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Investigating the Enhanced Heat Transfer Properties of Nanofluids in Laminar Flow Conditions Ikponmwoba Eloghosaa a Mechanical Engineering Department, Louisiana State University Dr Menon Abstract— This project explores the enhancement of heat transfer prop-erties using nanofluids as compared to conventional water in a laminar flow regime within a heated pipe. Utilizing a 2D flow configuration with a constant wall heat flux of 5000 𝑊∕𝑚2, the project systematically examines the per-formance across a range of Reynolds numbers (250, 500, 750, and 1000). Employing multiphase Eulerian models of nanofluids with varying volume fractions, this investigation seeks to quantify improvements in heat transfer coefficients and Nusselt numbers. Computational Fluid Dynamics (CFD ) sim-ulations are conducted in ANSYS Fluent, supported by a grid independence study to validate the computational mesh's sufficiency. Analytical comparisons are drawn using simplified models to evaluate the computational findings against theoretical expectations. Preliminary results indicate that nanofluids can significantly enhance heat transfer rates, particularly at higher concen-trations and flow velocities. This research not only contributes to a deeper understanding of nanofluid dynamics but also underscores their potential in improving industrial heat transfer processes. keywords— nanofluids, heat transfer, Numerical modeling, Heat transfer enhancement, CFD Contents 1 Introduction 1 2 Description of the Model 1 2. 1 Geometry............................. 1 2. 2 Assumptions and Simplifications................. 2 2. 3 Boundary Specifications..................... 2 3 Governing Equations and Boundary Conditions 2 3. 1 Properties of Nanofluids..................... 2 Density Specific Heat Capacity Viscosity Thermal Conductivity 3. 2 Single-Phase Flow Equations.................. 2 3. 3 Mixture Model for Multiphase Flow................ 3 3. 4 Boundary Conditions....................... 3 4 CFD Model Development 3 5 Analytical Solution Development 4 5. 1 Velocity Profile........................... 4 5. 2 Heat Transfer and Nusselt Number ( 𝑁𝑢)............ 4 6 Results 4 6. 1 Implications for Industrial Applications.............. 4 6. 2 Future Research Directions................... 4 7 Conclusions 6 References 7 1. Introduction Heattransferfluidsplayapivotalroleinvariousindustrialappli-cations,including HVAC,automotive,andelectroniccooling systems. Traditional fluids such as water, oil, and ethylene glycol havebeenextensivelyusedduetotheirinherentpropertiesandcost-effectiveness. However, the increasing demand for more efficient heattransfermediahasledtotheexplorationofnanofluids—fluids enhanced with nano-sized particles. The mixture that 1-100 nm solid particles homogeneously dispersed in a base liquid is called nanofluids[8]. Nanofluidshaveshownpotentialtosurpassthether-mal performance of conventional heat transfer fluids due to their enhancedthermalconductivityandheatcapacity[2]. Thisstudyfocusesoncomparingtheheattransfercharacteristicsof nanofluidswithtraditionalwaterinacontrolledsetting. Theprimary