rib-microchannel parameters of laminar water–Al O nanofluid in a Investigation of rib’s height effect on heat transfer and flow Applied Mathematics and Computation

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Applied Mathematics and Computation

journalhomepage:www.elsevier.com/locate/amc

Investigation of rib’s height effect on heat transfer and flow parameters of laminar water–Al 2 O 3 nanofluid in a

rib-microchannel

Omid Ali Akbari

^a

, Davood Toghraie

^a

, Arash Karimipour

^b

,

Mohammad Reza Safaei

^c,∗

, Marjan Goodarzi

^c

, Habibollah Alipour

^a

, Mahidzal Dahari

^d

aDepartment of Mechanical Engineering, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Iran

bDepartment of Mechanical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran

cYoung Researchers and Elite Club, Mashhad Branch, Islamic Azad University, Mashhad, Iran

dDepartment of Electrical Engineering, Faculty of Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysia

a r t i c l e i n f o

Keywords:

Rib-microchannel Nanofluid

Finite Volume method Friction factor

a b s t r a c t

Thelaminarforcedconvectionheattransferofwater–Al2O3nanofluidsthroughahorizon- talrib-microchannelwasstudied.Themiddlesection ofthe downwallofmicrochannel wasatalowertemperaturecomparedtotheentrancefluid.Simulationswereperformed forReynoldsnumbers10and100and nanoparticlevolumefractionsof0.00to0.04,in- sideatwo-dimensionalrectangularmicrochannelwith2.5mmlengthand25μ^mwidth.

Thetwo-dimensionalgoverningequationswerediscretizedusingafinitevolumemethod.

Theeffects ofrib’s hightand position,nanoparticleconcentrationand Reynoldsnumber onthe thermaland hydraulicsbehaviorofnanofluid flowwereinvestigated.Theresults wereportrayedintermsofvelocity,temperatureandNusseltnumberprofilesaswellas streamlinesandisothermcontours.Themodelpredictionswerefoundtobeingoodagree- mentswiththosefrompreviousstudies.Theresultsindicatethatthenormalinternalribs orturbulators,cansignificantlyenhancetheconvectiveheattransferwithinamicrochan- nel.However, theaddedhighribscan causealargerfrictionfactor,comparedtothatin thecorrespondingmicrochannelwithaconstantheightoftheribs.Theresultsalsoillus- tratethatbyincreasingtherib’sheightsandvolumefractionofnanoparticles,frictionco- efficient,heattransferrateandaverageNusseltnumberoftheribbed-microchannelstend toaugment. Inaddition, the simulationresults confirmthat changingthe solidvolume fractionandtherib’sheight,causesignificantchangesintemperatureanddimensionless velocityalongthecenterlineoftheflow,throughtheribbedareas.

© 2016 Elsevier Inc. All rights reserved.

1. Introduction

Heattransferenhancementisoneoftheimportantfieldsinengineeringresearch.Nowadays,rapidgrowthofresearchac- tivitiesandindustriesfocusedondownsizingtheheattransferspacerequiresnewmethodswithhighefficiency.Improving

∗ Corresponding author at: Young Researchers and Elite Club, Mashhad Branch, Islamic Azad University, Mashhad, Iran. Tel.: + 60 111 435 4102;

fax: + 60 37 967 5317.

E-mail address: cfd_safaei@yahoo.com , cfd_safaei@um.edu.my (M.R. Safaei).

http://dx.doi.org/10.1016/j.amc.2016.05.053 0 096-30 03/© 2016 Elsevier Inc. All rights reserved.

H=h/h,L=l/h dimensionlessmicrochannelheightandlength k thermalconductivitycoefficient,W/mK

n rangeofnumbersintheequationplacedorcounter

Nu Nusseltnumber

p fluidpressure,Pa

Pe=(usds/

α

f) Pecletnumber Pr=

υ

f/

α

f Prandtlnumber Re=

ρ

fuch/

μ

f Reynoldsnumber

T temperature,K

u,v velocitycomponentsinx,ydirections,m/s

uc inletflowvelocity,m/s

u_s Brownianmotionvelocity,m/s

(U,V)=(u/U₀,v/U₀) dimensionlessflowvelocityinx-ydirection

x,y Cartesiancoordinates,m

(X,Y)=(x/h,y/h) dimensionlesscoordinates Greeksymbols

α

^thermaldiffusivity,m²/s

β

^{ribheightcoefficientinFig.1}

ϕ

nanoparticlesvolumefraction

κ

b Boltzmannconstant,J/K

μ

^{dynamicviscosity,Pas}

θ

=(T–T_C)/(T_H–T_C) dimensionlesstemperature

ρ

^{density,kg/m3}

υ

^{kinematicsviscosity,m2/s}

Super-andSub-scripts

c cold

eff effective

f basefluid(purewater)

h hot

m mean

nf nanofluid

s solidnanoparticles

heattransferrateinfunctionalindustriessuchasautomobiles,aerospace,electronicindustries,heatingandcoolingdevices, materialprocessing,fuelcellsandnuclearreactors,throughselectingpropermethodscaninduceimportanttechnicalbene- fits,considerablesavingincostsandreductionofenvironmentalpollutants.

Theheat transfermethodshavebeendividedintoactive andpassivemethods byBergles[1].Inpassivemethods,heat transferisenhancedusingspecificgeometriessuchasroughsurfacesoradditivesinthebasefluid;whileinactivemethods, mechanical,electrical,sonicandsurfacevibrationexternalpowersourcesare usedtoenhancetheheattransferrate[2,3]. Among existing passivemethodswithwide applicationsin engineeringandindustry research, grooved surfacesandsolid additivesinbasefluidhavebeenprovedtocauseimprovedconductionandconvectionheattransfercoefficients[4].

Manystudieshavebeenrecentlycarriedoutonmicro-scaledevicesusingpassivemethodwhichshowstheimportance ofheattransferinminiandmicrochannelsaswellasenclosures[5–11].Whenthefluidflowswithinagroovedchannel,it issubjectedtoattachmentandreattachmentbetweentwo consecutiveribscausingthelaminarsub-layer tobreakup and localturbulencetobecreatedwhichinturncausemorecontactbetweenfluidandsurfaceandfinallyreduceheatresistance intheareanearthesurfaceandenhancetheheattransfermechanism.

