one with large measurement range (0150 PSI) was used for smaller micro-channels/larger flowrates, and the other one with small range (015 PSI) were

used for larger micro-channels/smaller flow rates. The datastarted recording when the pressures did not change heav-ily for some time, which can be considered as steady state.The test sections were placed horizontally, and all experi-ments were conducted at room temperature.

3. Data reduction and uncertainty analysis

With the flow rate Q, hydraulic diameter Dh, cross-sec-tion area A, channel length L, frictional pressure dropDP and additional pressure drop DPb due to the miterbend, the Poiseuille number fRe and bend loss coefficientKb can be calculated by using the following equations:

fRe2DPD2hA

DLlQ 1

KbDPb=qg

U2=2gDPbA

2

2qQ2 2

For fully developed laminar flow in rectangular channelswith channel aspect ratio a, the theoretical prediction offriction factor was report by Shah and London [26] andexpressed as

fRe 9611:3553a1:9467a2 1:7012a3

0:9564a4

0:2537a5

3

Fig. 1. (a) Photograph of a group of micro-channels (Dh= 0.209 mm). (b)Schematic of the straight micro-channel. (c) Photograph of serpentine

micro-channels. (d) Schematic of the serpentine micro-channel.

R. Xiong, J.N. Chung / Experimental Thermal and Fluid Science 31 (2007) 805812 807


4/8

For the current micro-channels, the aspect ratio is from 0.9to 0.97, so all of the theoretical Poiseuille numbers arearound 57. This empirical equation can approximate the

two-dimensional exact solution for the fully developed fric-tion factor within 0.05%. However, the current micro-channels may be not long enough for the flow to becomefully developed under laminar flow conditions. Since forlaminar flow in a rectangular channel, the length of thedeveloping flow in the entrance region was approximatedby[26]:

Ld 0:060:07a0:04a2ReDh 4

So for near-square channels, the entrance length is around0.09ReDh. SinceL/Dhfor the current channels is from 6.74to 113, the flow may still be developing at relatively mod-

erate and high Reynolds numbers. The pressure drop from

the beginning of the channel to a location x is given by(Kakac et al.[27]):

DPdev fRefdx KxqU2

2 5

x x

Re Dh6

where K(x) is the pressure drop defect given by

Kx fappRe fRefdx 7

fappRe 4 3:44

x0:5K1=4x fRefd=4 3:44=x

0:5

1 Cx2

( )

8

wherefappis apparent friction factor. For the current chan-

nels, C= 2.93 10

4. The pressure drop defect K(x) will

Table 1Dimensions of micro-channels

Channel no. Width W 2 lm Depth S 2 lm Hydraulic diameterDh (mm) Total length of the micro-channelsL 0.3 (mm)

Long L l Short Lsh Serpentine Ls

Channel 1 213 206 0.209 23.6 4.1 118Channel 2 402 388 0.395 23.7 4.2 118

Channel 3 579 522 0.549 23.6 4.0 119

Fig. 2. Schematic of experimental apparatus.



5/8

begin at a value of 0 and increase to some fully developedconstant valueK(1) which has a dependence upon channelaspect ratio for rectangular channels. Eq. (9) determinesthe fully developed K(1) for a rectangular channel withan accuracy of 0.04%.

K1 0:67961:2197a 3:3089a2 9:5921a3

8:9089a4 2:9959a5 9

So the pressure drop for the straight short and straight longchannel can be expressed as

DPsh DPio DPdev x Lsh 10

DPl DPio DPdev x Ll 11

where DPio is the inlet and outlet losses from changing intubing diameter and tees. Straight short and straight longmicro-channels have the same channel size but differentchannel length. Since the inlet and outlet pressure lossesare proportional to U2, the inlet and outlet losses are thesame for both lengths of the channels under a certain Renumber since both have two ends placed in the same inletand outlet assembly.DPsh and DPl are the measured pres-sure drop for the straight short and straight long channelrespectively. Hence, the experimental fully developedPoiseuille number is calculated by

fReexp DPl DPsh

qU2=2 KLl KLsh

ReDh

Ll Lsh12

For the serpentine micro-channels, the measure pressuredrop can be expressed as

DPs DPio DPdevx Ls N DPb 13

whereDPsis the measured pressure drop for the serpentinechannel andDPbis the additional pressure drop due to themiter bend. N is the number of miter bends. So, DPb andthe bend loss coefficient can be written as