objectiveistoinvestigatethethermalperformanceofnanofluidsina laminarflowregimewithinaheatedpipe. Byvaryingthe Reynolds numbers and using different mass fractions of nanoparticles, the studyaimstoshowthepotentialbenefitsofemployingnanofluidsin practicalapplications. Heattransferenhancementtechniquesarecrucialinavarietyof industrialapplications,rangingfromautomotivecoolingsystemsto nuclearreactors. Oneinnovativeapproachtoimprovingtheefficiency ofheattransferprocessesinvolvestheuseofnanofluids-fluidswith nanoparticlessuspendedwithinabasefluidsuchaswateroroil. The additionofnanoparticlescansignificantlyalterthethermalproperties ofthebasefluid,potentiallyleadingtoenhancedthermalconductivity andheattransferperformance[3]. The concept of nanofluids was first proposed by Choi et al. [2], whodemonstratedthatasmallquantityofnano-sizedparticlesdis-persedinafluidsignificantlyenhancesitsthermalproperties. Since thisseminalwork,nanofluidshavebeenextensivelystudiedfortheir potentialtooutperformconventionalheattransferfluids. However, despitenumerousexperimentalandtheoreticalstudies,thepracti-calimplementationandoptimizationofnanofluidsinengineering systemsremainchallenges. Discrepanciesbetweendifferentstudies, attributedtovariationsinparticlematerial,size,shape,andconcen-tration,aswellasthestabilityofthesuspension,highlighttheneed formorecomprehensiveanddetailedinvestigations[6],[7]. This project focuses on the computational investigation of heat transfer in a laminar pipe flow scenario, where the wall is heated at a constant heat flux of 5000W/m2. We aim to explore whether nanofluidscanachievehigherheattransfercoefficientscomparedto conventionalfluidslikewaterunderthesameoperationalconditions. Specifically,thisstudysimulatestheflowofananofluidwithconstant properties,usingthe Eulerianmixturemodel,throughaheatedpipe. The simulation outcomes could provide valuable insights into the thermalbehaviorofnanofluidsandhelpindesigningmoreefficient coolingsystems. Therelevanceofthisstudytoconvectiveheattransfer,issubstantial. Itprovidespracticalapplicationsoftheoreticalprinciplessuchasthe Nusseltnumberand Reynoldsnumberinassessingandenhancing theperformanceofheattransferfluids. Thefindingscouldcontribute tothedevelopmentofmoreeffectivethermalmanagementstrategies inindustrieswhereheattransferisacriticalconcern. 2. Description of the Model This study investigates the thermal performance of nanofluids in a simplified 2D model of a pipe with a heated wall. The primary aimistounderstandthepotentialenhancementintheheattransfer coefficientwhenusingnanofluidscomparedtoconventionalfluids likewater. 2. 1. Geometry Thegeometryofthemodelconsistsofastraight,circularpipewith a constant diameter. The computational domain is simplified to a two-dimensional cross-section to reduce computational costs and complexity. Thissimplificationallowsfordetailedanalysisandcon-trolovertheboundaryconditionsandfluidproperties. Advance Heat Transfer II Louisiana State University May 02, 2024 1-7