Ontheother hand,roughnesscausesanincreaseinfrictionlosseswhichleadstoincreasedturbulenceinthearea near theheattransfersurface[12].Wang&Sunden[13]emphasizedthatlocalheattransferisdependentontherib’sshape.Saha et al.[14]concluded that Nusseltnumber andfriction factor increase by increasing flow turbulator height andReynolds

numberin square, rectangular andcircular channelswith ribsinserted inopposite walls. Liet al.[15] investigated heat transferandfluidflowofnanofluidsinmicrochannelwithdimpleandprotrusion.Theyfoundthatflowstructureschanges significantlyasnanoparticlevolumefractionincreasesforthesameinletvelocityandgeometrystructure.Chaietal.[16]in- vestigatedtheoptimizationofthermaldesignofinterruptedmicrochannelheatsinkwithrectangularribsinthetransverse micro-chambers.Theyfound that thethree mostnotableeffects ofthemicrochannel withrectangularribs includemain- streamflow separation,recirculation orvortex andinterrupted boundary layer. Manca etal.[17] performeda numerical analysison airfluid flow insquare, rectangular, triangular andtrapezoid channels andconcluded that inturbulent fluid flowregime,frictionfactorincreasesasNusseltnumberaugments.

Izadietal.[18]investigatedforcedconvectionandfullydevelopedfluidflowinanannulusandconcludedthat volume fractionofnanoparticleshasanimportanteffectonthermalprofilesandnoeffectondimensionlessvelocity.

Numerousstudiesoffluidflowinthechannelandmicrochannelsandcavityhasbeendonerecently[19–27].Theshapeof thechannel andtypeofribshavebeenalsoevaluatedandoptimizedinotherstudiesaswell[28–30].Recently,nanofluids havebeen introduced as potential coolants in a significant number ofstudies [31–37].When itcomes to thefluid flow through ribbedmicrochannels, the role ofrib’s height seems to need more investigations asit has not been sufficiently addressedpreviously. In this paper, the effect of the rib’sheight in the two-dimensional microchannel is analyzed.The water–Al₂O₃ nanofluidasacoolanthasbeenstudiedinalaminarregime.Reynoldsnumbers10and100withthevolume fractionof0,2%and4%ofthenanoparticleshavebeenconsideredfortheperformedsimulation.Theresultsofthepresent studymaycontributeto theapplicationsinmicrochannelheatsinkusedincoolingdevicesforhighpowerLightEmitting Diodes(LED),Very-Large-ScaleIntegrated(VLSI)circuitsandMicro-ElectroMechanicalSystem(MEMS)[29].

2. Governingequationsforlaminarnanofluids

Dominantdimensionlessequationsincludeequationsofcontinuity,momentumandenergywhicharesolvedforsteady stateandlaminarflowinCartesiancoordinates[38].

∂

^U

∂

^X+

∂

^V

∂

^{Y =0 (1)}

U

∂

^U

∂

^X+V

∂

^U

∂

^{Y =−}

∂

^P

∂

^X+

μ

n f

ρ

n f

ν

f

1 Re

∂

^2U

∂

^{X2 +}

∂

^2U

∂

^Y2

(2)

U

∂

^V

∂

^X+V

∂

^V

∂

^{Y =−}

∂

^P

∂

^{Y +}

μ

n f

ρ

n f

ν

f

1 Re

∂

^2V

∂

^X2+

∂

^2V

∂

^Y2

(3)

U

∂θ

∂

^X+V

∂θ

∂

^{Y =}

α

n f

α

f

1 RePr

∂

²

θ

∂

^X2+

∂

²

θ

∂

^Y2

(4)

Intheaboveequations,followingdimensionlessparametersareused[38–41]: X = x

h, Y= y

h, U= u

uc, V=

v

uc, Pr=

υ

f

α

f

H= h

h=1

θ

⁼ _T^T−Tc

h−Tc, Re= uch

υ

f

(5) TocalculatethelocalNusseltnumberalongthelowerwall,thefollowingrelationisused[38]:

Nu

(

^X

)

^=−k_k^eff

f

∂θ

∂

^Y

Y=0

(6) ThelocalNusseltnumberacrosstheribsisgivenas:

Nu

(

^Y

)

=−k_{e f f} k_f

∂θ

∂

^X

X=0

(7) ThelocalNusseltnumberalongeachhorizontalpartofthelowerwallcanbeexpressedas[38]:

Num

|

X= 1

(

^L/7

)

(ⁿ+1)^L/7 nL/7

Nu

(

^X

)

^dX; n=1,2,3,4,5 (8)

TheaverageNusseltnumberacrosseachribisdeterminedfrom:

Num

|

Y = 1

( α

^nH

)

αnH 0

Nu

(

^Y

)

^{dY; n=1,2 (9)}

TotalNusseltnumberonthesurfaceofeachribiscalculatedby:

Numtota l =Num

|

^{X+ Num}

|

^{Y (10)}

Fig. 1. Schematic of the analyzed configuration.

Table 1

Thermophysical properties of water, aluminum oxide powder (Al 2O 3) [39] and nanofluid.

Water Al 2O 3 Nanofluid ϕ = 0.02 Nanofluid ϕ = 0.04

C p(J/kg.K) 4179 765 3922.4 3693.2

ρ(kg/m ³) 997.1 3970 1056.6 1116

k (W/m.K) 0.613 40 0.6691 0.7276

μ^{(Pa .s) 8.91 ×10 −4 – 9.37 ×10 −4 9.87 ×10 −4}

Tocalculatethelocalfrictionfactoralongthelowerwall,thefollowingrelationisused:

Cf=

μ

f∂^u

∂^y 1

2

ρ

fuc2 (11)

SubstitutingdimensionlessparametersofEq.(5)inEq.(11),relation(12)and(13)areobtainedasfollows:

C_f

(

^X

)

= 2 Re

∂

^U

∂

^Y

Y=0

(12)

C_f

(

^Y

)

= 2 Re

∂

^V

∂

^X

X=0

(13) Theaveragefrictionfactoralongeachhorizontalpartofthelowerwallcanbecalculatedas:

C_fm|^X = 1

(

L/7

)

^(n+1)L/7

nL/7

C_f

(

^X

)

^dX; n=0,1,2,3,4,5,6 (14) Theaveragefrictionfactoracrosseachribisdefinedas:

C_fm|Y= 1

( α

nH

)

αnH 0

C_f

(

^Y

)

^dY; n=1,2 (15)

Localfrictionfactor:

C_f^m_total=C_f^m

|

^X+Cf^m

|

^{Y (16)}

2.1. Nanofluidproperties

The thermophysical properties of water (as base fluid) and aluminum oxide powder (Al₂O₃) (as nanoparticles) and nanofluidare presentedin Table1. Thenanoparticle’sshape isassumedto be spherical.The nanofluidpropertiescan be obtainedfromthebasefluidandnanoparticles’properties.

