TheOhioStateUniversity

DepartmentofChemical&BiomolecularEngineering

ExperimentNo.2

SHELLANDTUBEHEATEXCHANGER

Authors:

GroupLeader–ConorHughes

OperationsEngineer–KyleHofacre

DesignEngineer–DrewShort

DevelopmentEngineer–ScottReinhart

QualityEngineer–HusseinAlkhatib

DateDue: DateSubmitted:

February16,2015 February16,2015

SubmittedTo:

Dr.JohnClay–Instructor

MichaelDenney–TeachingAssistant

Abstract

The objective of the shell and tube heat exchanger experiment and research is to

determinetheeffectofflowrateandflowconfigurationontheperformancecharacteristicsofa

forced convection shell and tube heat exchanger. Three analytical approaches are taken to

analyze the data. These approaches include the effectiveness/NTU method, heat and

momentumtransfercorrelations,andtheWilsonplotandmodifiedWilsonplotmethods.

Theeffectiveness/NTUmethoddeterminestheeffectivenessandefficiencyoftheshell

andtubeheatexchangeratvaryingflowrates.Thecounter-currentflowconfiguration(themost

effective)hasamaximumeffectivenessof0.47withashellsideflowrateof9.46gpmandtube

sideflowrateof2.97gpm.

TheheatandmomentummethodusesrelationshipsbetweenRe,Pr,andNutocalculate

convectiveheattransfercoefficients,whichareinturnusedtocalculatetheaverageoverallheat

transfercoefficient. Theaverageoverallheat transfercoefficient forco-currentandcounter-

currentfloware1268.47and836.76W/m2Krespectively.

TheWilsonandmodifiedWilsonPlotmethodcorrelatestheoverallthermalresistance

andReinordertocalculatetheaverageoverallheattransfercoefficient.ThroughtheWilsonplot

method,overallheattransfercoefficientsforco-currentandcounter-currentarecalculatedto

be 1386.26 and 1085.37W/m2K respectively. The overall heat transfer coefficient using the

modifiedWilsonmethod is 1387.89 and 1317.97W/m2K for co-current and counter-current

respectively.

The shell and tube heat exchanger data and analysismethods are used in the design

extension todeterminewhich combinationof tubebundle,diameter, and lengthof theheat

exchangerwillmeetthespecifications.Theapproachistoiterativelysolveforthecombination

ofdimensionspecificationsthatwillhaveapressuredropoflessthan200Pa,andminimizesteam

flowrateandsurfaceareaoftheheatexchanger.Theresultsconcludethatthemostoptimal

heatexchangerforthisdesignhas400tubes,adiameterof0.3inches,andalengthof0.75m.

Theflowconfiguration iscounter-currentwithasurfaceareaof7.182m2,steamflowrateof

0.321kg/sandoverallheattransfercoefficientof3.417kW/m2K.

TableofContents

Purpose..........................................................................................................................................1

Introduction...................................................................................................................................2

ExperimentDescription..................................................................................................................5

ResultsandDiscussion...................................................................................................................9

TemperatureProfiles................................................................................................................10

Effectiveness-NTUMethod.......................................................................................................14

HeatandMomentumTransferCorrelation..............................................................................18

WilsonPlotMethod..................................................................................................................20

ModifiedWilsonPlotMethod..................................................................................................24

ErrorAnalysis...............................................................................................................................29

Conclusion....................................................................................................................................31

Recommendations.......................................................................................................................33

DesignExtension..........................................................................................................................34

Notation.......................................................................................................................................41

LiteratureCited............................................................................................................................43

AppendixA-PreliminaryPreperationAssignment.....................................................................44

AppendixB–ExperimentalSummaryReport..............................................................................48

AppendixC–ReportFormulas.....................................................................................................55

Effectiveness-NTUMethod.......................................................................................................55

HeatandMomentumTransferCorrelation..............................................................................55

Wilson/ModifiedWilsonPlotMethod......................................................................................55

ExperimentDesignExtension...................................................................................................56

ErrorAnalysis............................................................................................................................56

AppendixD–SampleCalculations...............................................................................................57

Effectiveness-NTUMethod.......................................................................................................57

HeatandMomentumTransferCorrelation..............................................................................57

Wilson/ModifiedWilsonPlotMethod......................................................................................58

ExperimentDesignExtension...................................................................................................60

ErrorAnalysis............................................................................................................................61

AppendixE–MATLABCode.........................................................................................................62

Co-CurrentOperation(WilsonPlot).........................................................................................62

Counter-CurrentOperation(WilsonPlot)................................................................................64

NTU3DScatterPlot..................................................................................................................66

Co/Counter-CurrentOverallHeatTransferCoefficientvs.FlowRates....................................68

AppendixF–CalibrationCurves..................................................................................................71

AppendixG–AdditionalData......................................................................................................72

Co-CurrentandCounter-CurrentOperationTemperatureProfiles.........................................72

TableofParametersandConstants..........................................................................................78

ExperimentTimeLog................................................................................................................79

ListofFiguresFigure1.Experiment2SystemFlowchart..............................................................................................5

Figure2.Co-CurrentOperationTemperatureProfile(Run10).........................................................11

Figure3.Counter-CurrentOperationTemperatureProfile(Run8).................................................12

Figure4.Co-CurrentNon-SteadyStateTemperatureProfile............................................................13

Figure5.Counter-CurrentNon-SteadyStateTemperatureProfile..................................................13

Figure6.Effectivenessvs.NTUforCo/Counter-CurrentOperation.................................................14

Figure7.EffectivenessofCo-CurrentOperation(3DScatter)...........................................................17

Figure8.EffectivenessofCounter-CurrentOperation(3DScatter).................................................17

Figure9.Co/Counter-CurrentFlowRatesvs.OverallHeatTransferCoefficient............................20

Figure10.OriginalWilsonPlotMethodAppliedtoCo-Current........................................................23

Figure11.OriginalWilsonPlotMethodAppliedtoCounter-Current..............................................23

Figure12.DifferenceinmValuesvs.GuessedmValuesforCounter-Current...............................25

Figure13.DifferenceinmValuesvs.GuessedmValuesforCo-Current........................................26

Figure14.ModifiedWilsonPlotforCounter-CurrentOperations....................................................26

Figure15.ModifiedWilsonPlotforCo-CurrentOperations.............................................................27

Figure16.ShellSideFlowrateCalibrationCurve.................................................................................71

Figure17.TubeSideFlowrateCalibrationCurve................................................................................71

ListofTables

Table1.Co-CurrentOperationDesignSpace........................................................................................6

Table2.Counter-CurrentOperationDesignSpace...............................................................................7

Table3.Co-CurrentExperimentalData..................................................................................................9

Table4.Counter-CurrentExperimentalData......................................................................................10

Table5.CalculatedDataforNTUAnalysisMethod............................................................................16

Table6.CalculatedCorrelationData–Co-CurrentOperation..........................................................19

Table7.CalculatedCorrelationData–Counter-CurrentOperation................................................19

Table8.Counter-CurrentvaluesforRovand1/RemforWilsonPlot.................................................22

Table9.Co-CurrentvaluesforRovand1/RemforWilsonPlot...........................................................22

Table10.OriginalWilsonPlotLocalandOverallHeatTransferCoefficients..................................24

Table11.LocalandOverallHeatTransferCoefficientsforModifiedWilsonMethod...................27

Table12.ConfidenceIntervalCalculations..........................................................................................30

Table13.DesignExtensionIterationsandConclusions.....................................................................38

Table14.CalculationConstantsandProperties..................................................................................78

Table15.DesignExtensionConstants..................................................................................................78

Table16.OperationTimeLog................................................................................................................79

1

Purpose

ExperimentNo.2usesashellandtubeheatexchangertoanalyzetheeffectofflowrate

and flow configuration changes on the performance of the apparatus. This is evaluated by

calculating several variables related to performance. The heat exchanger is run in both co-

currentandcounter-currentconfigurationsinordertocompareandcontrasttheperformance

results.Inordertodothis,theeffectiveness,overallheattransfercoefficients,andtheinnerand

outer convective heat transfer coefficients are calculated. After these calculations are

performed,thedataisanalyzedusingthefivedifferentmethodslistedonpage2oftheShelland

Tube Heat Exchanger Operating Procedure (Denney, 2015). These methods have different

assumptionsandprocedures,whichmayormaynotleadtosimilarresults.Theresultsculminate

intoconclusionsanderroranalysis,whichpavethewayforthedesignextension. Thedesign

extensionrequiresuseofcalculationmethodslearnedinthelabinordertodeterminespecifics

foranewheatexchangertobepurchasedbyBuckeyeFoodsInc.Theyalsowouldliketoknow

thepressuredropthroughthetubesideoftheheatexchanger, theflowrateofsuperheated

steamneeded,andtheoverallheattransfercoefficient.

2

Introduction

Theimportanceofthisreportistoperformcalculations,makeconclusions,andevaluate

sourcesoferrorwithregardtotheshellandtubeheatexchanger.Thisinformationalongwith

the methods of analysis are applied to the design extension in order to solve the supplied

problem.

The experiment being performed involves a forced convection shell and tube heat

exchanger.Thisheatexchangercanbeoperatedindifferentflowconfigurationsandatdifferent

flowratestoachievecertainoutputtemperatures.Ashellandtubeheatexchangerrunsacold

fluid through the tubes of the apparatus and a hotter liquid through the shell side of the

apparatus.TheheatexchangerbeingusedinthisexperimentisaHampdenModelH-6850-40

ShellandTubeHeatExchangerwhichcontains112coppertubesalongwith3equallyspaced

baffles intheshell. Inthisexperiment,thetwofluidsbeingusedarewater. Thehotterfluid

comes intocontactwiththetubepipesas it flowsandheattransferoccursbetweenthetwo

fluids.Thecolderfluidgainsheatandthehotterfluidlosesheat.

Operationcanoccurinco-currentorcounter-currentflowpatterns.Inco-currentflow,

thetubeandshellliquidsflowinthesamedirection,howeverincounter-currentflow,thetube

and shell liquids flow in opposite directions. These configurations lead to different output

temperaturesandthereforedifferentexperimentalresults.Allofthefluidtemperaturesinthe

systemaremeasuredbytenthermocouplesplacedatvariouspointsthroughouttheapparatus.

Theflowratesalsovarythroughouttheexperimentreachingamaximumof10gpmand6.6gpm

for the shell and tube sides respectively. These parameters change over the course of the

experiment in order to evaluate the shell and tube heat exchanger performance. The heat

exchangerisallowedtoreachsteadystateforaboutsevenminutesaftereachchangeinflow

rates. Beforesevenminutes isallowedtoelapse,thesystemisconsideredtobe inunsteady

state.Inunsteadystate,thetemperaturesofboththeshellandtubefluidsarefluctuating.A

designspaceisusedtofindrandomcombinationsofshellandtubeflowratesinordertoproduce

themostrepresentativeresultspossible.About11datapointsforeachco-currentandcounter

currentflowarecollectedalongwithonetrialforeachconfigurationatunsteadystate.

3

Theexperimentalvariablesincludetheshellandtubesideflowrates,allthermocouple

readingsastemperatures,andthetubeandshellsidepressurereadings. Thesevariablesare

studiedbecausetheyareusedincalculationsinordertoevaluatetheperformanceoftheheat

exchanger.Theeffectiveness,overallheattransfercoefficient,andinnerandouterconvective

heattransfercoefficientsarecalculatedforbothco-currentandcounter-currentconfigurations.