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Investigating the Enhanced Heat Transfer Properties of Nanofluids in Laminar Flow Conditions Figure 1. Problemgeometry 2. 2. Assumptions and Simplifications Severalassumptionsandsimplificationsaremadetomaketheprob-lem tractable and to focus on the heat transfer characteristics of nanofluids: Homogeneous Mixture: Thenanofluidistreatedasahomo-geneousmixturewiththenanoparticlesevenlydispersedwithin the base fluid. This eliminates the need to model particle dy-namicsseparately. Constant Properties: The thermophysical properties of the nanofluid(thermalconductivity,viscosity,density,andspecific heat) are assumed constant. This assumption is standard for theoreticalstudiestoisolatetheeffectofnanoparticleaddition onheattransfer. Laminar Flow: Theflowwithinthepipeisassumedtobelam-inar,characterizedbya Reynoldsnumberof250,500,750and 1000allwhicharewithintheconditionof5000forlaminarflow. This assumption is valid for low-velocity flows and simplifies thefluiddynamicsinvolved. No Chemical Reaction: Itisassumedtherearenochemical interactionsbetweenthenanoparticlesandthebasefluid,which couldalterthefluidproperties. Heated Wall: The wall of the pipe is uniformly heated with a constant heat flux of 5000W/m2, representing an external thermalload. Two-Dimensional Analysis: Toreducecomputationalcosts, theflowismodeledinatwo-dimensionalaxisymmetricsection insteadofafullthree-dimensionalgeometry. Thisassumption isvalidgiventhesymmetricalnatureoftheproblemandhelps infocusingcomputationalresourcesonsimulatingheattransfer dynamicseffectively. 2. 3. Boundary Specifications Thefollowingboundaryconditionsareappliedtothemodel: Inlet:Thefluidentersthepipewithauniformvelocityprofile correspondingtothechosenandatemperatureof 290K. Outlet:Apressureoutletconditionisused,allowingthefluid toexitthecomputationaldomainwithoutsignificantbackpres-sure. Walls:Thepipewallsaresubjectedtoaconstantheatflux,while the outer boundaries of the 2D model are assumed adiabatic, withnoheattransfertothesurroundings. Theobjectiveofthissimplifiedmodelistoaccuratelycapturethe heat transfer characteristics of nanofluids in a controlled setting, therebyprovidinginsightsintotheirpotentialbenefitsoverconven-tionalfluidsundersimilarconditions. 3. Governing Equations and Boundary Conditions Thissectionoutlinesthefundamentalequationsgoverningfluiddy-namicsandheattransferinthepipe,focusingfirstonsingle-phase flowandthenexpandingtothemultiphaseflowofnanofluids. 3. 1. Properties of Nanofluids Nanofluidsaremixturesofwaterandnanoparticles,suchas Al2O3 particles,withvaryingconcentrations. Intheexperimentscited[5],the concentration ranges from 0 to 0. 5 wt% (mass fraction) and 0 to1. 6%(volumefraction, 𝜙)respectively. Thephysicalpropertiesof Al2O3andwaterarelistedin Table1. 3. 1. 1. Density Thedensityofnanofluids( 𝑞nf)canbecalculatedusingthefollowing equation: 𝑞nf=𝜙np+ (1-𝜙)𝑞bf(1) Where𝑞npisthedensityofnanoparticles, 𝑞bfisthedensityofthe basefluid(water),and 𝜙isthevolumefractionofnanoparticles. 3. 1. 2. Specific Heat Capacity Thespecificheatcapacityofnanofluids (𝑞𝑐𝑃)nfiscalculatedusing theequation: (𝑐𝑝)nf=𝜙(𝑐𝑝)np+ (1-𝜙)(𝑐𝑝)bf(2) Where (𝑐𝑝)npis the specific heat capacity of nanoparticles, and (𝑐𝑝)bfisthespecificheatcapacityofthebasefluid. 3. 1. 3. Viscosity Theeffectiveviscosityofnanofluids( 𝑙𝑛f)canbecalculatedusingthe correlationproposedby Maigaetal. [7]: 𝜇f= (1 + 7. 