Thefollowingcorrelationisusedtocalculatethenanofluid’sdensity[42]:

ρ

n f =

(

¹−

ϕ ) ρ

f+

ϕ ρ

^{s (17)}

Brinkmancorrelationisusedtocalculatetheeffectivedynamicviscosityofnanofluids[43]:

μ

n f =

μ

f

(

¹⁻

ϕ )

^{2.5 (18)}

Effectivethermaldiffusioncoefficientofnanofluidiscalculatedbythefollowingformula[39]:

α

n f= ke f f

( ρ

^Cp

)

n f

(19)

Table 2

Investigated cases of different rib heights in the present study.

Case Length of microchannel L(m) Height of microchannel h(m) β1 β2

(1) 0 .2 0 .2

(2) 0 .3 0 .3

(3) 2 .5 ×10 ⁻³ 2 .5 ×10 ⁻⁵ 0 .2 0 .3

(4) 0 .3 0 .2

Re=100-ϕ=0.02

X

20 30 40 50 60 70 80

uNs

0 5 10 15 20 25 30

a

b

35

present study

Aminossadati et al [39].

Ha=0

Water-Al₂o₃

X(m)

0.00 0.05 0.10 0.15 0.20

uN X

0 10 20 30 40

ϕ=1%-Num.[47].

ϕ=1%-Exp.[47].

ϕ=1%-Num. Pressent study.

Re=90

Fig. 2. Comparison of the local Nusselt number variations with results from (a) Aminossadati et al. [39] & (b) Salman et al. [47] .

SpecificheatcapacityofnanofluidcanbecomputedusingtheexpressionsuggestedbyHungandYan[44]:

( ρ

^Cp

)

n f =

(

¹⁻

ϕ ) ( ρ

^Cp

)

f+

ϕ ( ρ

^Cp

)

s (20)

Fig. 3. Isotherms (a) and Streamlines (b) contours for Re = 10 and Re = 100 and volume fraction of 4%.

Fig. 4. Local Nusselt number on lower rib-roughened wall for Re = 100.

Tocalculatetheeffectivethermalconductivityofnanofluidforsuspensionswithsphericalparticles,Pateletal.[45]cor- relationisused:

ke f f =kf

1+ ksAs

kfAf +cksPe As

kfAf

(21)

Whereexperimentalconstantisc=36,000and:

As

A_f = d_f ds

ϕ

1−

ϕ

⁽²²⁾

Pe= usds

α

f

(23)

Fig. 5. Dimensionless temperature profiles at center line of the microchannel for Reynolds numbers of 10 and 100.

Wherewatermoleculediameterisconsideredasd_f=2Ǻandaluminumnanoparticlemoleculediameterd_s=50nm.u_s istheBrownianmotionvelocityofnanoparticlesandiscalculatedbythefollowingformula:

us= 2

κ

bT

πμ

fds2 (24)

where

κ

b=1.3807×10⁻²³J/KistheBoltzmannconstant[46].

3. Boundaryconditions

Theanalysisisperformedforatwo-dimensionalmicrochannelwithtworectangularribs.Inordertoinvestigatetheheat transferandfluiddynamicswhichincludesstudyingthevelocity,thermalfieldandfrictioneffectsineachoftheinvestigated cases,theribsheightsaredifferent.

Fig. 6. Dimensionless velocity profiles at center line of microchannel for Reynolds numbers of 10 and 100.

Fig.1showstheschematicrepresentationofthetwo-dimensionalmicrochannelinvestigatedinthisresearch.Thelength andheightofthemicrochannelare2.5mmand25

μ

^m,respectively.Themicrochannel’slengthonthelower wallhasbeen dividedtoseven equalparts.Themicrochannel’sdimensionlesslengthisL= _h^l =100anditsdimensionlessheightisH= h/h=1.Dimensionlesslength ofeachparton lowerwall is ^L₇ =14.28. ConstanttemperatureofT_c =293Kis appliedto themiddleofthelower wall ofthemicrochannel thathasa lengthof ⁵₇^L.Wholelength oftheupperwall (L)andL/7of thelower wallofthemicrochannelareinsulatedfrombothsides.Forall cases1,2,3and4,lengthandpitchribarefixed andequalto₇^l. Forall casesstudied,the lengthsoffirst andsecond teeth are equal to ₇^l.The first andsecond teeth are locatedonthebottom wallofthemicrochannel andtheupperwallistoothless.Firsttooth islocatedatx=²₇^l tox= ³₇^l, andthesecondtoothatx=⁴₇^l tox= ⁵₇^l.InCase1,thefirstandsecond ribhasaheightequivalentto20%oftheheightof themicrochannels.InCases1and2,thefirstandsecondribshaveaheightequivalentto20%and10%ofthemicrochannel, respectively.Incase3,the firstrib heightequals to10% andthesecond rib hasa heightof20% ofthemicrochannels. In case4,theribshavethesamesizeasthatinCase3,yetwithlocationsopposite ofthatinCase3.Thetemperatureofthe inletfluid tothemicrochannel isT_h = 303K.Thelaminarflow isinvestigatedforReynoldsnumbersof10 and100. Base fluidiswatermixedwithaluminumoxidenano-powder(Al₂O₃)withvolumefractionof0%,2%and4%(

ϕ

=0,0.02,0.04).

Theinvestigatedcases1,2,3and4havebeenshowninTable2alongwithFig.1basedonribs’heights.

In this investigation, flow is assumed to be two-dimensional, incompressible, Newtonian, laminar and single-phase.

Nanofluidpropertiesareassumedtoremainunchangedwithtemperature.