Enoughdataiscollectedinordertoaccuratelyevaluatetheperformanceindicatorsmentioned

above.Thedataisthenanalyzedusingfivedifferentmethods.ThesemethodsincludeWilson

plot method, modified Wilson plot method, heat and momentum transfer correlations,

effectiveness-NTUmethod,andproducingtemperatureprofileplots.Eachmethodhasdifferent

theories, assumptions, and analytical procedures that are examined and used effectively by

referring to the referenced literature. TheWilsonplotmethod isused to find relationships

betweenthetemperaturedifferenceandheatfluxoneithertheshellortubesideoftheheat

exchanger.Thismethodusesmeasurementsofthetemperaturedifferencebetweenthefluids

andheat-transferrates.ConstantsarefoundusingtheWilsonplotmethodandtheseconstants

areusedtocalculateheattransfercoefficients.Factorsthataffecttheaccuracyofthismethod

include,accuracyofdata,amountofdatapoints,aswellasthescopeofthedata(Rose,2004).

ThemodifiedWilsonplotmethodbuildsoffoftheWilsonplotmethodbyutilizingtheoretically

“better”valuestofindnewconstantsandthenfinallynewandmoreaccuratevaluesforheat

transfercoefficients(Fernandez-Seara,2005). TheNTUmethodofanalysiscanbeusedifthe

inletandoutlettemperaturesareknown.ItusescollecteddatatocalculateNTUor“Numberof

TransferUnits”fromefficiency.NTUcanthenbeusedtocalculatetheeffectivenessoftheshell

andtubeheatexchanger,givingaquantitativemeasureofperformance(Incropera,2007).This

methodoperates under the assumptions that the process is steady state, the properties are

constant,andtherearenegligiblelossestothesurroundings.Theseassumptionscanbeanalyzed

todeterminetheaccuracyandvalidityofthismethod.Thenextmethodisheatandmomentum

transfercorrelations. ThisusesrelationshipsbetweenReynoldsnumber(Re),Prandtlnumber

(Pr),andtheNusseltnumber(Nu)tocalculatetheheattransfercoefficientsalongwiththeheat

flux. Thismethodusesdifferent equations and correlationsbaseduponwhether the flow is

laminar or turbulent as determinedby the valueof theReynolds number. Newton’s Lawof

4

Coolingisusedinthismethodsosomeassumptionsaremade. Theno-slipconditionisused,

whichstatesthatthevelocityofthefluidatthewallsofthetubesequalszero.Dragforceand

frictioneffectsarealsoignoredintheuseofthismethod.Finally,itisassumedthattheflowis

eitherlaminarorturbulent,notsomewhereinbetween.Thelastmethodforanalyzingthedata

istheplottingoftemperatureprofilesalongtheheatexchanger.Thismethodisrathersimple

andonlyrequiresplottingtemperaturevs.distancealongthetubes.Theoretically,thesegraphs

shouldmatch their corresponding graphs that appear in Figure1of the Shell andTubeHeat

ExchangerOperatingProcedure(Denney,2015).Thetemperaturechangesasthefluidmoves

downthetubesareconveyedbythegraph.Amoreindepthlookatthegraphscanshowtrends

incomparisonwitheachotheraswellaswiththereferencegraphs.Althoughthisisasimple

methodforanalyzingthedata,therearestillacoupleassumptionsthataremade.Itisassumed

that the thermocouples are reading and reporting accurate temperatures. In addition, it is

assumedthatthethermocouplesarenottouchingthewallsofthetubesinanyway.Thiswould

causethemtoreportthetubewalltemperatureinsteadofthetemperatureofthefluid.

Manyreferences,manuals,anddatasheetsareusedinthisexperiment.TheShelland

TubeHeatExchangerOperatingProcedure(Denney,2015)isreferencedfrequently.Aprepared

data sheet is used for calculation, graphing, and creating table of data used in this report.

FundamentalsofHeatandMassTransfer(Incropera,2007)isusedfrequentlyinmanyportions

ofthereport.AgeneralReviewoftheWilsonPlotMethodandIt’sModificationstoDetermine

ConvectionCoefficientsinHeatExchangeDevices(Fernandez-Seara,2006)isusedforWilsonand

Modified Wilson Plot analyses. Finally, the NIST Chemistry Webbook is used in the design

extensionportioninordertoobtainthermophysicalpropertiesofsaturatedsteam.

5

ExperimentDescription

Theexperimentwasdesignedtoobservetheeffectsofflowratesandflowconfigurations

ontheperformanceoftheforcedconvectionshellandtubeheatexchanger.Therewerelittle

materials needed for this experiment. The Hampden Model H-6850-40 shell and tube heat

exchangerwas comprised of 112 copper tubeswith an inner tube diameter of .21 inches, a

thicknessof.02inchesandatubelengthof14inches.Acitywaterlinewasconnectedtothe

systemprovidingamediumthroughwhichheattransfertookplace.Waterwasallowedtorun

foraboutsevenminutestoensurethesystemfilledwithwater.Ascrewdriverwasneededto

openandclosetheneedlevalvetoallowanexcessairinthesystemtoescape.Thermalgloves

wereusedtoturnvalvesasasafetyprecautionfromthehotpipes.Seenbelowisaflowchart

schematicoftheheatexchangersystemtakenfromtheShellandTubeHeatExchangerOperating

Procedure(Denney,2015).

Figure1.Experiment2SystemFlowchart

6

As shown in Figure 1, tube and shell side water was supplied from the city water

lineslocatedinthe"CITY"portion.Wateronthetubesideflowedthroughvalve10and1,the

rotometer, and then theheatexchanger. Finally tube sidewater flowed throughvalve7and

thendrained.Tubesideoperationswerecompletedinanopenloopsystem.Theshellsidewas

firstpurgedofairthroughtheuseofvalves12,13,and14.Valve11wasthenclosed,placingthe

shellsideinaclosedloopedsystem.Waterflowedfromthesurgetankthroughthepumpand

into the rotometer. During co-current operations, water flowed through valve 4, the heat

exchanger, and then back through valve 6. During counter-current operations,water flowed

through valve 5, the heat exchanger, and then out valve 2. Afterward shell sidewaterwent

throughtheheaterandthenbackintothepumptocontinuetocyclethrough.

Startingtheheatexchangerrequiredatwo-stepprocess.First,thetubesideoftheheat

exchangerwasfilledandthenshellside.Thepurposeofthetwoseparatefillingstepswasto

removeairfromthesystem.Aftertheheatexchangerwasfilled,thesystemwasallowedtorun

foraminimumofsevenminutestocheckthateverythingwasworkingproperly.Afterstartup

wascompleted,trialswereconductedtotestdifferentvariables.Therewereseveralvariables

that were manipulated to provide data for analysis. Operation of the heat exchanger was

observed inboththeco-currentandcounter-currentconfigurations.Also,tubeandshell flow

rateswerevariedrandomlywithinoperationallimits.Therandomselectionofflowratesinsured

unpredictabledatasothatcorrelationscouldbeconcludedonlyafteranalysis.Theselectionwas

createdusingthedesignspacesobservedbelow.

Table1.Co-CurrentOperationDesignSpace

7

Table2.Counter-CurrentOperationDesignSpace

Variablesrangedfrom1gpmto10gpmintheshellsideandfrom2.5gpmto6.5gpminthetube

side.However,thedesignspacewasconstructedforsteadystateoperationsothelowerlimitof

thedesignspacewasadjustedtoaminimumof2gpmfortheshellsideand2.5gpmforthetube

side.11trialswereconductedforboththeco-currentandcounter-currentconfigurations.Each

trialhadvariedflowratesthatwererandomlyselectedwithinthedesignspace.Flowrateswould

beadjustedusingvalves3and7.Onceflowrateswereadjusted,thesystemwouldcontinuously

run for at least sevenminutes to ensure steady state was achieved. The same process was

repeatedforeachtrial.

Non-steady state operation was also observed for co-current and counter-current.

Predeterminedflowrateswereselectedfortheshellandtubesothattherewouldbenon-steady

stateheatexchange.Onlyonetrialforbothconfigurationswasconductedfornon-steadystate

operationbyrecordingtheexitingtemperaturesoftheflowsfromtheshellandtubeevery20

secondsfor400seconds.

Data collected from the shell and tube heat exchanger was analyzed using several

methods.Theeffectivenessandefficiencyoftheheatexchangerwasdeterminedbyusingthe

NTU-Effectiveness plot. The overall heat transfer coefficient was calculated using Wilson,

Modified Wilson, and heat and momentum transfer correlation methods. Non-steady state

operationwasobservedbycreatingatemperatureprofile.

Safety was the biggest priority during the experiment. Everyone participating in the

experiment wore hard hats and safety glasses. Pressure gauges and thermocouples were

8

constantlymonitoredthroughouttheexperimentsothatoverpressurizationwouldnotoccur.

However,theshellandtubeheatexchangerwasneglectedonceforaperiodoftimeresultingin

theheateroverheatingandshuttingdown.Thermalgloveswereusedtoturnvalvesconnected

totheshellsidebecauseofthehotfluidflowingthroughthecopperpipesmadethepipeshot.

Allparticipantsinthelabstudiedtheemergencyshutdownandevacuationprocedurespriorto

the experiment in case of an emergency so shutdown and startup ran smoothly. No safety

incidentsoccurredduringthelab.

9

ResultsandDiscussion

During the shell and tube heat exchanger experiment, a sufficient amount of data is

gatheredandorganizedinordertoanalyzeexperimentalresults.Differentanalyzingtechniques

areusedincludingtemperatureprofileplots,effectiveness-NTUmethod,WilsonandModified

Wilson plot method, and heat and momentum transfer methods. Approximately five hours

allowsforthoroughoperationoftheheatexchangerincludingstartupandshutdown.Execution

oftheexperimentbeginsat8:00ambeginningwithfillingthesystemwithwaterfromacityline

whilekeepingsurethesystemisfreeofairbuildup.Trialsbeginanhourlateroperatingacross

theentiredesignspaceoftwodifferentflowconfigurations,co-currentandcounter-current.A

timelogiskeptinadataspreadsheetrecordingthetimeinwhichanewtrialbeganoperation.In

addition,thespreadsheetcontainsflowrate,pressure,andtemperaturereadingsforeachtrial

listed. Temperature data is read using LabVIEW software displaying the readings from ten

thermocouples,fiveshellsideandfivetubeside,positionedatvariousdistancesalongtheheat

exchanger.Table3,shownbelow,listsalldatarecordedduringco-currentoperationincluding

seventrialsofsupplementaldata.

Table3.Co-CurrentExperimentalData

10

Anidenticaldatatableprovidesthetimelog,flowrates,pressures,andtemperaturesforeach

counter-currenttrial.TherecordeddataisshownbelowinTable4.

Table4.Counter-CurrentExperimentalData

TemperatureProfiles

Graphs of temperature profiles are produced to show how the temperature changes

along the length of the tubes. These are produced by recording the temperature at each

thermocoupleafterthesystemhasreachedsteadystateandthenplottingtemperature(K)vs.

positionalongtube(in).TheoreticaltemperatureprofilesareprovidedintheShellandTubeHeat

ExchangerOperatingProcedure(Denney,2015).Temperatureprofilesfor11co-currentruns,11

counter-current runs, and unsteady state runs are produced. These plots are found in the

appendixandlabeledaccordingtotherunconfigurationandnumber.

