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Laboratory Demonstrations/Experiments in Free and Forced Convection Heat Transfer

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Laboratory Demonstrations/Experiments in Free and Forced Convection Heat Transfer 2006-1488: LABORATORY DEMONSTRATIONS/EXPERIMENTS IN FREE AND FORCED CONVECTION HEAT TRANSFER Edgar Clausen, University of Arkansas EDGAR C. CLAUSEN Dr. Clausen currently serves as Adam Professor of Chemical Engineering at the University of Arkansas. His research interests include bioprocess engineering (fermentations, kinetics, reactor design, bioseparations, process scale-up and design), gas phase fermentations, and the production of energy and chemicals from biomass and waste. Dr. Clausen is a registered professional engineer in the state of Arkansas. William Penney, University of Arkansas W. ROY PENNEY Dr. Penney currently serves as Professor of Chemical Engineering at the University of Arkansas. His research interests include fluid mixing and process design. Professor Penney is a registered professional engineer in the state of Arkansas. Page 11.857.1 Page © American Society for Engineering Education, 2006 Laboratory Demonstrations/Experiments in Free and Forced Convection Heat Transfer Introduction Anumberof papershave beenwrittenrecentlyonmethodsforimprovingorsupplementingthe teachingofheattransferincludingtheuseofspreadsheetstosolvetwo-dimensionalheattransfer problems 1,anewtransportapproachtoteachingturbulentthermalconvection 2,theuseof computerstoevaluateviewfactorsinthermalradiation 3,andanewcomputationalmethodfor teachingfree convection 4.Supplementalexperimentsforuseinthelaboratoryorclassroomhave alsobeenpresentedincludingrathernovel experimentssuchasthedrying ofatowel 5andthe cookingofFrenchfry-shapedpotatoes 6.HunkelerandSharp 7foundthat42%ofstudentsin seniorlaboratoryovera four year periodwereType3learners,thatis,actionoriented“hands- on”commonsenselearners.Thus,anexcellent methodforreinforcingcoursecontentisto activelyinvolvestudentsinlaboratoryexercisesordemonstrationswhicharedesignedto comparetheirexperimentaldatawithdataor correlationsfromtheliterature. As partofthe combinedrequirementsforCHEG 3143,HeatTransport,andCHEG3232, Laboratory II,juniorlevelchemicalengineeringstudentsattheUniversity ofArkansaswere requiredtoperformsimpleheattransfer experimentsordemonstrationsusinginexpensive materialsthatarereadily availableinmostengineeringdepartments.Duringthefirstofferingin theFallsemesterof2004,thestudentswere requiredtodesign,implement andanalyzethe resultsfrom basicexperiments.Duringthesecondofferinginthe Fallsemesterof2005,the studentswere askedtosuggestandimplementimprovementsinthe basicexperimentaldesign whichcouldleadtobetteragreement betweentheirexperimentalresultsandresultsfrom literaturecorrelations.Thisexercisehasseveral benefits: • It providesanopportunity forstudentstohaveadditional“hands-on”experience; • Itdemonstratesa physicalapplicationofcorrelationsfoundinthetextbook;and, • Ithelpsstudentsdevelop anappreciationforthelimitationsofliteraturecorrelations. Resultsfromthreeoftheseexperiments(freeconvectioncoolingofanupward-facing plate, forcedconvectioncooling byflowing air over anupwardfacinghorizontal plate,andforced convectionheatingof arodbyflowing airthroughanannulus)aredescribedbelow.Inaddition, surveyandtestresultsare presentedwhichhelptodemonstratewhetherthe experiments/demonstrationsimprovedorenhancedthestudents’understandingofthe appropriatenessandlimitationsofheattransfer correlationsfoundintheliterature. Free Convection Heat Transfer from an Upward Facing Horizontal Plate Freeconvectionheattransferisencounteredinmany practical applications,includingheat transfer from pipes,transmissionlines,baseboardheaters andsteamradiators.Correlationsare availablefor predictingfreeconvectionheattransfercoefficientsformany different geometries. Oneoftheimportant geometriesistheupwardfacinghorizontalheatedsurfaceor plate,the subjectofthisinvestigation.Theoverall objectivesofthisexperimentwereto: 1. Determinethe experimentalfree convectionheattransfer coefficientforthe topsurfaceof Page 11.857.2 Page ahorizontalhot plateexposedtoair,and 2. Comparetheseresultswithresultsgeneratedfrom theappropriatecorrelationof ChurchillandChu 8: 1 Nu = 0.54Ra 4 104 < Ra < 107 (1) 1 Nu= .0 15Ra 4 107 < Ra <1011 (2) Figures 1 and 2 show schematics of the experimental apparatus, and Figures 3-5 show photographs of the actual equipment used in the experiment. A list of equipment and detailed safe experimental procedures was presented by Clausen et al. 9, and may also be obtained from the corresponding author. Briefly, an aluminum plate was heated to ~65°C by setting it on a wooden platform in an insulated box, closing the lid and heating the surrounding air in the box with an ordinary hair dryer inserted in the top of the box. After heating the plate, it was set on an insulated surface in a still room and