Fig. 7. Average Nusselt number profiles for Reynolds numbers of 10 and 100.

Fig. 8. Average friction factor profiles for Reynolds numbers of 10 and 100 and ϕ = 0.

4. Numericalmethod

The2-Dgoverningequationsaresolvedbyfinitevolumemethod.Thesecondorderupwindschemeisusedtodiscretize alltheterms.TheSIMPLECalgorithmisusedtosolvethepressure-velocitycoupledequations.Theconvergencecriterionis toreducethemaximummassresidualbelow10⁻⁶.After solvingthegoverningequations,quantitiesoffluiddynamicsand heattransfercanbedetermined.

5. Numericalprocedurevalidation

Tovalidate thepresentstudy,theresultsfromthisworkwere contrastedagainstthose carriedoutby Aminossadatiet al.[39] andSalmanetal.[47].InAminossadatiwork, ValidationhasbeenperformedforRe = 100 and

ϕ

=2% andina smoothmicrochannel.AswellasinSalmanetal.[47]work,ValidationhasbeenperformedforRe=90and

ϕ

=1%andin asmooth microtube.From quantitiescomparisonpointofview,theaverageobtainedvalueinthepresentstudyisaround 22% lessthan experimentaland9% morethannumericalresultsofSalmanetal.[47]work.Itis inferredfromFig.2that thelocalNusseltnumberisinareasonableconcordancewiththosefromthementionedreferences[39,47].

Fig. 9. Poiseuille number along microchannel at Re = 10 and ϕ = 0.

Table 3

Grid study for Re = 10, ϕ = 0.00 in case 1.

Grids Nu m C fm

33,600 5 .285 10 .211

46,200 5 .310 10 .221

60,800 5 .32 10 .26

77,400 5 .321 10 .37

5.1. Gridindependence

ThegridindependencestudyofthepresentsimulationisshowninTable3whichillustratestheresultsforpurewater incase(1) throughaverage Nusseltnumberandfrictionfactorvariation. Theresultsindicate thatforthe gridnumberof 46,200,theaverageNusseltnumber andfrictionfactorvariation owna maximumerroroflessthan 2%.Furthermore,for thisnumberofgrids,compared withothers (60,800and77,400)computationtime isreducedandthenumericalerroris negligible.

Fig. 10. Poiseuille number variation profiles along the length of the microchannel for Re = 100 and ϕ = 0.

6. Resultsanddiscussions

Forcedconvectionheattransferofwater–Al₂O₃ nanofluidinatwo-dimensionalmicrochannelwithtworectangularribs (Fig.1) is studiedusing finitevolume method.In thepresentnumerical simulations,the distances betweentheribs and thelengthofribsareconsidered tobeconstant.Eachofcases1,2,3and4separately discusseseffectsofvariationinrib height.Behaviorofnanofluidheattransferandfluid flowforallcaseshavebeenstudiedandillustrated.Theresultsofthe simulationare plottedinthe formsofdiagrams.Laminar flowofwater–Al₂O₃ withdifferentvolume fractionsofparticles weresimulatedfortwoReynoldsnumbers.

Fig.3showsthestreamlineandisothermcontoursforcases1to4withReynoldsnumbers of10and100atavolume fractionof4%.Afterenteringthemicrochannel,flowreachesahydrodynamicfullydevelopedregime.Streamlinevariations attheinletsectionforRe=100aremoresignificantthanthatforRe=10.Astherib’sheightincreases,thesevariationsalso increaseintherib-roughenedareas.Itismainlyduetothevariationsexertedonthefluidvelocitythroughthemicrochannel asaresultofexistingbarriers(ribs)withdifferentheights.Asthefluidhitstheribs,itisdivertedandasaresultthevertical componentofthevelocityisincreased.As seenfromthefigures,increasingReynoldsnumberandrib’sheight resultinan increaseinstreamlinesvariations.FromFig.3,inisothermsdiagramsalongmicrochannel,whenthefluidwithtemperature ofT_h enters intorib-roughenedareaswithsurfacetemperatureof Tc, fluid temperaturedropsandheat transfer between

Fig. 11. Poiseuille number profiles along the dimensionless length of the microchannel on upper wall, for Reynolds numbers of 10 and 100 and ϕ = 0.

fluidandrib-roughenedsurfaces takesplace.Thisheat transferrateincreasesasReynoldsnumberdecreases. Itis dueto thefactthatinlowerReynoldsnumber,hotfluidisincontactwithcoldsurfaceforalongertime.

Byincreasingrib’sheight,heattransferincreaseswhichisduetoabetterflowmixing.Ribsalongthemicrochannelact asmixeranddecreasethetemperaturegradientbetweenfluidandsurfaceandsubsequentlyincreasetheheattransferrate.

Overall,heattransferrateincreasesbyincreasingheattransfersurface(ribheight)andvolumetricpercentageofnanopar- ticles.

Fig.4isthecomparisonoflocalNusseltnumberoverthedimensionlesslengthofthemicrochannelforpurewaterand aluminumoxide-waternanofluidsatvolume fractionof0,2and4percenton lowerwallofthemicrochannel forcases1, 2,3and4andReynoldsnumbersof10and100. Itisobservedthat nanofluidhasa higherNusseltnumbercompared to purewater.Thisincrease isduetotheexistenceofnanoparticleswithhigherthermalconductivityandeffectofBrownian motionon the thermal conductivityof nanofluid.Ribs are anotherfactor in increasing the Nusselt numberwhich cause suddenincrease in Nusseltnumberinrib-roughenedareas.The main reasonbehindthisincreaseis thebetter mixingof fluid layers betweenhot andcold areas.When the fluid comes acrossthe ribs,thermal boundarylayer is disturbedand reshapedwhichultimatelyleadstoariseinheattransferrate.

Fig. 12. Friction factor variation profiles along the length of the microchannel (cases 2 and 4) for Reynolds numbers of 10 and 100 and pure water.

Fig. 5 shows the dimensionless temperatureprofiles along the length ofthe microchannel fordifferent volume frac- tions of nanoparticlesin cases 1,2, 3and 4for Reynoldsnumbers of 10 and100. Dimensionless temperaturealong the microchannel tends to decrease dueto some factors such as: decrease inReynolds number, increase involume fraction ofnanoparticles,andexistenceofribsinthedirectionoffluidmotion.Itcanbesaidthatby decreasingReynoldsnumber, fluidhasmoreopportunitytoexchangeheatwithrib-roughenedsurfaces,alongthemicrochannel.Byincreasingthevolume fractionofnanoparticles,theheattransfermechanismsarereinforced.