11

Figure2.Co-CurrentOperationTemperatureProfile(Run10)

WhencomparedtoFigure1intheShellandTubeHeatExchangerOperatingProcedure

(Denney,2015),Figure2fortheco-currentflowoperationresemblesthereferencegraphforthe

shellside.Theshellsidecurvesweepsslightlydownwardwithanegativeslopeastheposition

alongthetubeincreases.Although,thiscurveinFigure2doesn’thaveasmuchofanegative

slopeasthereferencegraphdoes.Thismeansthatoverallthetemperaturedidnotdecreaseon

theshellsideasmuchasispredictedbythereferencegraph.Ontheotherhand,theshapeof

the tubesidecurveshowssomediscrepancy. Insteadofasmooth increase, theslopeof the

Figure2tubesidecurveissemi-parabolic.Thisparabolicshapeshowsatemperaturedecrease

ataboutthehalfwaypointalongthetubes.Thiscausesadepressioninthesemi-parabolicshape.

Accordingtothereferencefigure,thetubesidecurveshouldshowapositiveslopealongthe

entirelengthofthetube,levelingouttowardstheendofthetube.Figure2showsapositive

slopeuntilabout5inches,anegativeslopeuntil7inches,anotherpositiveslopeuntilabout10

inches,andthenfinallyanegativeslopeuntiltheendofthetubeisreached.Thisdiscrepancy

couldbecausedbythermocoupleerror. Ifanyofthethermocouplesthatreadthetubeside

temperaturesaretouchingthewallofthetubeinsteadofplacedinthecenterofthetubethen

theywouldreadahighertemperature.Thisisbecausethecoppertubesaresurroundedbythe

shellsidehotwatercomingfromthewaterheater.Inaddition,thermocouple10isplacedatthe

tubeoutletandisnotcontainedwithintheinsulationoftheheatexchanger;thecopperpiping

12

isexposedtothelaboratorytemperatureair.Thiscausestheoutlettemperatureofthewaterto

dropabout20Kas indicatedbyFigure2. However, theshelland tubeheatexchangerdoes

increasetheoveralltemperatureofthetubesidewaterbyabout20Koverthecourseoftherun.

Figure3.Counter-CurrentOperationTemperatureProfile(Run8)

Figure3showsthetemperatureprofileforcounter-currentrunnumber8.Thisrunhad

similarflowrateswhencomparedtoFigure2co-currentrunnumber10.Theseflowrateswere

about9gpmand3gpmfortheshellandtubesidesrespectively.Figure3isverysimilartoFigure

2withrespecttothetubesidecurve.Theshellsidecurvehasapositiveslope,whichisexpected

becausetheenteringhotwaterflowisnowenteringatthe14in.positionalongthetube,sothe

waterwilldecreaseintemperatureasthepositionalongthetubedecreasesfrom14in.to0in.

Thetubesidecurveendswithanegativeslopejust like inFigure2forco-currentflow,this is

becauseofthesamethermocoupleerrormentionedinthediscussionofFigure2.Overall,the

tube sidewater increasesabout24Kas indicatedbyFigure3. Whencompared to the20K

increaseinFigure2,graphicallyitcanbeconcludedthatcounter-currentflowproducesslightly

higheroutputwatertemperaturesthanco-currentflowconfiguration.

13

Figure4.Co-CurrentNon-SteadyStateTemperatureProfile

Figure5.Counter-CurrentNon-SteadyStateTemperatureProfile

Figure4and5shownabovearetemperatureprofilecurvesforco-currentandcounter-

currentconfigurationsinunsteadystate.Theseareproducedbysettingtheflowratesequalto

values outside of the steady state regime as shown in Figure 4 in the Shell and Tube Heat

ExchangerOperatingProcedure(Denney,2015)andrecordingtemperaturesevery20seconds

for400seconds.ThetemperatureinKelvinisthengraphedvs.theelapsedtimeinseconds.Both

graphshaveverysimilarcurveshapes.Theybothhaveapositiveslopefrom0secondstoabout

220seconds,decreasesharplyto280seconds,increaseagainto375seconds,andthenfinally

decreaseto400seconds.Thecounter-currentcurveshowsasharpertemperaturedropfrom

220secondsto280secondsthantheco-currentcurve.Thecounter-currentcurveisatanoverall

highertemperaturerange.Thiscouldbebecausethecounter-currentgraphisrecordedatshell

side thermocouple9andtheco-currentgraph is recordedatshell side thermocouple5. The

unsteadystatecurvesshowhowthetemperaturefluctuateswhentheflowratesareeitherout

ofthesteadystateregimeorinthetimebeforethesystemisallowedtoequilibrate,asaresult,

thetemperaturesinthethermocouplesarefluctuating.Overall, inthecounter-currentcurve,

the temperature fluctuates about 12 K in the elapsed time period whereas the co-current

temperatureonlyfluctuatesabout3.5Kovertheelapsedtimeperiod.Therefore,therewould

be larger error associatedwith recording unsteady state temperature in the counter-current

configuration.

14

Effectiveness-NTUMethod

TheNTU-Effectivenessplotisagoodwaytoanalyzeheatexchangerperformancewhen

littlevariablesareknown.Theeffectivenessoftheheatexchangercanbecalculatedtodetermine

howwellheatisbeingtransferthroughoutthesystem.Tocalculateeffectivenessfortheshell

andtubeheatexchanger,thefollowingequationisused.

! = #$∗('$,)*'$,+)#-+.∗('/,+*'$,+)

(C-1.1)

Thisequationcanbesimplifiedbecausebothofthefluidsintheshellandtubearewater

soheatcapacitiesanddensitiescanceloutandbecomearatioofflowrates.Effectivenessranges

fromzerotoonewithonebeingthemosteffective.

Figure6.Effectivenessvs.NTUforCo/Counter-CurrentOperation

Figure6showsaplotofNTUverseeffectiveness.Theplotshowscountercurrentflowachieves

thehighesteffectivenesswithin theheatexchanger.Theeffectivenessof theheatexchanger

reachesamaximumof0.47whenrunningincounter-currentwithashellsideflowrateof9.46

gpmand tube side flow rateof 2.97 gpm.However, there are several other factors that can

diminishtheeffectivenessoftheheatexchanger.Foulingofthetubeswithinthebundlecanadd

15

thermal resistance and decrease heat exchange. Laminar flowwith in the shell or tube also

decreases effectiveness because layers are formed within the flowing fluid reducing heat

exchange.

Theplotalsoshowsthataseffectivenessincreases,sodoesthenumberoftransferunits

(NTU).NTUisafunctionofefficienciesandtheratioofheatcapacityrates.NTUisamaximumof

0.71atthegreatesteffectiveness.Itiscalculatedbythefollowingequation:

012 = − 1 + 678 *9:;< =*>=?>

(C-1.2)

Theefficiencyof theheat exchanger canbe also calculated in theNTUmethod. Efficiency is

governedbytheratiooftheminimumandmaximumheatcapacityratesandeffectiveness.The

efficiency of the heat exchanger determines how well energy is transferred throughout the

system.Table5,shownonthefollowingpage,providestheefficiencies forboththecounter-

currentandco-currenttrials.Thefollowingequationisusedtocalculateefficiency.

@ =A:*(>?#B)

(>?#B:)9/: (C-1.3)

16

Table5.CalculatedDataforNTUAnalysisMethod

OverallheattransferforasingletubeiscalculatedbymultiplyingNTUwithCminandthendividing

bytheoutsidesurfaceareaofthetube.Thisvaluetellstheoverallheattransferredofeachtube

inthetubebundle.Table5providesthevaluesofUtubeforallthetrailsintheexperiment.The

equationbelowshowsthatasNTUincreases,sodoestheoverallheattransfer.

2DEFG =#-+.∗H'IJKLMN

(C-1.4)

TheoverallheattransferfortheentirebundleiscalculatedbymultiplyingUtubebythenumberof

tubesinthebundle.

Optimal operation of the heat exchanger is determined at the greatest effectiveness

becausethatiswherethemostheattransferistakingplace.Co-currentoperationoftheheat

exchangerisoptimalwhentubesideflowratesarehighandshellsideflowratesarelow.

17

Figure7illustratesthevariousflowratesforthedifferenttrialsandshowstheeffectivenessof

eachtrial.Amaxeffectivenessisreachedwhen2.71gpmisflowingthroughtheshellsideand

10.11gpmthroughthetubeside.

Figure7.EffectivenessofCo-CurrentOperation(3DScatter)

Counter-currenthasoptimaloperationwhenthereisalargedifferencebetweentheshelland

tubeflowrates.Figure8providesavisualoftheeffectivenessforcounter-currentoperationfor

eachtrialpreformedintheexperiment.

Figure8.EffectivenessofCounter-CurrentOperation(3DScatter)

18

HeatandMomentumTransferCorrelation

TheheatandmomentumcorrelationmethodusesrelationshipsbetweenRe,Pr,andNuto

calculateconvectiveheattransfercoefficients.TheReynoldsandPrandtlnumberswere

calculatedusingthefollowingformulas:

OP = QRS+T

(C-2.1)

U7 = #V,WT

X (C-2.2)

Forlaminarflowregimes(i.e.Re<2300),theNusseltnumberismodeledbytheequation

below:

0Y = 1.953 OPU7 S+^

>/_ (C-2.3)

Eachtrialwasassumedtobelaminarinthisaspect,andthususedequation(C-2.3).Usingthe

definitionoftheNusseltnumberinequation(C-2.4),theinnerconvectiveheattransfer

coefficient(hi)canbecalculated.

0Y = b+S+X (C-2.4)

Oncetheinnerconvectiveheattransfercorrelationiscalculated,theouterconvectiveheat

transfercoefficientiscalculatedusingequation(C-2.6)below.Roviscalculatedusingrelations

describedintheWilsonplotmethodsection.

OcR =>

b)J)+ >

b+J+ (C-2.6)

Afterdeterminingtheinnerandouterconvectiveheattransfercoefficients,theoverallheat

transfercoefficient(U)canbefoundusingthefollowingequation:

2d' =>

9/)e)

? 9/+e+

(C-2.8)

SampleintermediatecalculationsareprovidedinAppendixD.Below,inTable6andTable7are

theintermediateparametervaluesforeachoperationaltrial,co-currentandcounter-current

flow.

19

Table6.CalculatedCorrelationData–Co-CurrentOperation

Table7.CalculatedCorrelationData–Counter-CurrentOperation

Whencompletingthecalculationsinthetables,thermocouple10isignoredduetosignificant

temperaturedropasaresultofpoorinsulation.Thus,thermocouple4isusedfortemperature

20

outputonthetubeside.Someofthetubeoutputtemperaturesreadhigherthantheshell

outputtemperatureswhichresultedintheerrorsseeninthetables.Theaverageoverallheat

transfercoefficientsforco-currentandcounter-currentfloware1268.47and836.76W/m2K

respectively.Avisualrepresentationoftheeffectsofvaryingtubesideandshellsideflowrates

ontheoverallheattransfercoefficientisshowninFigure9below.

Figure9.Co/Counter-CurrentFlowRatesvs.OverallHeatTransferCoefficient

AsseeninFigure9,theco-currenttrialsresultedinahigheroverallheattransfercoefficient

thanthecounter-currenttrials.Thisiscontrarytoresearchtheorythatcounter-current

operationistheoptimalconfigurationforaheatexchanger.Thisresultcouldhavebeen

producedbypoorthermocoupleplacementandreadingsaswellassignificantlylowflow.

Furtherexplanationsofthisphenomenoncanbefoundintherecommendationssection.