3𝜙+ 123𝜙2)𝜇bf(3) Where𝜇bfistheviscosityofthebasefluid. 3. 1. 4. Thermal Conductivity Thethermalconductivityofnanofluids( 𝑘nf)isdeterminedusingthe followingequation: 𝑘nf= (1 + 2. 72𝜙+ 4. 97𝜙2)𝑘bf(4) Where𝑘bfisthethermalconductivityofthebasefluid. Theseequationsprovidemethodsforcalculatingthekeyproperties ofnanofluids,whicharecrucialformodelingandsimulatingtheir behaviorinvariousapplications. Table 1. Physicalpropertiesofnanoparticles(Al 2O3)andwaterat 𝑇= 295K. Property Al2O3Water Density,𝑞(kg/m3) 3970. 0 998. 2 Specific Heat Capacity, 𝑐𝑝(J/kg ⋅K) 680. 0 4182. 0 Thermal Conductivity, 𝑘(W/m ⋅K) 16. 3 0. 6 Dynamic Viscosity, 𝜇(Ns/m2) 0. 001003-3. 2. Single-Phase Flow Equations For single-phase in-compressible flow, the governing equations in cylindricalcoordinates,assumingaxis-symmetryandlaminarflow, areasfollows: Continuity Equation: ∇⋅𝐯= 0 where 𝐯isthevelocityvector,ensuringmassconservation. Momentum Equations: 𝜌(𝐯⋅∇)𝐯=-∇𝑝+𝜇∇2𝐯 These equations represent the conservation of momentum, where𝜌isthefluiddensity, 𝑝thepressure,and 𝜇thedynamic viscosity. Energy Equation: 𝜌𝑐𝑝(𝐯⋅∇)𝑇=𝑘∇2𝑇+𝑞 Thisequationaccountsforenergyconservationwithintheflow, where𝑇is the temperature, 𝑐𝑝is the specific heat at constant 2 Advance Heat Transfer II Ikponmwoba Eloghosa
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Investigating the Enhanced Heat Transfer Properties of Nanofluids in Laminar Flow Conditions pressure,𝑘isthethermalconductivity,and 𝑞representsinternal heatgeneration,whichiszeroforthismodel. Theseequationsaretypicallysufficientforsingle-phasefluidswith uniformproperties. However,theydonotaccountforthecomplexi-tiesintroducedbythepresenceofasecondaryphase(nanoparticles) innanofluids. 3. 3. Mixture Model for Multiphase Flow The mixture model addresses the interactions between multiple phases,incorporatingequationsforthevolumefractionsandrelative velocities: Volume Fraction Equation: ∇⋅(𝜌𝑚𝐯𝑚) = 0 Thisequationensuresmassconservationforthemixture,where 𝜌𝑚and𝐯𝑚arethemixturedensityandvelocity,respectively. Momentum Equation for the Mixture: ∇⋅(𝜌𝑚𝐯𝑚𝐯𝑚) =-∇𝑝+ ∇ ⋅(𝜇𝑚∇𝐯𝑚) + ∇ ⋅(𝑛∑ 𝑘=1𝜙𝑘𝜌𝑘𝐯𝑑𝑟,𝑘𝐯𝑑𝑟,𝑘) Thisequationaccountsforthemomentumconservationinthe mixture,incorporatingthedriftvelocities 𝐯𝑑𝑟,𝑘ofthedispersed phases. Energy Equation for the Mixture: ∇⋅(𝑛∑ 𝑘=1𝜙𝑘𝐯𝑘(𝜌𝑘𝐻𝑘+𝑝))= ∇ ⋅(𝑘∇𝑇) Thisequationconsiderstheenergyconservationforeachphase, where𝐻𝑘isthesensibleenthalpy. Relative Velocities: 𝐯𝑑𝑟,𝑘=𝐯𝑘-𝐯𝑚 Thisdefinesthedriftvelocityforeachdispersedphase,essential formodelingtherelativemotionbetweenphases. 3. 4. Boundary Conditions Theboundaryconditionsforthecomputationalmodelareasfollows: Inlet:𝐯=𝐯in, 𝑇 =𝑇in Attheinlet,thevelocity 𝐯inandtemperature 𝑇inarespecified, reflectingtheconditionsasthefluidentersthepipe. Outlet:𝜕𝑝 𝜕𝑧= 0,𝜕𝑇 𝜕𝑧= 0 A pressure outlet condition is used, allowing the fluid to exit withoutsignificantbackpressure. Pipe Wall:-𝑘𝜕𝑇 𝜕𝑟=𝑞wall Thewallissubjectedtoaspecifiedheatflux 𝑞wall,simulatingthe heatedboundary. Symmetry Axis: 𝜕𝑢𝑟 𝜕𝑟= 0,𝜕𝑇 𝜕𝑟= 0 Theseconditionsapplyalongthecenterlineofthepipe,assum-ingsymmetry. 4. CFD Model Development Thecommercialcode ANSYSFluent18. 