Existenceofribsinthedirectionoffluidmotionandincreasingribsheightscausethedisappearanceandreinforcement ofthermalboundarylayerinrib-roughenedareas.Theseparameterscausedecrementsindimensionlesstemperaturealong themicrochannelandbetterincorporationoffluidlayersandfinallyincrementsinheattransfer.

Fig.6illustrates thedimensionlessvelocity atthemid-heightofmicrochannel. Accordingtothesimulation results,di- mensionless velocityincreases inrib-roughenedareas.Thisincrease is causedby blockageof cross-sectionofthe cooling fluidflowinmicrochannelsbytheribs.ThesevariationsinReynoldsnumberof100arelessthanthoseinReynoldsnumber of10.Itisbecauseofbetterincorporationofflowwithrib-roughenedsurfaceofthemicrochannelinlowReynoldsnumbers.

InlowReynoldsnumbers,flowtendstotaketheshapeofthecontactsurface.

Fig.7demonstratestheaverageNusseltnumberprofilesinallcasesforReynoldsnumbersof10and100.Thesimulation resultsconfirmthatbyincreasingtheReynoldsnumber,nanofluidvolumefractionandribheight,averageNusseltnumber valueincreased.AtRe=100,theNusseltnumberincreasessubstantiallyforallthestudiedcases.Itisbecauseofthebetter mixingofthefluidlayerandtheeffectofimprovedheattransferby solidnanoparticlesathigherReynoldsnumbercom- paredwithlower Reynoldsnumber(Re=10). Itis alsoobservedthat amongthe casesexplored inthispaper,Case2 has thehighestaverageNusseltnumberattheexaminedReynoldsnumbersof10and100.Betweencases3and4,itisfound atCase4ownsthehigherNusseltnumber.Thereasonisduetoabettermixingofthefluidasaresultoftheexistingdent andlocationofribsinthiscase.

Fig.8representstheaveragefrictionfactoronupperandlower wallsofthemicrochannelfor

ϕ

=0.Itisobservedthat average friction factordecreases by increasing Reynoldsnumber anddecreasingrib’s height.This isdueto more contact betweenthe fluidandthe rib-roughenedsurface. Bydecreasingthe Reynoldsnumber,thecooling fluid comesin contact withthesurfacemoreslowlyandtherefore,effects ofshearstress betweenfluid andrib-roughenedsurfaceinfluidlayer nearthe surfacebecomesmoresubstantial. Bydecreasing therib’s height,contactsurfacebetweenthe fluid andrib de- creases.Byenlargingthecross-sectionofflowasaresultofreduction intherib’sheight,componentsofthefluidvelocity changepartiallyandfinally thefrictioncoefficientdecreasesastheoutcomeoftheabovefactors.Acomparisonoffriction factor forupper wall (without ribs) and lower wall (rib-roughened) is delineated inthis figure aswell. The resultsalso presentthattherateofPoiseuillenumbervariationsare significantespeciallyintheregions beforeandaftertherib.Itis duetovariationsofvelocity andfriction factorintheseareas.Byincreasingthe rib’sheight, Poiseuillenumbervariations tendtoincreaseaswell.Poiseuillenumbervariationsinentrancelengthofthemicrochannelremainedunchanged.Itisdue tothefactthatintheentrancelengthofthemicrochannel,allcasesarethesameintermsofcontactconditionswiththe microchannelsurface.

Fig. 13. Dimensionless temperature variation profiles along dimensionless length of the microchannel in different cross-sections of the microchannel for Re = 10.

Figs. 9 and10 show the Poiseuille number profiles along the microchannel for pure water andall casesat Reynolds numbers10and100.Inareaswithoutribs,PoiseuillenumbervariationsrateishigherforRe=10comparedwiththatfor Re=100.Before andaftertheribs,PoiseuillenumbervariationsrateishigherforRe= 100comparedwiththat forRe = 10.Itismainlybecausethevariationsofvelocityandfrictionfactorintheseareasintensifyastheribheightisincreased.

Fig.11portraitsthePoiseuillenumberprofilealongtheupperwallofmicrochannelfor

ϕ

=0.Asnotedfromthisfigure, Poiseuillenumber valuesincrease along the ribs asReynoldsnumber andheight of the rib augments.In the areaswith highervelocitygradient(likebeforeandaftertherib)thesevariationsaremore.

Fig. 14. Dimensionless temperature variation profiles along the dimensionless length of the microchannel at different cross-sections for Re = 100.

Fig.12 displaysthefrictionfactorvariationsofpure wateralong thelengthofthe microchannelforcases2 and4 for Reynoldsnumbersof10and100.Itcanbeobservedthatastheheightoftheribincreases,frictionfactorshowsasudden rise. By increasing the fluid velocity (Reynolds number) these variations also increase. However, for cases 2 and 4, the friction factor along the microchannel is 10 times higherat lower Reynolds numbers (Re= 10) compared withthat for higherReynoldsnumbers(Re=100).

Figs.13and14representthedimensionlesstemperatureprofilesalongthelengthofthemicrochannelindifferentcross- sectionsfor thestudied casesatReynolds numbers of10and 100.ComparingFigs. 13 and14,it isobserved that forall cases,atthe lower Reynoldsnumber(Re= 10compared toRe = 100)increasing nanoparticlesvolumetricpercentage or approachingoutletcross-sectionofthemicrochannelcauseadeclineindimensionlesstemperatureofhotfluid.Decreasing thedimensionlesstemperatureindifferentcross-sectionsofthemicrochannelindicatesthatfluid andsurfacetemperature becomeequaltoT_h andTc,respectively.DimensionaltemperaturevariationismoreprominentatlowerReynoldsnumber.

Itisduetothemoreavailable timeforheatexchangebetweenthehot fluidandthecoldsurfacewithintheflowwhena lowerReynoldsnumberispresent.