WilsonPlotMethod

InformationregardingWilsonplotmethodcanbefoundinreference[2].Thismethodof

analysiscreatesalinearcorrelationbetweenthermalresistance(Rov)andamodificationofthe

Reynoldsnumber(Re).Therelationshipusedisthefollowing:

OcR = 6> + 68>

fG- (C-3.1)

The final form of theWilson relationship, shown above, is after the following assumptions:

21

turbulent flow, the tube wall thermal resistance is constant, the outer and inner fouling

resistanceisconstant,andthermalresistanceduetooutsidetubesconvectionisconstant.Using

theoriginalWilsonplotmethodm= 0.8, Rov can alsobe calculatedusing the followingheat

transferrelations:

OcR =∆'hij

(C-2.6)

Where,

∆1̂ k = '/,+*'$,+ *('/,+*'$,+)mn[

p/,+qp$,+p/,+qp$,)

] (C-2.5)

s = tu6vu(1c − 1w) (C-4.5)

Reiscalculatedusingthefollowingequation:

OP = QRS+T

(C-2.1)

Thesevaluesarethencalculatedfromtemperatureprofiledataforshellandtubesideatvarying

flowrates.Alinearregressionisthenappliedtothefirstequation.TheresultingvaluesforC1

andC2areusedtocalculatetheconvectiveheattransfercoefficientforinsideandoutsidevia

thefollowingequation:

ℎw =fG-

#:J+ (C-3.3)

ℎc =>

#9* fy,)?fK?fy,+ J)

AssumingthatOz,c + OD + Oz,w = 0:

ℎc =>

#9∗J) (C-3.2)

Thefollowingequationcanbeusedtoobtaintheoverallheattransfercoefficient(U)fortheheat

exchangeroncehforbothouterandinnerheattransferareobtained:

2d' =>

9/+e+

? 9/)e)

(C-3.4)

UisthevaluedesiredtobeobtainedfromapplyingtheWilsonplotmethod.Itprovidesanoverall

heattransfercoefficientthatcanbeappliedtotheheatexchangerandfurtherusedtodetermine

theeffectivenessthereof.

BoththeReandRovwerecalculatedforallcounter-currentandco-currentexperimental

22

trials.InAppendixDisanexamplecalculationofbothReandRovfromrun#1counter-current

experiment.Belowistheresultingtableafterapplyingtheabovecalculationstoalltrials:

Table8.Counter-CurrentvaluesforRovand1/RemforWilsonPlot

Table9.Co-CurrentvaluesforRovand1/RemforWilsonPlot

Note that thereareseveralvalueswithin the table that readerror.That isbecause in

thesetrialsthetubetemperatureishotterthantheshellside,disallowing∆1̂ kcalculation.The

error can be from poor thermocouple placement and/or readings. The assumption that

thermocouple10ismisreadingtemperatureisappliedtothissectionaspreviouslymentionedin

theheatandmomentumtransfercorrelationsectionoftheresultsanddiscussion.Bothdatasets

shown in Table 8 and 9 were plotted and linearly regressed. The results are shown on the

followingpage:

1 0.00056 0.00322 0.00068 0.00483 0.00063 0.00344 0.00068 0.00325 0.00065 0.00406 0.00064 0.00407 0.00071 0.00438 0.00067 0.0054S1 error errorS2 error errorS3 error errorS4 0.00046 0.0020S5 0.00050 0.0020S6 0.00056 0.0020S7 0.00055 0.0025S8 0.00057 0.0020S9 0.00054 0.0025S10 0.00057 0.0025

Run# Rov

(K/W)

1/Rem

(m=0.8)

Counter-Current

1 0.00038 0.00302 0.00042 0.00323 0.00041 0.00344 0.00050 0.00325 0.00041 0.00486 0.00050 0.00347 0.00047 0.00408 0.00043 0.00399 0.00039 0.004310 error error11 error errorS1 0.00041 0.0020S2 0.00050 0.0025S3 0.00049 0.0025S4 0.00054 0.0020S5 0.00054 0.0020S6 0.00048 0.0025S7 0.00048 0.0020

Run#Rov

(K/W)

1/Rem

(m=0.8)

Co-Current

23

Figure10.OriginalWilsonPlotMethodAppliedtoCo-Current

Figure11.OriginalWilsonPlotMethodAppliedtoCounter-Current

Forco-currentoperationsa68valueof-0.0329K/Wanda6>valueof0.0006K/Ware

achieved.Forcounter-currentoperationsa68valueof0.0545K/Wanda6>valueof0.0004K/W

areachieved.Notethat68forco-currentoperationsachievesanegativenumber.Thismaybe

duetothelackofturbulentflowwithinthetrial.Alsoco-currentflowislessoptimalofaheat

transferconfigurationandthusWilson’smethodcannotbeasreadilyapplied.Theresultsofthe

24

regressionareusedtocalculateconvectiveheattransfercoefficientsviaequations(C-3.2)and

(C-3.3). Samples calculations can be found in Appendix D. The overall heat transfer (U) is

calculated using both convective heat transfer coefficients. Below is the results of these

calculationforbothco-currentandcounter-currentoperations:

Table10.OriginalWilsonPlotLocalandOverallHeatTransferCoefficients

ℎw iscalculatedtobe8170.52W/m2Kforcounter-currentand-11811.44W/m2Kforco-current.

ℎciscalculatedtobe3146.56W/m2Kforcounter-currentand2497.27W/m2Kforco-current.2

iscalculatedtobe1085.37W/m2Kforcounter-currentand1386.26W/m2Kforco-current.The

valueofℎw forco-currentoperationsisanegativevalue,thisisbecauseofthenegativevaluefor

68.Theoverallheattransfercoefficientforco-current isstillsimilartotheaveragecalculated

value obtained using heat and momentum correlations (1199.98 W/m2K). The overall heat

transfercoefficientforcounter-currentoperationsisalsosimilartothosecalculatedbyheatand

momentumcorrelations(921.97W/m2K).Showingconfidenceinthevalidityoftheresultsvia

the Wilson method. 2is similar for both configurations which contradicts what would be

expected:counter-current tohaveasignificantly larger 2 thanco-current.Thismaybe from

factors such as thermocouple placement, and ignoringOz,c, OD, andOz,w in some calculations.

During the experiment rust is seen in the drain for both shell and tube side. Making tube

resistanceaswellasfoulingresistanceapotentialfactor.

ModifiedWilsonPlotMethod

ThismethodreliesheavilyontheWilsonplotmethodbutinvolvesasimplevariation.An

adaptedversionoftheoriginalWilsonequationisfirstmanipulatedusinglogarithmstoobtain

thefollowing:

ln >f)Ä*#9

= ln >#:

+ t ∗ ;<(OP) (C-3.5)

Counter-Current 8170.52 3146.56 1085.37Co-Current -11811.44 2497.27 1386.26

ho(W/m^2K)

Uo(W/m^2K)

hi(W/m^2K)

25

Aniterativeapproachisusedtofindtheoptimalvalueofm.TheoriginalWilsonmethod

iscompletedforavalueofm.Theobtained6>and68arethenusedinequation(C-3.1)andthis

equationis linearlyregressedtofindthenewm.Ifbothmvaluesareequalthenasolutionis

found;thisiscompletedusingMATLAB.Theoriginalcodeforbothoperationscanbefoundin

AppendixE.Theprogramgoesthroughvaluesofmfrom0.01to1incrementingby.01eachtime

andlinearlyregressestheoriginalWilsonequationinordertofind6>and68.Oncetheseare

foundtheyareplacedintoequation(C-3.5)andthisislinearlyregressedtofindthenewvalueof

m.Aconditionalstatementisplacedtoassurethat6>isapositivenumber.Ifthevalueof6>is

negative there will be negative resistance and may lead to a negative overall heat transfer

coefficient,thisphysicallycannothappenthusonlypositive6>valuescanbeused.Theoptimized

valueofmforco-currentandcounter-currentare0.01and0.24respectively.Theloweredvalues

showthatReynoldsnumberislesssignificantforthisheatexchangersystemthatthoseassumed

for theoriginalWilsonplot. Belowareplots created inMATLAB showinghow thedifference

betweencalculatedandinputmvalueschangewithchanginginputmvalues.

Figure12.DifferenceinmValuesvs.GuessedmValuesforCounter-Current

26

Figure13.DifferenceinmValuesvs.GuessedmValuesforCo-Current

Thefollowingmodifiedplotswereformedusingtheseoptimizedvalues:

Figure14.ModifiedWilsonPlotforCounter-CurrentOperations

27

Figure15.ModifiedWilsonPlotforCo-CurrentOperations

Usingequations(C-3.2),(C-3.3),and(C-3.4)valuesforℎw,ℎc,and2arecalculatedusingthe

modifiedmvalues:

Table11.LocalandOverallHeatTransferCoefficientsforModifiedWilsonMethod

ℎw iscalculatedtobe2464.64W/m2Kforcounter-currentand-159.18W/m2Kforco-current.ℎcis

calculatedtobe179803.68W/m2Kforcounter-currentand178.38W/m2Kforco-current.2is

calculatedtobe1317.97W/m2Kforcounter-currentand1387.89W/m2Kforco-current.Likethe

originalWilsonplotmethod,theslopeoftheco-currentlineofbestfitisnegative,thusleading

toanegativeinnerlocalheattransfercoefficient.InFundamentalsofHeatandMassTransfer,

typicalvaluesofforcedconvectionheattransfercoefficientsforliquidsrangefrom100to20,000

W/m2K(Incropera,2007).Thismatchesthevaluesforhointheco-currentandhiinthecounter-

current.AfterapplyingthemodifiedWilsonplotmethodthevalueof2forbothconfigurations

approachedamoresimilarvalue,howeverbothgrewfartherawayfromthe2calculatedthrough

heatandmomentumtransfer relations.2is similar forbothconfigurationswhichcontradicts

Counter-Current 2464.64 179803.68 1317.97Co-Current -159.18 178.38 1387.89

ho(W/m^2K)

Uo(W/m^2K)

hi(W/m^2K)

28

whatwouldbeexpected:counter-currenttohaveasignificantlylarger2thanco-current.This

maybe fromfactorssuchas thermocoupleplacement,and ignoringOz,c, OD, andOz,w insome

calculations.Duringtheexperimentrustisseeninthedrainforbothshellandtubeside,making

tuberesistanceaswellasfoulingresistanceapotentialfactor.

29

ErrorAnalysis

Theshellandtubeheatexchangerexperimentpresentsvariouspossiblesourcesoferror.

Thefirstglaringsourceoferrorcanbeseenintheanalysisofthetemperatureprofilecurves.

This error is discussed briefly in the discussion of the temperature profile curve results. A

thermocoupleworksbyproducingavoltagebetweentwounlikemetalswhentheyareheated

orcooled.Thisvoltageisthencorrelatedtoatemperatureandthistemperatureisoutput.There

isn’t any information available as to the last calibration of the thermocouples. If any of the

thermocouplesarenotcalibratedorhavenotbeencalibratedforanextendedperiodoftime,

theymayreadincorrecttemperatures.Theserecordedtemperaturesareusedineverymethod

ofdataanalysis.Iftheyareincorrectlydisplayedandrecorded,thisaffectsallofthecalculations

performed.Inaddition,thethermocouplesmaybemisplaced.Ifatubesidethermocoupleis

touchingthewallofoneofthetubes,itwillreadahighertemperaturebecauseofthehotliquid

intheshellsurroundingthecoppertubes.Ifathermocoupleoutsideoftheshellistouchinga

copperwall,itwillreadalowertemperature.Thisisbecausethecopperpipingoutsideofthe

shell is exposed to the laboratory air and not contained within the insulation of the heat

exchanger.Theassumptionthatthermocouple10ismisreadingtemperatureisappliedtothis

sectionaspreviouslymentionedintheheatandmomentumtransfercorrelationsectionofthe

resultsanddiscussion.