0[4]wasused. The COU-PLEDalgorithmwasadoptedtotreatpressure/velocitycoupling. The second-order upwind scheme was used for the convective and dif-fusive terms. During the iterative process, the scaled residuals forthevelocitycomponentsandenergyweresetequalto 10-6and10-8, respectively. Astructuredrectangularmeshwasusedthroughoutthedomain in design modeller, in which the grid is finer in the vicinity of the wallusinginflationwithagrowthrateof1. 2andamaximumlayer of2. Thetotalnumberofnodeusedis51051with50000elements. Figure 2. Mesh Information Thepredictionoflocal Nusseltnumberswasbenchmarkedagainst thewell-known Shahequation[1]presentedasfollows: 𝑁𝑢𝑥=⎧ ⎨ ⎩1. 953Re Pr𝐷 𝑥-1∕3 if Re Pr𝐷 𝑥>33. 3 4. 364+0. 0722Re Pr𝐷 𝑥 1+0. 0722Re Pr𝐷 𝑥if Re Pr𝐷 𝑥≤33. 3 wherethecalculationwasbasedontheeffectivethermophysical propertiesofnanofluids. Figure 3. Comparisonoflocal Nusseltnumberwith Shahand London equationat Re=250 Theheattransfercoefficient( ℎ)and Nusseltnumberarecalculated usingthefollowingequations: ℎ𝑥=𝑞 𝑇𝑤(𝑥)-𝑇𝑓(𝑥) 𝑁𝑢𝑥=ℎ𝑥𝐷 𝑘𝑓 where𝑞,𝑇𝑤,𝑇𝑓,𝐷,𝑘𝑓, and𝑥are the constant heat flux, wall temperature,fluidtemperature,tubediameter,thermalconductivity ofthefluid,andaxiallocationfromtheentranceofthetestsection, respectively. Theaverageheattransfercoefficient( ℎav)isdefinedbyequation (23): ℎav=1 𝐿∫𝐿 0ℎ(𝑧)𝑑𝑧 And the average Nusselt number ( 𝑁𝑢av) is defined by equation (24): Ikponmwoba Eloghosa Louisiana State University May 02, 2024 3
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Investigating the Enhanced Heat Transfer Properties of Nanofluids in Laminar Flow Conditions 𝑁𝑢av=ℎav𝐷 𝑘0 5. Analytical Solution Development Inthissection,wepresenttheanalyticalsolutionprocedureforthe laminarflowofwaterina2Dpipe,aswellastheanalyticalsolution for the heat transfer in the same geometry. The reduced problem isasinglephaseflowofwaterina1mand0. 05diameterpipewith constant heat flux 𝑞= 5000𝑊 𝑚2. We shall solve analytically the velocityprofileand Nusseltnumberforthisproblemwhichwould laterbecomparedwiththecomputationalresult. 5. 1. Velocity Profile For laminar flow in a circular pipe, the velocity profile can be de-scribedbythefollowingparabolicdistributioninthefullydeveloped region. The analytical solution is derived from the Navier-Stokes equationundertheassumptionsofsteady-state,laminarflow,andin-compressibility. The Navier-Stokesequationfor2Dflowincylindrical coordinatessimplifiesto: 𝜕2𝑈 𝜕𝑟2-𝑈 𝑟= 0 Subjecttotheboundaryconditions 𝑈(0) = 0and𝑈(𝑅) = 0,where𝑅 istheradiusofthepipe. Thegeneralsolutiontothisequationis: 𝑈(𝑟) =𝐴ln𝑟+𝐵 Using the boundary conditions, we find 𝐴=-2𝑈0∕𝑅2and𝐵= 2𝑈0. Therefore,thevelocityprofile 𝑈(𝑟)isgivenby: 𝑈(𝑟) = 2𝑈0(1-𝑟2 𝑅2) Where𝑈0isthemaximumvelocityatthecenterlineofthepipe, 𝑟 istheradialdistancefromthecenterline,and 𝑅istheradiusofthe pipe. Given the Reynolds number (Re), the pipe diameter (D), fluid density (𝜌), and dynamic viscosity ( 𝜇), the fluid velocity (u) inthe pipecanbecalculatedusingtheformula: Re=𝜌⋅𝑢⋅𝐷 𝜇 Rearrangingtosolveforvelocity(u): 𝑢=Re ⋅𝜇 𝜌⋅𝐷 Forwateratroomtemperature( 𝜌= 1000kg/m3,𝜇= 0. 001Pa⋅s),a pipediameterof0. 025m,anda Reynoldsnumberof250,thevelocity iscalculatedasfollows: 𝑢=250 ⋅0. 001 1000 ⋅0. 1= 0. 