Table4showstheaverage NusseltnumberandPercentageofincrease Num valuesforallcasesandReynoldsnumbers of10and100withdifferentvolume fractionofnanoparticles.Thesevalueshavebeencalculatedforthelowerwall ofthe microchannel. Based on the tabulated values,the average Nusselt numberof Re = 10 for all the casesand nanoparticle

Table 4

Average Nusselt number and Percentage of increase Nu mfor cases 1, 2, 3 and 4, Reynolds numbers of 10 and 100 with different nanoparticle volume fractions.

Nu m Percentage of enhancement Nu mbased on the same case and Re in ϕ = 0.

Re Case ϕ = 0.00 ϕ = 0.02 ϕ = 0.04 ϕ = 0.02 ϕ = 0.04

Re = 10 Case(1) 5.31 5.34 5.36 0.56% 0.94%

Re = 100 17.70 18.68 19.67 5.53% 11.13%

Re = 10 Case(2) 5.48 5.51 5.52 0.55% 0.73%

Re = 100 18.83 19.85 20.88 5.42% 10.88%

Re = 10 Case(3) 5.36 5.39 5.40 0.56% 0.75%

Re = 100 18.22 19.22 20.26 5.49% 11.2%

Re = 10 Case(4) 5.44 5.47 5.49 0.55% 0.92%

Re = 100 18.31 19.32 20.33 5.52% 11%

Table 5

Average friction factor and Percentage of increase Cf mfor cases 1, 2, 3 and 4, at Reynolds numbers of 10 and 100 on upper and lower walls.

Cf min ϕ = 0.0 Percentage of enhancement Nu mbased on the same case and Re in ϕ = 0.

Case(1) Case(2) Case(3) Case(4) Case(2) Case(3) Case(4) Re = 10 lower wall 10 .22 11 .61 10 .91 10 .91 13 .6% 6 .75% 6 .75%

upper wall 1 .40 1 .57 1 .49 1 .49 12 .14% 6 .43% 6 .43%

Re = 100 lower wall 0 .96 1 .11 1 .05 1 .05 15 .63% 9 .38% 9 .38%

upper wall 0 .14 0 .16 0 .15 0 .15 14 .3% 7 .15% 7 .15%

volume fractionhaslessvariations comparedto those ofRe = 100. Thisis the resultofthe increase influid velocity at higherReynoldsnumberandreinforcement ofnanoparticleheattransfermechanismsbyincreasing thevolumetricpercent ofsuspendednanoparticlewithinthebasefluid[48–55].

Table5representstheaveragefrictionfactorvaluesandPercentageofincreaseCfm forcases1,2,3and4forReynolds numbersof10and100inupperandlowerwallsofthemicrochannel.ThisvalueisabouttentimeshigheratRe=10than thevalueatRe=100.Thisisbecauseatthelower Reynoldsnumber,fluid isincontactwithupperandlower wallsfora longertimewhileathigherReynoldsnumber,fluiddoesnothaveenoughopportunitytobeincontactwiththesurfacedue toahigherfluidvelocity.

Increasingtheribheightalsoresultsinmorecontactbetweenthefluidandthesurfacewhicheventuallycausesanin- creaseintheaveragefrictionfactorofthewalls.Averagefrictionfactorforthewallwithoutribs(upperwall)hasdecreased significantlycomparedtothelowerwallwhichimpliesthatexistenceoftheribscausesanincreaseinfrictionfactorcom- paredtothecaseofno-ribssurface.

7. Conclusion

Inthepresentstudy,theeffectofribheightonfluidflowandheattransferparametersoflaminarwater–Al₂O₃nanofluid flowina two-dimensionalrectangularmicrochannel wasinvestigated.The finitevolumemethodwasusedtosimulatethe problem. Discretization ofthe governingequations wasperformedusing thesecond orderupwindscheme. Inthis work, theforcedconvection heat transferandfluid flow within a rectangularribbed-microchannel were investigated.Boundary conditionsincludetheinsulatedupperwallandbottomwallsubjectedtoaconstanttemperature.TheReynoldsnumberfor thelaminarflowwasselectedtobe10and100.Thevolumefractionsofsolidparticleswere0,2%and4%.

Through the investigations performedin thisresearch, it can be outlined that heat transfer ratecan be enhanced by increasingtheribheightandvolumetricpercentageofnanoparticlesandReynoldsnumber.However,existenceofribswithin thepathcausesvelocitygradientandenhanced contactbetweenthefluid/microchannelsurfaceswhichinturnengenders anincreaseintheaveragefrictionfactor.

Existenceofnanoparticlesdoesnot haveamajor effecton hydrodynamicparameters suchasfluid velocityandcauses merevariationsinthestreamlinesthroughtheinletsectionofthemicrochannel.InlowerReynoldsnumbers,heattransfer ratebetweenthesurfaceandthefluidincreasesandfluidhasmoreopportunityforthermalexchangewiththesurface;on theother hand,morecontactofthefluidwiththe surfacecauses anincrease infriction factor.Among thestudiedcases, case(2)withthegreatestribheighthasthemaximumheattransferduetoabettermixingofthefluidlayers,andcase(1), withthelowestribheight,ownsthelowestNusseltnumber.Comparingcases3and4,theusageofcase4isrecommended tobenefitfromahigherheattransfercoefficientyetthesamefrictionfactor.Theuseofcombinedteeth-likeribs,asincase (4),causesabettermixingofthecoolingfluidandincreasestheheattransfermorethancase(3).

[4] S.U.S. Choi , Nanofluids: from vision to reality through research, J. Heat Transf. 131 (2009) 1–9 .

[5] M. Goodarzi, M.R. Safaei, H.F. Oztop, A. Karimipour, E. Sadeghinezhad, M. Dahari, S.N. Kazi, N. Jomhari, Numerical study of entropy generation due to coupled laminar and turbulent mixed convection and thermal radiation in an enclosure filled with a semitransparent medium, Sci. World. J. 2014 (2014) 8 Article ID 761745, doi: 10.1155/2014/761745 .

[6] A . Karimipour , A .H. Nezhad , A . D’Orazio , E. Shirani , Investigation of the gravity effects on the mixed convection heat transfer in a microchannel using lattice Boltzmann method, Int. J. Therm. Sci. 54 (2012) 142–152 .