Foulingisanothersourceoferrorcertainlyinvolvedintheoperationoftheshellandtube

heatexchanger.Foulingistheaccumulationanddepositofunwantedmaterialsonsolidsurfaces,

whichinthiscasearethewallsofthecoppertubing.Thisdepositioncausesaddedresistanceto

thetransferofheat,whichreducestheheatexchangereffectivenessandefficiency(Bott,2006).

Foulingcalculationscanbeperformedusingratesofdepositionandremovalalongwithfouling

factorsandresistances.However,thesefoulingcalculationsarenotperformedorusedinany

methodof analysis. Therefore, the calculated values forheat transfer coefficients are larger

becauseofthedisregardedfoulingfactors.

Confidenceintervalcalculationsareperformedontheaverageheatfluxandoverallheat

transfercoefficientdataforbothco-currentandcounter-currentconfigurations.

30

Table12.ConfidenceIntervalCalculations

Aconfidencecoefficientischosenas1.96fortheproduced95%confidenceintervals.Itisfound

thatfortheco-currentdata,theoverallheattransfercoefficientisbetween1187.25and1349.69

W/m2Kwith95%confidenceandtheaverageheatflux isbetween28307.77and32415.28W

with95%confidence. It is found that for the counter-currentdata, theoverall heat transfer

coefficientisbetween793.89W/m2Kand879.62W/m2Kwith95%confidenceandtheaverage

heat flux is between 18508.42 and 30897.21Wwith 95% confidence. It is noticed that the

counter-current overall heat transfer coefficient has a smallermargin of error while the co-

currentaverageheatfluxhasasmallermarginoferror.Itisalsointerestingthattheaverageof

theoverallheattransfercoefficientis largerfortheco-currentconfiguration. This iscounter-

intuitivebecauseaccordingtotheory,thecounter-currentflowconfigurationshouldhavelarger

valuesfortheoverallheattransfercoefficient.Thisdiscrepancycouldbearesultofanyofthe

sourcesoferrordescribedlikethethermocoupleerror.

31

Conclusion

The purpose of the experiment is to determine the effect of flow rates and flow

configurationson theperformancecharacteristicsofa forcedconvection shell and tubeheat

exchanger.Thereareseveral limitingfactorsthathindertheabilitytoeffectivelyanalyzeheat

exchanger performance characteristics. The undersized pump and low city water pressure

prevents high flow rates to flow through the shell and tube heat exchanger. The inability to

achieveturbulentflowwithintheheatexchangerlimitseffectiveheattransferbetweentheshell

andtubebundle.WilsonandmodifiedWilsonplotassumeturbulentflowintheircalculations.

Generatingturbulentflowwouldallowformoreaccurateresultssuchaspositiveslopesforco-

currentoperations.Thermocouplereadingswouldbenefitfromturbulentmixingreducingthe

axialthermalgradient.Thermocouple10showstemperaturescoolerthanexpectedduetolack

of insulation. This effects calculations that depend on the results of the thermocouple. The

effectiveness/NTUmethoddeterminestheeffectivenessandefficiencyoftheshellandtubeheat

exchanger at varying flow rates. The counter-current flow configuration has a maximum

effectivenessof0.47withashellsideflowrateof9.46gpmandtubesideflowrateof2.97gpm.

Similarly,co-currentconfigurationhasthegreatesteffectivenesswhenthereisalargedifference

between the shell and tube flow rates. Co-current configuration reaches a maximum

effectivenessof0.43whentheshellsideflowrateis2.71gpmandtubesideflowrateis10.11

gpm. Counter-current shows a higher effectiveness than co-current and should be used for

optimaloperation.

TheheatandmomentummethodusesrelationshipsbetweenRe,Pr,andNutocalculate

convectiveheattransfercoefficients,whichareinturnusedtocalculatetheaverageoverallheat

transfercoefficient.Theaverageoverallheattransfercoefficientsforco-currentandcounter-

currentfloware1268.47and836.76W/m2Krespectively.Accordingtotheseaverages,theco-

currentconfigurationproducesahigherheattransfercoefficientthancounter-current.This is

contrarytoheatexchangertheory.

TheWilsonandmodifiedWilsonplotmethodcorrelatestheoverallthermalresistance

andReinordertocalculatetheaverageoverallheattransfercoefficient.ThroughtheWilsonplot

method,anoverallheattransfercoefficientforco-currentandcounter-currentarecalculatedto

32

be 1386.26 and 1085.37W/m2K respectively. The overall heat transfer coefficient using the

modifiedWilsonmethod is 1387.89 and 1317.97W/m2K for co-current and counter-current

respectively. Similar to the heat and momentum correlation theory results, theWilson and

modifiedWilsonmethodshowedhigherheattransfercoefficientsforco-currentflow.Thisisalso

contrarytoheatexchangertheory.

Uponanalysisof theresults, it isconcludedthat theexperimentshouldbeperformed

againusingrecommendationsstatedabove.This includesreplacingthermocouples, insulating

theheatexchangerarea,turbulentflowwithinboththeshellandtubeside,carefulmonitoring

of the water heater and increase number of experimental trails. This would allow formore

reliabledataandanalysis.

33

Recommendations

Theshellandtubeheatexchangerexperimentprovidedhandsonexperienceofacritical

industryprocess.Therewerenomajorincidentswhenperformingthelabbutthelabcouldhave

been completed more efficiently. A common problem experienced was the water heater

consistentlyoverheatingresultingittoautomaticallyshutoff.Coldwaterthenhadtobebled

intothewaterheatersothatitwouldcooldown.Thecoolwaterinthewaterheaterthenhadto

beheatedupagain.Thisprocessdelayedthelab25-30minuteseachtimeandpreventedsome

ofthelasttrailsincounter-currentoperationtobeconducted.However,theproblemcouldhave

beenavoidedifhigherflowratesintheshellandtubewereuseandconsistentmonitoringofthe

temperaturegaugeonthewaterheaterwasdone.

Another possible improvement could have been calibrating or replacing the

thermocouples prior to the preforming the experiment. It was discovered that some of the

temperaturereadingscollecteddidnotmakinglogicalsenseuponanalysis.Insomeofthetrials,

the temperature in the shell increasedafterpassing through the tubebundle.Thermocouple

errorcouldbeattributedtobeing incontactwiththecopperpipesor lackofaccuracytothe

thermocouple itself.Replacingandcorrectly installingnewthermocoupleswould improvethe

data collected from the heat exchanger. Insulation should be provided to surround the heat

exchangerareaaroundthermocouple10.Thiswouldeliminatethesignificanttemperaturedrop

andtheneedtoomititsvalueduringanalysis.

Also, one of the pressure gauges was not properly calibrated to zero resulting in an

estimationofpressuresandnotcertainvalues.Thepressuregaugeshouldbeproperlycalibrated

togivemoreaccuratedata.Infutureexperiments,datatablesandthedesignspaceshouldbe

constructedbeforepreformingthelab.Experimentequipmentshouldbecalibratedandworking

properlybeforethelabformoreaccurateresults.Theaboveimprovementsandplanswillmake

futureexperimentscompletedmoreefficientlyandwithmoreaccuratedata.

34

DesignExtension

The objectives of the design extension are to determine which shell and tube heat

exchangerBuckeyeFoodsInc.shouldselectforoptimumqualityaswellasminimizingcost.The

inputandoutputtemperaturesoftheheatexchangeraregiven:25°Cand85°Cforthecoldwater

input and output temperatures. The input temperature for the steam is 150°C for both co-

currentandcountercurrentflow.Theoutputtemperaturesforco-currentandcountercurrent

floware100°Cand40°Crespectively.Theinputsteampressureis125kPaandthemaximum

pressuredropinthetubesideis200Pawhilethepressuredropfortheshellsideisassumed

negligible.Themassflowrateofwateris12,000kg/hr.

Further objectives for the shell and tube heat exchanger are to determine which

combinationof tubebundles, tubediameter,and lengthofheatexchangerwillmaximizethe

overallheattransfercoefficientwhiletryingtominimizethesteamflowrateandareaoftheheat

exchanger. Thepossiblechoices fortubebundlesare400,450,and500tubes. Thepossible

diameters are 0.2, 0.3, 0.4, and 0.5 inches. Finally, the possibilities for length of the heat

exchangerare0.75,1.25,and1.75meters.

Theapproachofthisdesignextensionistoiterativelysolveforthetubebundle,diameter,

andlengthoftheheatexchanger.Inordertodothis,anexceldocumentisusedthatholdstwo

variablesconstantwhilevaryingthethirduntilallpossiblecombinationsaredocumented.Once

allofthecombinationsarelisted,thecrosssectionalsurfaceareaofeachpipeiscalculated.The

velocityisthendeterminedusingthemassflowratepertubeanddividingbythecrosssectional

areaofeachtube.Thevelocityofwaterina0.2inchdiametertubewithamassflowrateof

12,000kg/hrand400tubebundleis0.414m/s.

With a known velocity, theReynolds number is calculated from thedensity ofwater,

velocity,diameter,andviscosity.

Re = QRST

(C-2.1)

Thedensityandviscosityofwaterat25°Care993kg/m3and6.95E-04kg/m*srespectively(NIST,

2015).Thevelocitiesanddiameterswillvaryamongsttrials.Foradiameterof0.2inandvelocity

of0.414m/s,theReynoldsnumberis3010.

35

Thequalificationofapressuredropof lessthan200Pais importanttoselection. The

pressuredropisfoundusingtheMoodyfrictionfactor(É).Thisfrictionfactoriscalculatedfrom

theReynoldsnumberandthecorrespondingequationsforlaminar,intermediate,andturbulent

flows.AnassumptionoffullydevelopedflowisusedtoaccessthenecessaryMoodyequations

tocalculatefrictionfactor.

Fullydevelopedlaminarflow(Re<2100):É = ÑÖfG (C-4.1)

Fullydevelopedturbulentflow(2100<Re<20,000):É = 0.316Re*>/Ö (C-4.2)

For the previously calculated Reynolds number of 3010, the fully developed turbulent flow

equation is used and the Moody friction factor is 4.27E-02. This friction factor is used to

determinethechangeinpressureandinthiscasethepressuredropacrossthetubesideofthe

heatexchanger.

ΔP = − âvä:ä9

= É QR:

8S âãå:å9

= É QR:

8S(ã8 −ã>) (C-4.3)

Thepressuredropofthe0.2indiametertubewithalengthof0.75mandatubebundleof400

tubesis536.34Pa(Incropera,2007).

Thenextstepintheapproachistominimizethesurfaceareaoftheheatexchangerwhich

will inturndeterminetheoverallheattransfercoefficient. Thesurfaceareaistheinnertube

surfaceareamultipliedbythenumberoftubes.Foradiameterof0.2inches,alengthof0.75m

andatubebundleof400tubes,thesurfaceareaoftheheatexchangeris4.788m2.Thefluxof

theheatexchangerismodeledbytheequation,

q = UA < ΔT >^k (C-4.4)

Theareaisknown,thetemperaturesareknownsointurn<ΔT>LMcanbedetermined,but

theflux,q,isnotknownandisnecessarytodeterminetheoverallheattransfercoefficient,U.