wrapped with insulation so that only the black painted surface was exposed (see Figures 2 and 4). A photograph of the second year modification of the experiment is shown in Figure 5, where a drop cloth curtain was used to better isolate the apparatus from air disturbances. A thermocouple was inserted into the plate, and temperature was measured as a function of time while observing the slow cooling of the plate due to free convection. Figure 1. Insulated Wooden Box for Heating the Aluminum Plate Page 11.857.3 Page Figure2.Experimental SetupforCoolingtheHorizontal InsulatedPlate Figure3.Photographof WoodenBoxFigure4.PhotographofApparatusfor UsedtoHeatthe AluminumPlateCoolingthe InsulatedHorizontalPlate Page 11.857.4 Page Figure5.Photographof DropClothusedtoIsolatetheEnvironment SurroundingtheAluminumPlate Itwasdesiredtocompareanexperimentallydeterminedheattransfercoefficientwith correlationsfoundintheliterature.Aheat balanceonthe plate,withnoheatgeneration,yields: dT − (hA (T − T ) + εσA (T 4 − T 4 )) = ρV ()C (3) S SURFACE ∞ S SURFACE ∞ P dt Althoughsmall,theheat balance wasalsocorrectedfortheheatflow byconductionfromthe aluminum platethroughtheinsulationtothetable.Experimentaldataoftemperaturevs.time werethususedtodeterminethe“bestfit”experimentalheattransfer coefficient byintegrating Equation3numericallyusingaTKSolver4 th orderRunga-Kuttaintegration.Theheattransfer coefficientfromtheliteraturewasdeterminedusingEquations1and2,wheretheRayleigh numberiscalculatedas: gβ (T − T )L3 Ra = SURFACE ∞ Pr (4) ν 2 InEquation4,thelengthofthe plateisthecharacteristiclengthinfreeconvectionand,for a horizontalflat plate,L = A S/P.Assumingthatthe surrounding airisanidealgas,thevolumetric expansioncoefficientmay be calculatedas: 1 β = (5) T Finally,theheattransfer coefficient,hCORR ,may becalculatedfromthe Nusseltnumberas: kNu h = (6) CORR L 11.857.5 Page Figure6shows a plotoftheexperimentaltemperaturewithnodropclothas afunctionoftime, aswellasa curveshowinganumericalintegrationofEquation3usingthe “bestfit” experimentalheattransfercoefficient.The emissivity(ε)ofthe blackpaintedsurfacewas assumedtobe0.98.The experimentalheattransfercoefficientwas8W/m 2Katasurface temperatureof352K,whilethecoefficient basedontheChurchill/Churelationshipwas5.6 2 W/m K.Thus,acorrectionfactor (h EXP /h CORR )of1.4wasneededinordertomatchthe experimentaldatawiththecorrelation.Whenthe dropclothwasadded,thecorrectionfactorfell to1.2,indicatingthattheadditionofthedropclothwassignificantineliminatingair currents. 360 + + + 355 + + + + + 350 + + + + + 345 + + + + + 340 + + + Temperature (K) Temperature + + 335 + + + + + 330 325 0 500 1000 1500 2000 2500 3000 3500 4000 Time (s) Figure6.Temperaturevs.Time ExperimentalData(+) andPredictedbyEquation4 2 Multipliedby aFactorof1.4(h EXP =8W/m Kat T SURFACE =352K) Forced Convection Heat Transfer from an Upward Facing Horizontal Plate Forcedconvectionheattransferoccurs whenthefluidsurrounding asurfaceissetinmotionby anexternalmeanssuchasafan,pumpor atmosphericdisturbances.Thisstudywasconcerned withforcedconvectionheattransferfromafluid(air)flowing paralleltoa flat plateat varying velocities.Theobjectivesofthisexperimentwereto: 1. Determinethe experimentalforcedconvectionheattransfer coefficientfor parallelflow overaflat plate. 11.857.6 Page 2. Comparetheexperiment heattransfercoefficientwiththecoefficientcalculatedfromthe correlations presentedbyCengel 8,whogivesthefollowingcorrelationsfor local heat transfer coefficientsfor forcedconvectionflowoverahorizontal plate: 5.0 3/1 Nu x = hx x / k = .0 332 Re x Pr forlaminarconditions,i.e.,Re<500,000 (7) 8.0 3/1 5 7 Nux = hx x / k = .0 0296Re Pr forturbulentconditions,i.e.,5x10 <Re<10 (8) Theintegrated average coefficientsare givenby 5.0 3/1 Nu = hx / k = .0 332 Re x Pr forlaminarconditions,i.e.,Re<500,000 (9) Nu = hx / k = .0( 037Re 8.0 −871)Pr 3/1 turbulentconditions,5x10 5<Re<10 7 (10) Theexperimentalsetup andprocedureswere essentiallythesame asshowninFigures1-4, exceptthatmultiple plateswereusedalongwitha threespeedfan.Thus,forcedconvectionheat transfer wasmeasuredforhorizontal platesat twoselecteddistancesfromthefanandatthree different airspeeds.Ananemometerwasusedtomeasurethe airvelocity overthe plate atfive differentlateral positionstodeterminetheaverageairvelocity.Aschematicoftheexperimental setupisshowninFigure7andphotographsoftheapparatus areshowninFigures 8and9. Asis showninFigure9,aseriesofcardboardhoneycombdiffuserswasusedduring year2inan attempttominimizeairturbulence.Thediffusers werelocatedjustafterthefan(connectedtothe fanoutlet by a plastic“garbage bag” channel)andimmediatelyinfrontofthealuminum plates. Onceagain,alistofequipmentanddetailedsafeexperimental procedures was presentedby Clausen et al. 10 ,andmayalsobeobtainedfromthecorrespondingauthor. Figure7.LocationofFanandPlatesfortheHorizontalPlateHeatTransferExperiment Page 11.857.7 Page Figure8.Photographof
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