0025m/s Substitutingtheflowvaluesintotheprofileequationgives: 𝑢(𝑟) = 0. 01(1-(𝑟 0. 025)2 )m/s (1) 5. 2. Heat Transfer and Nusselt Number ( 𝑁𝑢) Forheattransferanalysis,the Nusseltnumber( 𝑁𝑢)characterizesthe convectiveheattransfercoefficient. Westartwiththeenergyequation forlaminarflowandconstantheatfluxboundaryconditions: 𝜕𝑇 𝜕𝑡+𝑈𝜕𝑇 𝜕𝑟=𝛼𝜕2𝑇 𝜕𝑟2 Under steady-state conditions and with the assumption of fully developedflow,thetemperatureprofile 𝑇(𝑟)islinear. Theconvectiveheattransfercoefficient ℎcanberelatedtothe Nusseltnumber( 𝑁𝑢) andthethermalconductivity 𝑘as𝑁𝑢=ℎ𝐷∕𝑘. Fromempiricalcorrelations,forfullydevelopedlaminarflowand constantheatflux,the Nusseltnumberisgivenby 𝑁𝑢= 4. 36. There-fore,ℎ= 4. 36𝑘∕𝐷,where𝐷isthediameterofthepipe. 6. Results Theresultswereobtainedfortwo-phasemodelsfor 𝜙= 1,2,3,and 5%and Re= 250,500,750,and1000and𝑞= 5000𝑊 𝑚2,thesizeofthe sphericalparticlesis 10nm. Figure6showstheprofileoftheaxial velocityalongthetuberadiusatdifferentaxiallocationsforbasefluid only(water). Itisobservedthatthefluidisfullydevelopedjustafter the0. 5mdistancefromtheleadingedge. Thefullydevelopedvelocity profile correlates strongly with that obtained from the analytical solutioninsection5. Also,figure7showsthetemperaturevariation along the radius for several axial locations. We can see that as the fluidtravelsthroughthepipe,thetemperatureincreases. Fromthe plot,itisobservedthattheflowofwaterisnotthermallydeveloped. The relative local heat transfer coefficient and Nusselt number decreases with the axis location as shown in Figs 8 and 9. With thehighestvaluesattheentranceregion. The 𝜙= 5%linehasthe highest value showing that the heat transfer coefficient increases withconcentration. Alsothenusseltnumberalongtheaxiallength iscomparedwiththetheoreticalresultcalculatedinsection5. The simulationoverpredictsthe Nusseltnumberbyabout7. 4percent. Fig. 10showstheaverageheattransfercoefficientvariationwith Reynoldsnumberforeachvolumefractionofthenanofluid. Itshows that the average heat transfer coefficient increases with Reynolds number,thatisforaparticularfluidandgeometrytheaverageheat transfercoefficientincreaseswithflowvelocity. Theresultsdemon-strateasignificantenhancementinheattransfercharacteristicswhen employingnanofluidscomparedtotraditionalwater. Forallexam-ined Reynoldsnumbers(250,500,750,and1000),theincorporation ofnanoparticlesresultedinincreasedheattransfercoefficientsand Nusseltnumbers. Notably,theadditionofa0. 5%volumefractionof nanoparticlesledtothehighestobservedincreases,withheattransfer coefficientsand Nusseltnumbersincreasingbyasmuchas138%ata Reynoldsnumberof1000. Theinfluenceof Reynoldsnumberonheattransferenhancement wasprofound. Asthe Reynoldsnumberincreased,theeffectiveness ofnanoparticleadditionalsoincreased,indicatingthatfluidvelocity playsacriticalroleinenhancingnanoparticle-inducedthermalmix-ing. Thistrendsuggeststhatnanofluidsmaybeparticularlyeffective insystemswherehigherflowratesarefeasible. Additionally,theconcentrationofnanoparticleshadanoticeable impactonthermalperformance. Higherconcentrationsofnanopar-ticlesconsistentlyresultedingreaterenhancementsinboththeheat transfercoefficientand Nusseltnumber. Thiscanbeattributedtothe increasedthermalconductivityandthemodifiedmicroscaleflowdy-namicscausedbythedispersednanoparticles,whichenhanceenergy transportmechanismswithinthefluid. 