Thefluxcanalsobemodeledbytheequation,

q = t6vu(1ì,î −1ï,w) (C-4.5)

wherethemassflowratetis12,000kg/hr,thespecificheatcapacityofwater,Cp,w,at25°Cis

4.184kJ/kg*Kandthetemperaturesofcoldoutputand inputare85°Cand25°Crespectively.

Thefluxisthencalculatedtobe836.8kW.

36

The <ΔT>LM can be calculated for co-current and counter current flows using the known

temperatureinputsandoutputs.

< ΔT >^k= ñ' ^ *ñ'(ó)

mn[òp hòp ô ]

(C-4.6)

Foraco-currentheatexchangerwithcoldinputandoutputtemperaturesof25°Cand85°C,along

withsteaminputandoutputtemperaturesof150°Cand100°C,the<ΔT>LMccis51.88K.Using

the<ΔT>LMalongwiththecalculatedareasandflux,theoverallheattransfercoefficientisable

tobecalculated.Fora<ΔT>LMof51.88K,anareaof4.788m2,andafluxof836.8kW,theoverall

heattransfercoefficientUccforco-currentflowis3.369kW/m2K.

The final requirement of choosing the appropriate heat exchanger is tominimize the

steamflowrate.

tö = 6vö(1b,w–1ïcúù) +ΔHRüä +6vu(1ïcúù–1b,c) (C-4.7)

Thespecificheatcapacityofsteam,Cps,at150°Cis2.0039kJ/kg*K.Theheatofvaporization,

ΔHvap, is 2257 kJ/kg. The specific heat capacity of water at 25°C is 4.184 kJ/kg*K. The

temperature that steamcondenses,Tcond, is99.6°C (NIST,2015).Thesteam inputandoutput

temperaturesareusedalongwiththeNISTreferencedvaluestodeterminetheamountofsteam

required.Forco-currentflow,usingthetemperaturesof150°Cand100°C,thesteamrequiredis

0.355kg/s.

Withallofthepressuredropscalculatedforeachcombinationoftubebundle,diameter,

andlength,theheatexchangersthatdonotmeetthespecifications,theoneswithapressure

dropofmorethan200Pa,areeliminated.Afterwards,thesurfaceareaoftheheatexchanger

andthesteamflowratesareanalyzed.Thesmalleststeamflowrateandsurfaceareaarethe

desiredobjectivesoftheheatexchangerandallothercombinationsarethendiscarded.

Thedesignextension isbasedon theexperimentGroup13performed that involvesa

forced convection shell and tube heat exchanger. This heat exchanger can be operated in

differentflowconfigurationsandwithdifferentdesignspecificationstoachievecertainoutput

temperatures. A shell and tube heat exchanger runs a cold fluid through the tubes of the

apparatus and a hotter liquid through the shell side of the apparatus. The particular heat

exchangerbeingusedinthisextensionvariesthenumberofcoppertubes.Inthisextension,the

37

twofluidsbeingusedarewaterandsteam.Thehotterfluidcomesintocontactwiththetube

pipesasitflowsandheattransferoccursbetweenthetwofluids.Thecolderfluidgainsheatand

thehotterfluidlosesheat.Operationcanoccurinco-currentorcounter-currentflowpatterns.

Inco-current flow, thetubeandshell liquids flow in thesamedirection,however incounter-

currentflow,thetubeandshellliquidsflowinoppositedirections.Theseconfigurationsleadto

differentoutputtemperaturesandthereforedifferentexperimentalresults.

ThesummaryoftheresultscanbeseeninTable13onthefollowingpage.Theseresults

include the surface areas, steam requirements, and pressure drops, as well as overall heat

transfer coefficients. The results cover all of the distinct possibilities for tube bundle size,

diameter,and lengthof theheatexchanger.Calculationconstants for theresult tablecanbe

foundinAppendixG.

38

Table13.DesignExtensionIterationsandConclusions

39

From the results in Table 13, it can be seen that due to themaximum pressure drop of an

allowable200Pa,noneoftheheatexchangerswithadiameterof0.2inchescanbeused.The

pressuredrops in the0.2 inchdiameterheatexchanger range from362.95Pa to1251.46Pa

whichisextremelyhighandoverthelimit.Consequently,alloftheheatexchangerswitha0.2

inchdiameterhaveaReynoldsnumberofover2100.Theyrangefrom2400to3010,meaning

thattheflowthroughthetubesisturbulent.Forthediametersof0.3,0.4,and0.5,thepressure

dropinthetuberangesfrom5.48Pato123.35Pa.Allofthesepressuredropsinthetubeare

acceptable, and the correspondingReynoldsnumber for thesediameters are less than2100.

Theyrangefrom962to2000,meaningthattheflowforthesediametersislaminar.Itcanbe

shownthatonlylaminarflowtubesareacceptableforthemaximumallowablepressuredrop.

Thenextthingthatisconsideredisthesurfacearea.Whileminimizingsurfacearea,it

canbeseenthattheheatexchangerwithadiameterof0.3inches,atubebundleof400tubes,

andlengthof0.75metershasthelowestsurfaceareaof7.182m2.Alongwiththelowestsurface

area,thesteamflowrateneedstobeminimized.WhenreferencingTable13,itisseenthatthe

steamflowrateonlychangeswiththedirectionofflow.Inthiscase,alowersteamflowrateis

observedforthecountercurrentheatexchangerwith0.321kg/sasopposedtoco-currentsteam

flowof0.351kg/s.Consequently,thecountercurrentheatexchangerfortheabovespecified

dimensions,hasthelargestoverallheattransfercoefficientwith3.417kW/m2K.

TherecommendationforBuckeyeFoodsInc.istopurchasetheheatexchangerwith400

tubesinthetubebundle,adiameterof0.3inches,andalengthof0.75metersusingcounter

current flow. This combination meets the specifications for the pressure drop, minimizing

surfacearea,andminimizingsteamflowrate.Theflowinthetubewillbelaminar.Thepressure

dropinthetubeis52.86Pa.Thesurfaceareais7.182m2andthesteamflowrateis0.321kg/s.

Italsohasthehighestoverallheattransfercoefficientof3.417kW/m2K.Theheatfluxdoesnot

changethroughoutheatexchangers,buttheoverallheattransfercoefficientdoes.Alongwith

having the lowest surfacearea, thecorrespondingheat transfer coefficient is the largestand

mosteffective.Thisspecificheatexchangermeetsallofthespecificationsandcompletesallof

theobjectives.

40

The importanceofthedesignextension istorelatetheshellandtubeheatexchanger

experiment to industry and to scale-up the operation. In this case, determining which

combinationofmaterialsisthedesiredinformation.Bycalculatingandminimizingthesurface

areaandsteamflowrate,thiswillreducetheamountofmaterialneeded,inthisinstancecopper

andsteam.LimitingtheamountsofthesematerialswillreducecostandthereforesaveBuckeye

Foods Inc.money. Alongwith these calculations the heat exchanger needs to be themost

effectiveinordertogettheoptimalresultsfortheamountofmoneyspent.Thiswillincrease

overallprofit.Inthiscase,thehighestoverallheattransfercoefficientisdesiredwhichiswhy

thecountercurrentheatexchangerischosen.

41

NotationEnglishSymbols:

A Surfaceareaoftubes m2

Acs Crosssectionalareaoftube m2

Ai Thewettedsurfaceareaontheinsideofacoppertube m2

Ao Thewettedsurfaceareaontheoutsideofthecoppertube m2

C1 Wilsonmethodconstant K/WC2 Wilsonmethodconstant K/WCp,s Specificheatcapacityofsteam kJ/kg*KCp,w Specificheatofwater J/kg*KCmin Minimumflowrate gal/minCr Flowrateratio(min/max) DimensionlessD Diameter mDi Innertubediameter mDo Outertubediameter mDe Didyoucatchthisy/n DimensionlessE Efficiencyofheatexchanger DimensionlessFi Tubeflowrate gal/minFo Shellflowrate gal/min4 Moodyfrictionfactor Dimensionless

ΔHvap Heatofvaporizationofwater kJ/kghi Convectiveheattransfercoefficientontheinnertubesurface W/m2*Kho Convectiveheattransfercoefficientontheoutertubesurface W/m2*Kk Thermalconductivityofwater W/m*KL Length mm Wilsonconstant Dimensionlessmi Tubemassflowrate kg/smo Shellmassflowrate kg/s<w Massflowrateofwater kg/hr<s,cc Massflowrateofsteaminco-current kg/s<s,xc Massflowrateofsteamincounter-current kg/s

n Samplesize DimensionlessNu Nusseltnumber Dimensionless

NTU NumberofTransferUnits DimensionlessΔP Pressuredropintube PaPr Prandtlnumber Dimensionlessq Heatflux kW/m2

qavg Averageheatflux kW/m2qshell Heatflux(outertubeside) kW/m2qtube Heatflux(innertubeside) kW/m2Rf,i Innerfoulingresistance K/WRf,o Outerfoulingresistance K/W

42

Rov Overallthermalresistance K*m2/kWRt Tuberesistance K/WRe Reynoldsnumber Dimensionless

Tcond Temperaturethatsteamcondenses KTc,i Temperatureofcoldwaterinput KTc,o Temperatureofcoldwateroutput KTh,i Temperatureofhotwaterinput K

Th,o,cc Temperatureofhotwateroutputforco-current KTh,o,xc Temperatureofhotwateroutputforcounter-current K

Ti Innertubetemperature KTo Outertubetemperature KTS,i Temperatureofwateratshellinput KTS,o Temperatureofwateratshelloutput KTT,i Temperatureofwaterattubeinput KTT,o Temperatureofwaterattubeoutput KΔTLM Logmeantemperaturedifference K

<ΔT>LM,cc Logmeantemperaturedifferenceforco-current K<ΔT>LM,xc Logmeantemperaturedifferenceforcounter-current K

U Overallheattransfercoefficient W/m2*KUcc Overallheattransfercoefficientforco-current kW/m2*KUxc Overallheattransfercoefficientforcounter-current kW/m2*Kv Fluidvelocityinasingletube m/sO Statisicalmean various

zα/2 Confidencecoefficient DimensionlessGreekSymbols:

ρ Densityofwater kg/m3

µ Viscosityofwater kg/m*sσ Standarddeviation variousϵ Effectivenessofheatexchanger Dimensionless

43

LiteratureCited

[1]Fernandez-Seara,Jose."AGeneralReviewoftheWilsonPlotMethodandItsModifications

toDetermineConvectionCoefficientsinHeatExchangeDevices."AppliedThermalEngineering

(2006).ScienceDirect.Web.<http://fafnir.rose-

hulman.edu/~richards/courses/me462/ME462_Spring_2007-2008/Wilson_plot_method.pdf>.

[2] Fernández-Seara,José,FranciscoJoséUhía,JaimeSieres,andAntonioCampo."Experimental

ApparatusforMeasuringHeatTransferCoefficientsbytheWilsonPlotMethod."European

JournalofPhysics(2005):N1-N11.Print.

[3]"CorrelationsforConvectiveHeatTransfer."ChemicalEngineering,TheChemicalEngineers'

ResourcePage,Distillation,HeatTransfer,Design,SpreadsheetSolutions,Departments,

Chemistry.Web.16June2010.<http://www.cheresources.com/convection.shtml>.

[4]Incropera,FrankP.FundamentalsofHeatandMassTransfer.Hoboken,NJ:JohnWiley,

2007.Print.

[5]E.W.Lemmon,M.O.McLindenandD.G.Friend,"ThermophysicalPropertiesofFluid

Systems"inNISTChemistryWebBook,NISTStandardReferenceDatabaseNumber69,Eds.P.J.