DPb

DPsDPlqU2=2

DPlDPshqU2=2

KLl KLshn o

LsLlLlLsh

KLs KLlh i

N=qU2

2

14

Kb

DPsDPlqU2=2

DPlDPshqU2=2

KLl KLshn o

LsLlLl Lsh

KLs KLlh i

N

15

According to the error propagation analysis, the uncer-tainty of the friction factor and bend loss coefficient canbe expressed as

dfRe

fRe 2

dDh

Dh

2

dA

A

2

dQ

Q

2

dDP=DL

DP=DL

2 !1=2

16

dKb

Kb 2

dA

A

2 2

dQ

Q

2

dDPb

DPb

2 !1=217

Table 2summarized the uncertainties of the measurements

involved in this work.

4. Results and discussion

4.1. Straight micro-channels

Fig. 3shows the comparison between the experimentalpressure gradients without removing the entrance effect,(DPlDPsh)/(LlLsh), and theoretical results for the cur-

rent micro-channels. The dot lines represent the pressuregradients predicted by the 2-D conventional laminarincompressible flow theory, which shows a linear relation-ship with Re number theoretically. However, as the Renumber increases, the measured pressure gradients showsa non-linear relationship with Re number. Some formerresearchers attribute it to the early transition to turbulenceatRe= 700. However, fromFig. 4, we can conclude it doesnot result from the early transition to turbulence but mayfrom not accounting for additional pressure drop in theentrance region of the channel.

Fig. 4shows the comparison between the experimentalPoiseuille number calculated by Eq. (9) and theoretical

results predicted by Eq. (3). The solid line represents thepredicted friction factor for fully developed flow, and thevertical bars denote the measurement uncertainty. FromFig. 4, we can see after the experimental uncertainties areconsidered, the experimental results show agreement withstandard laminar incompressible flow predictions when

Table 2Measurement uncertainties

Parameters Uncertainty (%)

Water flow rate 0.5Pressure drop 0.71Pressure gradient 7.49Hydraulic diameter 0.4 to 1.05

Cross-section area 0.8 to 2.1Friction constant 10.2 to 15.1Bend loss coefficient 12.3 to 16.1

Fig. 3. Experimental pressure gradients without removing the entrance

effect (DPlDPsh)/(LlLsh) vs Re number.



6/8

Re< 1500. It is believed that the consistent offset observed

by the previous researchers is the result of unaccounted forbias in experimental setups. When Re equals to 15001700,fRebegins to deviate from the theoretical value which maysuggest the transition to turbulence.

4.2. Serpentine micro-channels

For laminar flow, the additional pressure drop is relatedwith the flow separation which need energy to bemaintained and results in an additional pressure drop notassociated with frictional losses. As we know, in micro-channels, the flow usually keeps in laminar flow region,

so the flow pattern along the miter bend affects the addi-tional pressure drop pretty much. Maharudrayya et al.[28] used CFD simulation and obtained the flow patternalong a miter bend at different Re numbers. Fig. 5 showsthe flow pattern atRe numbers equal to 100 and 210. Thisflow pattern has main flow and two eddies including innerwall eddy and outer wall eddy. When Re = 100, there is noeddies around the inner and outer wall. While Re= 210,significant recirculation at the inner and outer wallappears. The size and intensity of both vortices increasewith increasing Renumber.

Fig. 6shows the experimental additional pressure dropunder different Re numbers. The results are compatiblewith the flow patterns in Fig. 5. It can be divided intotwo regions. One is Re< 100. There is no eddies and theadditional pressure drop is very small for all of the chan-nels. The other one is the circulation appears on the inner

and outer wall and develops with increasing Re number.The criticalRenumber is in the range 100200. At this timethe additional pressure drop increases sharply. The experi-mental results also show the additional pressure dropincreases with decreasing hydraulic diameters. FromFig. 6, the additional pressure drop of the micro-channelwith hydraulic diameter 0.209 mm is around 0.5 atm whenRe number reaches around 850, which is approximatelyequal to the frictional pressure drop of the same sizestraight micro-channel with 23.7 mm length, 101% of thecurrent total length. Hence, the additional pressure dropdue to the miter bend is also a big source of the micro-channel pressure drop, especially for small size and short