6. 1. Implications for Industrial Applications Theobservedenhancementsinheattransfercapabilitiessuggestthat nanofluidsholdsignificantpotentialforimprovingtheefficiencyof thermalsystemsinvariousindustrialapplications,suchasautomo-tive cooling systems, electronic cooling, and process heat transfer. Theabilityofnanofluidstoachievehigherheattransferratesatcom-parableflowconditionscanleadtosmaller,moreefficientcooling systems,potentiallyreducingenergyconsumptionandmaterialcosts. 6. 2. Future Research Directions Whiletheresultsarepromising,furtherexperimentalvalidationis necessary to confirm the computational predictions and to ensure thereliabilityofnanofluidsinlong-termoperations. Futureresearch 4 Advance Heat Transfer II Ikponmwoba Eloghosa
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Investigating the Enhanced Heat Transfer Properties of Nanofluids in Laminar Flow Conditions Figure 4. Flow Velocity Profile Contour Figure 5. Flow Temperature Profile Contour Figure 6. Velocityprofile Figure 7. Temperatureprofile Figure 8. Heattransfercoefficientprofile b Figure 9. Nusseltprofile Ikponmwoba Eloghosa Louisiana State University May 02, 2024 5
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Investigating the Enhanced Heat Transfer Properties of Nanofluids in Laminar Flow Conditions Figure 10. Averageheattransfercoefficientfordifferentvolfractionand Re Figure 11. Average Nusseltnumberfordifferentvolfractionand Re Table 2. Comparisonof HTCand Nusselt Numberfor Various Volume Fractionsand Reynolds Numbers Reynolds Number Volume Fraction HTC(W/m2K) %Increase Nu %Increase HTCand Nusselt Number Increasesfrom0. 0%Volume Fraction 250 0. 0 101. 463 — 4. 27303 — 0. 1 136. 145 34. 18 5. 67271 32. 71 0. 2 164. 548 62. 15 6. 85618 60. 41 0. 3 189. 589 86. 67 7. 89952 84. 86 0. 5 232. 891 129. 48 9. 70377 127. 03 500 0. 0 140. 83 — 5. 86793 — 0. 1 164. 622 16. 91 6. 85927 16. 89 0. 2 229. 053 62. 68 9. 54388 62. 62 0. 3 265. 321 88. 43 11. 0551 88. 40 0. 5 328. 979 133. 64 13. 7075 133. 57 750 0. 0 165. 816 — 6. 90898 — 0. 1 222. 468 34. 13 9. 2695 34. 17 0. 2 271. 196 63. 53 11. 2998 63. 58 0. 3 314. 807 89. 85 13. 117 89. 91 0. 5 391. 743 136. 18 16. 3226 136. 21 1000 0. 0 188. 387 — 7. 84946 — 0. 1 253. 265 34. 40 10. 5527 34. 43 0. 2 309. 259 64. 18 12. 8858 64. 19 0. 3 359. 511 90. 80 14. 9796 90. 82 0. 5 448. 505 138. 06 18. 6877 138. 10 wouldfocusonthelong-termstabilityofnanofluids,includingthe effectsofnanoparticleaggregationandsedimentation,whichcould impactthefluid'sthermalperformanceandpressuredrop. Addition-ally, exploring a wider range of nanoparticle materials and shapes couldhelpintailoringnanofluidsforspecificapplications,optimiz-ing their thermal properties and compatibility with different fluid systems. 