LinstromandW.G.Mallard,NationalInstituteofStandardsandTechnology,GaithersburgMD,

20899,http://webbook.nist.gov,(retrievedFebruary13,2015)

[6]Denney,Michael.ShellandTubeHeatExchangerOperatingProcedure.OhioStateU,2015.

Print.

[7]"ChBE521HeatExchangers."OSUCarmen.JohnClay.Web.1Feb.2015.

[8]Bott,Theodore."FoulingofHeatExchangers."EncyclopediaofChemicalProcessing.Vol.10.

Birmingham:Taylor&Francis,2006.1043-1052.Print.

44

AppendixA-PreliminaryPreperationAssignmentExperimentIntroduction

Theexperimentbeingperformedinvolvesaforcedconvectionshellandtubeheatexchanger.Thisheat

exchangercanbeoperatedindifferentflowconfigurationsandatdifferentflowratestoachievecertain

outputtemperatures.Operationcanoccurinco-currentorcounter-currentflowpatterns.These

configurationswillleadtodifferentoutputtemperaturesandthereforedifferentexperimentalresults.

Theflowrateswillalsobevariedthroughouttheexperimentreachingamaximumof10GPMand6.6

GPMfortheshellandtubesidesrespectively.Theseparameterswillbechangedoverthecourseofthe

experimentinordertoevaluatetheshellandtubeheatexchangerperformance.Resultsobtainedwill

includetheshellandtubesideflowrates,allthermocouplereadings,andtubeandshellsidepressure

readings.Inordertoevaluatethisperformance,theeffectiveness,overallheattransfercoefficient,and

innerandouterconvectiveheattransfercoefficientswillbecalculatedforbothco-currentandcounter-

currentconfigurations.Enoughdatamustbecollectedinordertoaccuratelyevaluatetheperformance

indicatorsmentionedabove.Itissuggestedthattentotwentydatapointsbeacquiredforeach

configuration.Thedatamaythenbeanalyzedusingfivedifferentmethods.Thesemethodsinclude

WilsonPlotMethod,ModifiedWilsonPlotMethod,HeatandMomentumTransferCorrelations,

Effectiveness-NTUMethod,andproducingplotsofthetemperatureprofiles.Eachmethodhasdifferent

theories,assumptions,andanalyticalproceduresthatneedtobeexaminedandusedeffectivelyby

referringtothereferencedliterature.

SafetyHazardsandPrecautions

1) Hotpipesandhotwaterleaks

- Donottouchapparatuswithoutthermalgloves

2) Fallingobjects

- Wearhardhatandclosedtoedshoes

3) Slipperyconditionsfromleaksinequipment

- Wearclosedtoedshoeswithgoodtraction

- Cleanupleaksimmediately

4) Pressurebuildupintubes

- Befamiliarwithproceduretoavoiderrorsinvalveopeningsandclosingsthatcouldcause

pressurebuildup

45

- Wearsafetyglasses,hardhat,closedtoedshoes,longpantsandshirttoavoidleaksorpipes

burstingtoduepressure

5) Overheatingtheheater

- Alarmwillsound

- Donotrunheaterforextendedperiodoftimewithoutrunningcoldwaterthroughcold

tubeside

InformativeFlowSheet

Seeattachedcarbonpapersheetforexperimentflowvisual.

ExperimentalPlan

I. SequenceofOperations

• ThedocumentE-2ShellandTubeHXOperatingProcedure2014willbefrequently

referenced.Itisrecommendedtobringacopyofthisdocumenttothelaboratory.

• Followthetubesideoperationprocedureinordertosuccessfullybeginwaterflowthrough

thetubesideoftheheatexchanger.

o Initiallysettheflowrateto2.0GPM

o Donotlettheflowrateexceed6.6GPM

• Followtheshellsideoperationprocedureinordertofilltheshellsideandremoveallair

withinthesystem.

o Assurethattherearenobubbleswithintheflowmeter

o Setshellsidepressureto25psibyslowlybleedingoffpressurewiththedrainor

purgevalve

• Followtheco-currentoperationproceduretosettheHXintheco-currentposition

o Adjustshellsideflowrateto7GPM

o Donotlettheflowrateexceed10GPM

• Completethefollowingsetofadjustmentstothetubesideflowrate

o Settheflowratetothefollowingsetofpoints.Waitforsteadystatetobeachieved

andcollectconsistentshellsideflowrates,tubesideflowrates,allthermocouple

readings,tubesidepressurereadings,andhellsidepressurereadings.

o 2.0,2.5,3.0,3.5,4.0,4.5,5.0,5.5,6.0,6.5(GPM)

46

• Toanalyzeunsteadystateflowchangeintheco-currentconfigurationthetubesideflow

rateto1GPMandtheshellsideflowrateto3.5GPM

• Followthecounter-currentoperationproceduretosettheHXinthecounter-current

position

o Adjustshellsideflowrateto7GPM

o Donotlettheflowrateexceed10GPM

o Keeptheflowrateabove2GPM

• Completethefollowingsetofadjustmentstothetubesideflowrate

o Settheflowratetothefollowingsetofpoints.Waitforsteadystatetobeachieved

andcollectconsistentshellsideflowrates,tubesideflowrates,allthermocouple

readings,tubesidepressurereadings,andhellsidepressurereadings.

o 2.0,2.5,3.0,3.5,4.0,4.5,5.0,5.5,6.0,6.5(GPM)

• Toanalyzeunsteadystateflowchangeinthecounter-currentconfigurationthetubeside

flowrateto1GPMandtheshellsideflowrateto3.5GPM

• Completethepropershut-downprocedurewithdrainingwaterintheshellside

II. ResponsibilityAssignments

GroupLeader:ConorHughesisresponsibleformanagingallaspectsoftheexperimentincluding

planning,preparation,execution,analysis,design(orotherextensionofthedata),andreport

preparationanddelivery.Heisresponsibleformitigatinganyinternalissues.

DesignEngineer:DrewShortisresponsibleforthedesignextensionportionofthelaboratory.

Hemustfamiliarizehimselfwiththeequipmentinordertocompletethistask.

OperationsEngineer:KyleHofacreisresponsibleforpreparingexcelspreadsheetsanda

laboratorynotebookpriortothelab.Heisalsoresponsibleforrecordingalldatatakenduring

theexperimentandcreatingthecorrespondinggraphs.

DevelopmentEngineer:ScottReinhartisresponsibleforcompletingdataanalysis.Thisincludes

statisticalcomparisonsandapplyingtheoreticalknowledgetothedataset.

47

QualityEngineer:HusseinAlkhatibisasupporttoConorHughes,thegroupleader.Heis

responsibleforhelpingwithanyassistanceneeded.Alsoheisresponsibleformanagingthe

transitiontoanewexperiment.

III. PreparedDataSheets

DataspreadsheetsarepreparedinanExcelformat.

IV. MaterialSupplyChecklist

• HampdenModelH-6850-40ShellandTubeHeatExchanger

o 112CopperTubes

§ InnerTubeDiameter=0.21in

§ TubeThickness=0.02in

§ TubeLength=14in

• Flatheadscrewdrivertoreleaseairthrough“bleedairout”valve

• Inletcitywaterforhotandcoldinlets

• Thermalgloves

V. PersonalProtectiveEquipment(PPE)

• Hardhat

• Safetygoggles/glasses

• Closed-toedshoes

• Longpantsandshirt

• Thermalgloveswhenoperatingvalves

ExperimentPermissionForm

Seeattachedform.

48

AppendixB–ExperimentalSummaryReport

ExperimentSummaryReportExperimentNo.2

SHELL&TUBEHEATEXCHANGER

TheOhioStateUniversityChemicalEngineeringUnitOperationsSpring2015

Group13 GroupLeader–ConorHughes X

OperationsEngineer–KyleHofacre X

DesignEngineer–DrewShort X

DevelopmentEngineer–ScottReinhart X

QualityEngineer–HusseinAlkhatib X

TA:MichaelDenney

49

ExperimentalObservationManyobservationsandconclusionscanbemadefromapreliminaryassessmentofthedata

acquiredintheshellandtubeheatexchangerlab.Thetemperatureprofilesweregraphedforco-

currentandcounter-currentoperationaswellasunsteadystateoperation.Itwasexpectedthat

thesegraphswouldlooklikeFigure1inthelabproceduredocument,howevertheydeviatedfrom

theexpectedshape.Bothgraphsfollowedexpectedtrendsfortheshellside,butdidnotforthe

tubeside.Itcanbehypothesizedthatthisisduetothelocationofthethermocouplesandthelack

ofinsulationoneithersideofthetubes.Thenon-steadystatetemperatureprofileappearedas

expectedwithtemperaturesfluctuatingwithtime.Theheatfluxeswerealsocalculatedforevery

trial.Forthemostparttheseappearedasexpectedwithhighervaluesofheatfluxforcounter-

currentflowascomparedtoco-currentflow.However,thelasttwotrialsforco-currentflowhad

heatfluxvaluesofzero.Thisisnotpossible,asthetubeexittemperatureofwaterwouldhaveto

behigherthantheshellenteringtemperatureofwater.Itwasconcludedthatthismusthavebeen

theresultoffaultythermocouplereadings.Thesepreliminaryobservationsmayormaynotbe

validatedbyfurtherexplorationintoerroranalysis.

ExperimentDifficultiesSeveraldifficultieswereexperiencedwhenpreformingtheshellandtubeheatexchangerlab.The

mostprominentproblemwasthewaterheateroverheating.Whenlowflowrateswerebeing

tested,thewaterheatertendedtoreachhighertemperaturescausingittooverheat.Therewere

alsoperiodsoftimewhenthegroupwasdistractedfromthelabandthewaterheaterwouldover

heat.Restartingthewaterheaterrequiredittocooldownandthenheatbackupagaintoperform

thenexttrail.Thisseriesofeventstookuptoahalfhourcausingthelabtogolongerthanneeded.

Also,valveswerenoticedleakingbutitwasdeterminedthattheleakswouldnothaveasignificant

impactonthelab.Anotherdifficultyinlabwasthepressuregaugeontheleftshellsideoftheheat

exchangerwasnotproperlycalibratedtozero.However,thegaugeworkedproperlyafter

subtractingapproximatelythreepsioffthepressurereading.Trailsforthelabwererandomly

selectedatvariousflowrates.Thetargetflowratesvariedonthemetersoanaveragewas

determinedandaplusorminusfactorweretakenintoaccountwhenrecording.