[7] M. Goodarzi, M.R. Safaei, A. Karimipour, K. Hooman, M. Dahari, S.N. Kazi, E. Sadeghinezhad, Comparison of the finite volume and lattice boltzmann methods for solving natural convection heat transfer problems inside cavities and enclosures, Abst. Appl Anal. 2014 (2014) 15 Article ID 762184, doi: 10.1155/2014/762184 .

[8] Karimipour , M. Afrand , M. Akbari , M.R. Safaei , Simulation of fluid flow and heat transfer in the inclined enclosure, Int. J. Mech. Aerosp. Eng. 6 (2012) 86–91 .

[9] H.R. Goshayeshi , M.R. Safaei , Y. Maghmumi , Numerical simulation of unsteady turbulent and laminar mixed convection in rectangular enclosure with hot upper moving wall by finite volume method, in: Proceedings of the 6 ^thInternational Chemical Engineering Congress and Exhibition (ICheC’09), Kish Island, Iran, 2009 .

[10] T.C. Hung , W.M. Yan , Optimization of a microchannel heat sink with varying channel heights and widths, Numer. Heat Transf. A: Appl. 62 (2012) 722–741 .

[11] M.R. Safaei , B. Rahmanian , M. Goodarzi , Numerical study of laminar mixed convection heat transfer of power-law non-newtonian fluids in square enclosures by finite volume method, Int. J. Phys. Sci. 6 (33) (2011) 7456–7470 .

[12] I.A . Stogiannis , A .D. Passos , A .A . Mouza , S.V. Paras , V. P ˇenkavová, J. Tihon , Flow investigation in a microchannel with a flow disturbing rib, Chem. Eng.

Sci. 119 (2014) 65–76 .

[13] X.-D. Wang , B. An , L. Lin , D.-J. Lee , Inverse geometric optimization for geometry of nanofluid-cooled microchannel heat sink, Appl. Therm. Eng. 55 (2013) 87–94 .

[14] S.K. Saha , Thermal and friction characteristics of turbulent fl ow through rectangular and square ducts with transverse ribs and wire-coil inserts, Exp.

Therm. Fluid Sci. 34 (2010) 575–589 .

[15] P. Li , D. Zhang , Y. Xie , Heat transfer and flow analysis of Al 2O 3–water nanofluids in microchannel with dimple and protrusion, Int. J. Heat Mass Transf.

73 (2014) 456–467 .

[16] L. Chai , G. Xia , M. Zhou , J. Li , J. Qi , Optimum thermal design of interrupted microchannel heat sink with rectangular ribs in the transverse microcham- bers, Appl. Therm. Eng. 51 (2013) 880–889 .

[17] O. Manca , S. Nardini , D. Ricci , Numerical investigation of air forced convection in channels with differently shaped transverse ribs, Int. J. Numer.

Methods Heat Fluid Flow 21 (2010) 618–639 .

[18] M. Izadi , A. Behzadmehr , D. Jalali-Vahida , Numerical study of developing laminar forced convection of a nanofluid in an annulus, Int. J. Therm. Sci. 48 (2009) 2119–2129 .

[19] M.R. Safaei , Y. Maghmoumi , A. Karimipour , Numerical investigation of turbulence mixed convection heat transfer of water and drilling mud inside a square enclosure by finite volume method, in: 4th Int. Meet. Adv. Thermofluids, IMAT 2011, Melaka, Malaysia, 2011 .

[20] A . Karimipour , A .R. Hossein Nezhad , A . D’Orazio , M.H. Esfe , M.R. Safaei , E. Shirani , Simulation of copper–water nanofluid in a microchannel in slip flow regime using the lattice Boltzmann method, Eur. J. Mech. B: Fluids. 49 (2015) 89–99 .

[21] M.R. Safaei, O. Mahian, F. Garoosi, K. Hooman, A. Karimipour, S.N. Kazi, S. Gharehkhani, Investigation of micro and nano-sized particle erosion in a 90 º pipe bend using a two-phase discrete phase model, Sci. World. J. 2014 (2014) Article ID 740578, 12 pages, 2014, doi: 10.1155/2014/740578 .

[22] M.R. Safaei , H. Togun , K. Vafai , S.N. Kazi , A. Badarudin , Investigation of heat transfer enchantment in a forward-facing contracting channel using FMWCNT nanofluids, Numer. Heat Transf. A: Appl. 66 (2014) 1321–1340 .

[23] M.R. Safaei , M. Goodarzi , M. Mohammadi , Numerical modeling of turbulence mixed convection heat transfer in air filled enclosures by finite volume method, Int. J. Multiphys. 5 (4) (2011) 307–324 .

[24] H. Yarmand , G. Ahmadi , S. Gharehkhani , S.N. Kazi , M.R. Safaei , M.S. Alehashem , A.B. Mahat , Entropy generation due to turbulent flow of Zirconia-Water and three other different nanofluids in a square cross section tube with a constant surface heat flux, Entropy 16 (2014) 6116–6132 .

[25] P. Valeh-e-Sheyda , M. Rahimi , E. Karimi , M. Asadi , Application of two-phase flow for cooling of hybrid microchannel PV cells: a comparative study, Energy Convers. Manag. 69 (2013) 122–130 .

[26] A. Karimipour , M.H. Esfe , M.R. Safaei , D.T. Semiromi , S. Jafari , S.N. Kazi , Mixed convection of copper–water nanofluid in a shallow inclined lid driven cavity using the lattice Boltzmann method, Phys. A: Stat. Mech. Appl. 402 (2014) 150–168 .

[27] Z. Nikkhah , A. Karimipour , M.R. Safaei , P. Forghani Tehrani , M. Goodarzi , M. Dahari , S. Wongwises , Investigation of FMWCNT nanofluids forced convec- tion in a microchannel with oscillating heat flux and slip boundary condition, Int. Commun. Heat Mass Transf. 68 (2015) 69–77 .

[28] G. Xia , Y. Zhai , Z. Cui , Numerical investigation of thermal enhancement in a micro heat sink with fan-shaped reentrant cavities and internal ribs, Appl.

Therm. Eng. 58 (2013) 52–60 .

[29] X.-D. Wang , A. Bin , J.-L. Xu , Optimal geometric structure for nanofluid-cooled microchannel heat sink under various constraint conditions, Energy Convers. Manag. 65 (2013) 528–538 .