7. Conclusions Thisstudyinvestigatedthethermalperformanceofnanofluidsinlam-inarflowwithinaheatedpipe,comparingtheseresultswiththose oftraditionalwater-basedcoolingmethods. Ourcomputationaland analyticalfindingsindicatethatnanofluids,duetotheirenhanced thermalproperties,offersignificantimprovementsinheattransfer performance, as evidenced by increases in both heat transfer coef-ficientsand Nusseltnumbersacrossvariousconditionsofflowand nanoparticleconcentration. Specifically, the use of nanofluids resulted in up to 138% higher heattransfercoefficientsandsimilarimprovementsin Nusseltnum-berscomparedtowateratthesameoperationalconditions. These enhancementscanbeattributedtotheincreasedthermalconductiv-ityandthemodifiedfluiddynamicsintroducedbythenanoparticles. Furthermore,thestudyhighlightedthecriticalinfluenceofflowve-locityandnanoparticleconcentrationontheheattransferefficiency, suggestingoptimalrangesforindustrialapplications. However,thestudyalsoacknowledgescertainlimitations,suchas theassumptionsofconstantpropertiesandtheomissionofnanopar-ticleaggregationdynamics, whichcouldaffecttheaccuracyofthe predictions. Futureresearchcouldfocusonrelaxingsomeofthese assumptions, incorporating more complex interactions within the fluid,andexploringthelong-termstabilityandeconomicviabilityof nanofluidsinindustrialapplications. Overall,thisresearchcontributesvaluableinsightsintothefield of heat transfer fluids and supports the potential for nanofluids to enhancetheefficiencyofsystemswherehighthermalperformanceis 6 Advance Heat Transfer II Ikponmwoba Eloghosa
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Investigating the Enhanced Heat Transfer Properties of Nanofluids in Laminar Flow Conditions essential. Thefindingsencouragefurtherexperimentalandtheoreti-calstudiestofullyharnessthebenefitsofnanofluidsinheattransfer applications. References [1]R. Shah,“Acorrelationforlaminarhydrodynamicentrylength solutionsforcircularandnoncircularducts”,1978. [2]S. U. Choiand J. A. Eastman,“Enhancingthermalconductivity of fluids with nanoparticles”, Argonne National Lab. (ANL), Argonne,IL(United States),Tech. Rep.,1995. [3]S. Choi, Z. G. Zhang, W. Yu, F. Lockwood, and E. Grulke, “Anomalousthermalconductivityenhancementinnanotube suspensions”, Applied physics letters,vol. 79,no. 14,pp. 2252-2254,2001. [4] U. Manual,“Ansysfluent12. 0”, Theory Guide,vol. 67,2009. [5]S. Kim,H. Song,K. Yu, et al.,“Comparisonofcfdsimulations to experiment for heat transfer characteristics with aqueous al2o3 nanofluid in heat exchanger tube”, International Com-munications in Heat and Mass Transfer, vol. 95, pp. 123-131, 2018. [6]E. Onyiriuka,A. Obanor,M. Mahdavi,and D. R. E. Ewim,“Eval-uationofsingle-phase,discrete,mixtureandcombinedmodel of discrete and mixture phases in predicting nanofluid heat transfercharacteristicsforlaminarandturbulentflowregimes”, Advanced Powder Technology, vol. 29, no. 11, pp. 2644-2657, 2018. [7]M. Bahiraeiand S. Heshmatian,“Graphenefamilynanofluids: Acriticalreviewandfutureresearchdirections”, Energy Con-version and Management,vol. 196,pp. 1222-1256,2019. [8]Z. Ying, B. He, D. He, Y. Kuang, J. Ren, and B. Song, “Com-parisonsofsingle-phaseandtwo-phasemodelsfornumerical predictionsofal2o3/waternanofluidsconvectiveheattransfer”, Advanced Powder Technology,vol. 31,no. 7,pp. 3050-3061,2020. Ikponmwoba Eloghosa Louisiana State University May 02, 2024 7
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