length micro-channels.Since the pressure drop for channel 1 is pretty high, Re

number can only reach around 1300 and the upstreampressure will exceed the measurement range of the trans-ducer. Here the bend loss coefficients for channel 2 andchannel 3 are calculated by using Eq. (15) and comparedat Re number from 472268, which is shown in Fig. 7.The solid line represents the bend loss coefficient of themiter bend, 1.1, reported by Streeter [5]. FromFig. 7, wecan see bend loss coefficients of the micro-channels areall larger than 1.1. It is a similar conclusion with that ofYamashita et al. [7], the bend loss coefficient in laminar

flow region is larger than that in turbulent region. The sec-ond characteristic is it is dependent of Re number anddecreases with increasingRenumber, which is also differentwith turbulent flow. For macro-channel turbulent flow atlarger Re number, Kb almost would not change with Renumber. When Re is larger than some value in 13001500, Kb almost keeps constant and changes in the rangeof 10%. The last characteristic is the size effect on Kb.It is larger for smaller channel when there is flow separa-tion, namelyRe> 100200. After considering the measure-ment uncertainty, these two curves still have difference. The

Fig. 4. Experimental Poiseuille number vsRe number.

Fig. 5. Flow pattern along the miter bend at different Re numbers[28].

http://-/?-http://-/?-


7/8

quantitative relationship needs more experiments and sim-ulation to be determined.

5. Summary

The investigation of pressure-driven de-ionized waterlaminar flow in straight and serpentine micro-channels with

miter bends was conducted experimentally. The micro-channels had rectangular cross-sections with hydraulicdiameters of 0.209 mm, 0.395 mm and 0.549 mm. A shortstraight and a long straight micro-channel with the samechannel size were fabricated to achieve the reliablefrictional pressure drop and additional pressure drop.According to the experimental data, the following conclu-sions were obtained:

(1) For straight micro-channels, the experimental Poiseu-ille numbers show agreement with standard laminarincompressible flow predictions after considering the

measurement uncertainties when Re is less than a

value around 1500. The discrepancy observed bythe former researchers is the result of unaccountedfor bias in experiment setups, such as not accountingfor increased pressure drop in the entrance region orunreliable inlet and outlet losses. When Re is largerthan some value in 15001700, the onset of transition

to turbulence may happen.(2) For serpentine micro-channels, the additional pres-sure drop can be divided into two regions. One isRe< 100. There is no eddies and the additional pres-sure drop is very small for all of the channels. Theother one is the circulation appears on the innerand outer wall and develops with increasing Re num-ber. The critical Re number is in the range 100200.At this time the additional pressure drop increasessharply with Re number. The experimental resultsalso show the additional pressure drop increases withdecreasing hydraulic diameters.

(3) The bend loss coefficients for channel 2 and channel 3

have been calculated. It has three characteristics. Oneis in laminar flow region it is larger than the value inturbulent region, 1.1. The second is it is dependent ofRenumber and decreases with increasing Re number.Kbalmost keeps constant and changes in the range of10% when Re is larger than some value in 13001500. The last one is the channel size effect on it.The quantitative relationship needs more experimentsand simulation to be determined.

Acknowledgements

This research was supported by the NASA HydrogenResearch for Spaceport and Space Based Applications atthe University of Florida (Grant number NAG3-2930).The support by the Andrew H. Hines, Jr./Progress EnergyEndowment Fund is also acknowledged.

References

[1] G.H. Mohamed, TheMEMS Handbook, CRCPress, NewYork, 2002.[2] J.A.C. Humphrey, A.M.K.Taylor,J.H. Whitelaw,Turbulent-flow in a

square duct with strong curvature, J. Fluid Mech. 103 (1981) 443463.[3] S.A. Berger, L. Talbot, L.S. Yao, Flow in curved pipes, Annu. Rev.

Fluid Mech. 15 (1983) 461512.[4] P. Bradshaw, Turbulent secondary flows, Annu. Rev. Fluid Mech. 19

(1987) 5374.[5] V.L. Streeter, Handbook of Fluid Dynamics, McGraw-Hill, New

York, 1961.[6] H. Yamashita, G. Kushida, R. Izumi, Study on three-dimensional

flow and heat transfer in miter-bend (1st report, analysis of flow inlaminar region), Bull. JSME 27 (1984) 19051912.

[7] H. Yamashita, R. Izumi, G. Kushida, T. Mizuno, Fluid flow and heattransfer in a two-dimensional miter-bend (1st report, experiments andanalysis), Bull. JSME 29 (1986) 41644169.