[30] V. Leela Vinodhan , K.S. Rajan , Computational analysis of new microchannel heat sink configurations, Energy Convers. Manag. 86 (2014) 595–604 . [31] A. Malvandi , D.D. Ganji , Magnetic field effect on nanoparticles migration and heat transfer of water/alumina nanofluid in a channel, J. Magn. Magn.

Mater. 36 (2014) 172–179 .

[32] M.M. Rashidi , A. Hosseini , I. Pop , S. Kumar , N. Freidoonimehr , Comparative numerical study of single and two phase models of nanofluid heat transfer in a wavy channel, Appl. Math. Mech. 35 (2014) 831–848 .

[33] M. Goodarzi , A. Amiri , M.S. Goodarzi , Mohammad Reza Safaei , A. Karimipour , E. Mohseni Languri , M. Dahari , Investigation of heat transfer and pressure drop of a counter flow corrugated plate heat exchanger using MWCNT based nanofluids, Int. Commun. Heat Mass Transf. 66 (2015) 172–179 . [34] A. Malvandi , D.D. Ganji , Brownian motion and thermophoresis effects on slip flow of alumina/water nanofluid inside a circular microchannel in the

presence of a magnetic field, Int. J. Therm. Sci. 84 (2014) 196–206 .

[35] A. Malvandi , M.R. Safaei , M.H. Kaffash , D.D. Ganji , MHD mixed convection in a vertical annulus filled with Al 2O 3-water nanofluid considering nanopar- ticle migration, J. Magn. Magn. Mater. 382 (2015) 296–306 .

[36] H.R. Goshayeshi , M. Goodarzi , M.R. Safaei , M. Dahari , Experimental study on the effect of inclination angle on heat transfer enhancement of a ferro–

nanofluid in a closed loop oscillating heat pipe under magnetic field, Exp. Therm. Fluid Sci. 74 (2016) 265–270 .

[37] M.M. Sarafraz , F. Hormozi , Convective boiling and particulate fouling of stabilized CuO-ethylene glycol nanofluids inside the annular heat exchanger, Int. Commun. Heat Mass Transf. 53 (2014) 116–123 .

[38] A. Raisi , B. Ghasemi , S.M. Aminossadati , A numerical study on the forced convection of laminar nanofluid in a microchannel with both slip and No slip condition, Numer. Heat Transf. A: Appl. 59 (2011) 114–129 .

[39] S.M. Aminossadati , A. Raisi , B. Ghasemi , Effects of magnetic field on nanofluid forced convect ion in a partially heated microchannel, Int. J. Nonlinear Mech. 46 (2011) 1373–1382 .

[40] M. Gavara , Asymmetric forced convection of nanofluids in a channel with symmetrically mounted Rib heaters on opposite walls, Numer. Heat Transf.

A: Appl. 62 (2012) 884–904 .

[41] K. Vajravelu , S. Sreenadh , R. Saravana , Combined influence of velocity slip, temperature and concentration jump conditions on MHD peristaltic trans- port of a Carreau fluid in a non-uniform channel, Appl. Math. Comput. 225 (2013) 656–676 .

[42] T.-C. Hung , W.-M. Yan , X.-D. Wang , C.-Y. Chang , Heat transfer enhancement in microchannel heat sinks using nanofluids, Int. J. Heat Mass Transf. 55 (2012) 2559–2570 .

[43] H.C. Brinkman , The viscosity of concentrated suspensions and solution, J. Chem. Phys. 20 (1952) 571–581 .

[44] T.C. Hung , W.M. Yan , Enhancement of thermal performance in double-layered microchannel heat sink with nanofluids, Int. J. Heat Mass Transf. 55 (2012) 3225–3238 .

[45] H.E. Patel , T. Sundararajan , T. Pradeep , A. Dasgupta , N. Dasgupta , S.K. Das , A micro-convection model for thermal conductivity of nanofluids, Pramana

— J. Phys. 65 (2005) 863–869 .

[46] N.R. Kuppusamy , H.A. Mohammed , C.W. Lim , Thermal and hydraulic characteristics of nanofluid in a triangular grooved microchannel heat sink (TGM- CHS), Appl. Math. Comput. 246 (2014) 168–183 .

[47] B.H. Salman , H.A. Mohammed , A.Sh. Kherbeet , Numerical and experimental investigation of heat transfer enhancement in a microtube using nanoflu- ids, Int. J. Commun. Heat Mass 59 (2014) 88–100 .

[48] O.A. Akbari , D. Toghraie , A. Karimipour , Impact of ribs on flow parameters and laminar heat transfer of water–aluminum oxide nanofluid with different nanoparticle volume fractions in a three-dimensional rectangular microchannel, Adv. Mech. Eng. 7 (11) (2015) 1–11 .

[49] A. Karimipour , H. Alipour , O.A. Akbari , D. Toghraie Semiromi , M.H. Esfe , Studying the effect of indentation on flow parameters and slow heat transfer of water-silver nanofluid with varying volume fraction in a rectangular Two-Dimensional microchannel, Ind. J. Sci.Technol. 8 (15) (2015) 51707 . [50] M.E. Ali , O. Zeitoun , Nanofluids forced convection heat transfer inside circular tubes, Int. J. Nanoparticles. 2 (2009) 164–172 .

[51] O. Zeitoun , M.E. Ali , Nanofluids natural convection heat transfer in horizontal annulus, Int. J. Nanoparticles. 2 (2009) 173–181 .

[52] O. Zeitoun , M. Ali , H. Al-Ansary , The effect of particle concentration on cooling of a circular horizontal surface using nanofluid jets, Nanoscale Mi- croscale Thermoph. Eng. 17 (2013) 154–171 .

[53] O. Zeitoun , M. Ali , Nanofluid impingement jet heat transfer, Nanoscale Res. Lett. 7 (2012) 139 .

[54] M. Ali , O. Zeitoun , S. Almotairi , Natural convection heat transfer inside vertical circular enclosure filled with water-based Al 2O 3nanofluids, Int. J.

Therm. Sci. 63 (2013) 115–124 .

[55] M. Ali , O. Zeitoun , S. Almotairi , H. Al-Ansary , The effect of Alumina-water nanofluid on natural convection heat transfer inside vertical circular enclo- sure heated from above, Heat Transf. Eng. 34 (2013) 1289–1299 .