[8] G. Kushida, H. Yamashita, R. Izumi, Study on three-dimensionalflow and heat transfer in miter-bend (3rd report, effects of Reynoldsnumber and aspect ratio), Bull. JSME 28 (1985) 20002006.

[9] S.Y.K. Lee, M. Wong, Y. Zohar, Gas flow in microchannels with

bends, J. Micromech. Microeng. 11 (2001) 635644.

Fig. 6. Additional pressure drops vs Re number.

Fig. 7. Bend loss coefficients vs Re number.



8/8

[10] P. Wu, W.A. Little, Measurement of friction factors for the flow ofgases in very fine channels used for microminiature JouleThomsonrefrigerators, Cryogenics 23 (1983) 273277.

[11] X.F. Peng, G.P. Peterson, Convective heat transfer and flow frictionfor water flow in microchannel structures, Int. J. Heat Mass Transfer39 (1996) 25992608.

[12] G.M. Mala, D. Li, Flow characteristics of water in microtubes, Int. J.Heat Fluid Flow 20 (1999) 142148.

[13] I. Papautsky, J. Brazzle, T. Ameel, A.B. Frazier, Laminar fluidbehavior in microchannels using micropolar fluid theory, SensorsActuators 73 (1999) 101108.

[14] W. Qu, G.M. Mala, D. Li, Pressure-driven water flows in trapezoidalsilicon microchannels, Int. J. Heat Mass Transfer 43 (2000) 353364.

[15] D. Pfund, D. Rector, A. Shekarriz, Pressure drop measurements in amicrochannel, AIChE J. 46 (2000) 14961507.

[16] Z.X. Li, D.X. Du, Z.Y. Guo, Experimental study on flow character-istics of liquid in circular micro-tubes, Microscale Thermophys. Eng.7 (2003) 253265.

[17] X.F. Peng, G.P. Peterson, B.X. Wang, Frictional flow characteristicsof water flowing through rectangular microchannels, Exp. HeatTransfer 7 (1994) 249264.

[18] K.C. Toh, X.Y. Chen, J.C. Chai, Numerical computation of fluidflow and heat transfer in microchannels, Int. J. Heat Mass Transfer 45(2002) 51335141.

[19] Z.Y. Guo, Z.X. Li, Size effect on microscale single-phase flow andheat transfer, Int. J. Heat Mass Transfer 46 (2003) 149159.

[20] P. Wilding, J. Pfahler, H.H. Bau, J.N. Zemel, L.J. Kricka, Manip-ulation and flow of biological fluids in straight channels microma-chined in silicon, Clin. Chem. 40 (1994) 4347.

[21] B. Xu, K.T. Ooi, N.T. Wong, W.K. Choi, Experimental investigationof flow friction for liquid flow in microchannels, Int. Commun. HeatMass Transfer 27 (2000) 11651176.

[22] J. Judy, D. Maynes, B.W. Webb, Characterization of frictionalpressure drop for liquid flows through microchannels, Int. J. HeatMass Transfer 45 (2002) 34773489.

[23] H.Y. Wu, P. Cheng, Friction factors in smooth trapezoidal siliconmicrochannels with different aspect ratios, Int. J. Heat Mass Transfer46 (2003) 25192525.

[24] G. Hetsroni, A. Mostak, E. Pogrebnyak, L.P. Yarin, Fluid flow inmicro-channels, Int. J. Heat Mass Transfer 48 (2005) 19821998.

[25] M.J. Kohl, S.I. Abdel-Khalik, S.M. Jeter, D.L. Sadowski, Anexperimental investigation of microchannel flow with internalpressure measurements, Int. J. Heat Mass Transfer 48 (2005) 15181533.

[26] R.K. Shah, A.L. London, Laminar Flow Forced Convection inDuctsAdvances in Heat Transfer Supplement 1, Academic Press, NewYork, 1978.

[27] S. Kakac, R.K. Shah, W. Aung, Handbook of Single-phase Convec-tive Heat Transfer, John Wiley and Sons, New York, 1987.

[28] S. Maharudrayya, S. Jayanti, A.P. Deshpande, Pressure losses inlaminar flow through serpentine channels in fuel cell stacks, J. PowerSources 138 (12) (2004) 113.


flow characteristics of water in straight and serpentine

Documents