50

ExperimentalRawData

Co-CurrentFlow

Number'of'Tubes 112 tubes Intermediate'Data: 1000 kg/m^3 Gallon'>>'m^3 0Inner'Tube'Diameter 0.21 inches 0.65 W/m*K in'>>'m 0.03Thickness'of'Tube 0.02 inches 4.18 J/g*K min'>>'s 0.02Tube'Length 14 inches 0 kg/m*s

1

Material'Parameters: Water'DensityThermal'ConductivitySpecific'HeatViscosityμb/μw

Shell%Side Tube%SideTube%Left

Tube%Right

Shell%Left**

Shell%Right #1 #2 #3 #4 #10 #5 #6 #7 #8 #9

1 9:01 2.16 6.50 40 44 29 30 12.78 41.67 43.33 43.89 23.33 76.11 65.00 52.78 49.44 44.442 9:14 3.02 6.00 42 46 29 28 12.78 43.33 45.00 46.11 24.44 70.56 63.33 53.89 51.11 47.223 9:21 4.01 5.50 44 48 29 27 12.78 44.44 45.56 47.78 25.56 66.11 61.67 54.44 52.22 48.894 9:28 9.54 6.00 42 46 29 28 13.33 42.22 43.89 45.56 25.00 56.67 54.44 52.22 51.11 49.445 9:35 8.08 3.52 49.5 52 29 28.5 13.33 48.33 49.44 52.78 32.78 61.67 59.44 56.67 55.56 53.336 9:41 8.50 5.53 44 46 29 28 13.33 43.89 45.00 47.22 26.11 58.89 56.67 53.33 52.78 50.567 9:47 7.05 4.50 46.5 50 29 28 13.33 45.56 47.22 50.00 28.89 61.11 58.33 55.00 53.89 51.678 10:38 5.62 4.59 46 50 28 27.5 14.44 47.22 48.33 51.11 30.00 64.44 61.11 56.67 55.00 52.229 10:44 5.53 4.02 48 50 28 27.5 14.44 49.44 50.00 52.78 32.22 67.78 63.89 58.33 56.67 53.3310 10:50 9.47 3.00 50 52 30 29 15.00 53.33 53.33 57.22 37.78 64.44 62.78 60.00 59.44 57.2211 11:24 3.30 3.75 48 52 26.5 26.5 15.00 47.78 48.33 51.11 31.67 70.00 64.44 57.78 53.89 50.00

Time

Thermocouple+Readings+(°C)

Tube+Side Shell+SidePressure+(psi)Flow+Rate+(GPM)

Run%#

51

Counter-CurrentFlow

Re Pr ψ

Nu(Re)<)2030) h ΔTL ΔT0 ΔTLM

Shell)Side

Tube)Side

1408.57 3.22 4.08 9.11 1117.68 0.56 63.33 13.25 14.81 2.43 6.29 0.13311301.82 3.22 3.98 8.88 1088.70 1.11 57.78 14.34 15.61 3.31 5.81 0.12301195.07 3.22 3.86 8.63 1058.09 1.11 53.33 13.49 14.27 4.32 5.34 0.11291301.82 3.22 3.98 8.88 1088.70 3.89 43.33 16.36 17.81 9.99 5.81 0.1230772.34 3.22 3.34 7.46 914.80 0.56 48.33 10.70 9.79 8.49 3.45 0.07301201.48 3.22 3.87 8.64 1059.98 3.33 45.56 16.15 17.11 8.92 5.36 0.1135981.57 3.22 3.62 8.08 990.91 1.67 47.78 13.74 13.62 7.44 4.38 0.09271000.79 3.22 3.64 8.13 997.33 1.11 50.00 12.84 12.81 5.97 4.47 0.0946879.09 3.22 3.49 7.79 955.15 0.56 53.33 11.56 11.04 5.88 3.92 0.0831661.32 3.22 3.17 7.08 868.69 0.00 49.44 0.00 0.00 9.91 2.95 0.0625821.45 3.22 3.41 7.61 933.79 A1.11 55.00 0.00 0.00 3.59 3.67 0.0776

Tube)Velocity)(m/s)

Calibrated*Flow*Rate*

Heat)Flux)

(kW/m^3)

Shell%Side Tube%Side Tube%LeftTube%RightShell%Left Shell%Right #1 #2 #3 #4 #10 #5 #6 #7 #8 #9

1 11:42 9.08 5.97 42 44 29.5 27.5 15.00 40.56 45.00 47.22 26.67 48.33 51.11 53.89 55.00 56.672 11:47 7.08 3.56 49 52 29.5 27 15.00 46.67 50.00 55.00 34.44 52.22 55.56 59.44 60.56 62.783 12:24 5.56 5.48 44 46 28 25.5 14.44 40.56 45.00 48.33 27.22 47.22 51.11 55.56 57.22 60.004 12:32 3.05 6.01 42 45 28 25 14.44 37.78 44.44 47.78 26.11 43.33 50.00 57.78 62.22 66.675 12:38 6.11 4.49 46 50 28.5 25.75 14.44 43.33 47.22 51.67 30.00 49.44 53.33 57.22 58.89 61.676 12:44 8.04 4.48 46 48 28.5 26.25 14.44 42.22 46.67 50.00 28.89 49.44 52.78 55.56 56.67 58.897 12:50 5.04 4.08 48 50 28 25.5 14.44 43.33 48.33 52.78 31.67 49.44 53.89 58.33 60.56 63.898 12:56 9.03 3.02 50 52 29 27 14.44 48.89 52.22 57.22 37.22 54.44 56.67 60.00 60.56 62.78

Tube%Side Shell%Side

Run%# Time

Flow%Rate%(GPM) Pressure%(psi)

Thermocouple%Readings%(°C)

52

Non-SteadyState

Re Pr ψ

Nu(Re)<)2030) h ΔTL ΔT0 ΔTLM

Shell)Side

Tube)Side

1295.42 3.22 3.97 8.86 1086.91 9.44 33.33 18.94 20.59 9.52 5.78 0.1224780.88 3.22 3.35 7.49 918.16 7.78 37.22 18.81 17.27 7.47 3.49 0.07381190.80 3.22 3.86 8.62 1056.83 11.67 32.78 20.44 21.60 5.91 5.32 0.11251303.96 3.22 3.98 8.88 1089.30 18.89 28.89 23.54 25.64 3.34 5.82 0.1232979.44 3.22 3.62 8.07 990.19 10.00 35.00 19.96 19.76 6.47 4.37 0.0925977.30 3.22 3.61 8.07 989.47 8.89 35.00 19.05 18.85 8.45 4.36 0.0923891.90 3.22 3.51 7.82 959.76 11.11 35.00 20.82 19.98 5.38 3.98 0.0843665.59 3.22 3.18 7.10 870.55 5.56 40.00 17.45 15.19 9.46 2.97 0.0629

Calibrated*Flow*Rate*Tube)

Velocity

Heat)Flux)

(kW/m^3)

Time Tube Shell

0 121 13710 127 14020 130 14130 132 14340 133 14450 135 14660 138 14770 139 14980 140 15090 142 151

100 143 152110 144 153120 145 155

53

TemperatureProfiles

Figure1.Temperatureprofileforrun3ofco-currentoperation

Figure2.Temperatureprofileforrun3ofcountercurrentoperation

54

Figure3.Temperatureprofilenon-steadystateoperation

55

AppendixC–ReportFormulasEffectiveness-NTUMethod

! =#$∗('$,)*'$,+)

#-+.∗('/,+*'$,+) (C-1.1)

012 = − 1 + 678 *9:;<

=*>

=?> (C-1.2)

@ =A:*(>?#B)

(>?#B:)9/: (C-1.3)

2DEFG =#-+.∗H'I

JKLMN (C-1.4)

67 =#-+.

#-OP (C-1.5)

HeatandMomentumTransferCorrelation

QR =STU+V

(C-2.1)

W7 =#X,YV

Z (C-2.2)

0[ = 1.953 QRW7U+`

>/a (C-2.3)

0[ =b+U+Z (C-2.4)

∆1̀ d ='e,)*'e,+ *('f,)*'f,+)

ghfe,)ife,+(ff,)iff,+)

(C-2.5)

QjT =∆'klm

=>

b)J)+

>

b+J+ (C-2.6)

no =p q.a∗>ris S(')*'+)#X,Y

(>>8)(>rrr)tU+` (C-2.7)

2u' =>

9/)v)

?9

/+v+

(C-2.8)

Wilson/ModifiedWilsonPlotMethod

QjT = 6> + 68>

wG- (C-3.1)

ℎj =>

#9∗J) (C-3.2)

56

ℎo = (wGOz{)-

#:J+ (C-3.3)

2 =>

[9

/+v+?

9/)v)

]Jf (C-3.4)

ln>

w)z*#9= ln

>

#:+ Ä ∗ ;<(QR) (C-3.5)

ExperimentDesignExtension

Fullydevelopedlaminarflow(Re<2100):Å = qÇ

wG (C-4.1)

Fullydevelopedturbulentflow(2100<Re<20,000):Å = 0.316Re*>/Ç (C-4.2)

ΔP = − âäã:ã9

= ÅST:

8U âå

ç:ç9

= ÅST:

8U(å8 −å>) (C-4.3)

q = UA < ΔT >`d (C-4.4)

q = Ä6äî(1ï,ñ −1ó,o) (C-4.5)

< ΔT >`d= ò' ` *ò'(r)

gh[ôf kôf ö

] (C-4.6)

Äõ = 6äõ(1b,o–1ójùû) +ΔHT†ã +6äî(1ójùû–1b,j) (C-4.7)

ErrorAnalysis

å = ç

ù (C-5.1)

° = (ç*ç):

ù*> (C-5.2)

6¢ = å ± §•/8 ∗¶

ù (C-5.3)

57

AppendixD–SampleCalculations

Effectiveness-NTUMethod

CalculatingHeatCapacityRates

Ä = 10ß®©6ã = 4180

¨ß®≠

6ó = 10ß®©∗ 4180

¨ß®≠

= 41800Æ≠

Ä = 8ß®©6ã = 4180

¨ß®≠

6Øoù = 8ß®©∗ 4180

¨ß®≠

= 33440Æ≠

CalculatingEffectiveness:

1ó,j = 296.48≠1ó,o = 285.93≠1b,o = 349.29≠

! =41800

Æ≠ ∗ (296.48≠ − 285.93≠)

33440Æ≠ ∗ (349.29≠ − 285.93≠)

= .21

67 =33440

Æ≠

41800Æ≠

= .8

CalculatingEfficiency:

@ =

2. 21 − (1 + .21)

(1 +. 218)>/8= 8.14

CalculatingNumberofTransferUnits(NTU):

012 = − 1 +. 218 *>8;<

8.14 − 18.14 + 1

= .25

HeatandMomentumTransferCorrelation

CalculatedReynoldsnumber:

QR =

989.83ß®Äa ∗ .15

Ä© ∗ .21±< ∗

.0254ı<

. 00058ß®Ä ∗ ©

= 1327.71

58

CalculatedPrandtlnumber:

Pr =4066

¨ß® ∗ ≠ ∗ 0.00058

ß®Ä ∗ ©

0.63842Æ

Ä ∗ ≠

= 3.69([<±¥;R©©)

CalculatedNusseltnumber:

0[ = 1.953 ∗ (1327.71 ∗ 3.69 ∗ .21±<

14±<)>a = 8.18

Calculatedconvectiveheattransfercoefficient(inner):

ℎo =8.18 ∗ 0.63842

ÆÄ ∗ ≠

. 21±< ∗ .0254ı<

= 979.32Æ

Ä8≠

Calculatedconvectiveheattransfercoefficient(outer):

ℎj =>

r.rrrµq8∂∑*

ö.∏π-:

π∏π.∫:∑

-:∂∗ö.ª∏-:

= −1529.13º

Ø:Ω

Wilson/ModifiedWilsonPlotMethodPhysicalpropertiesofwaterat45oC:

æ = 989.83ß®Äa ß = .6384

ÆÄ ∗ ≠

6ã = 4066¨

ß® ∗ ≠ø = .00058

ß®Ä ∗ ©

Physicalpropertiesoftubeandshellside:

¿o = .21±<¿j = .25±<uo = .67Äauj = .79Äa¡ = 14±<Collecteddatafromcounter-currentrun#1:

¬o = 5.78®√;ı<

¬j = 9.52®√;ı<

1b,o = 329.82≠1b,j = 321.48≠1ó,o = 288.15≠1ó,j = 320.37≠Calculatedmassflowrate:

Äo = 5.78®√;ı<

∗. 0038Äa

®√;∗. 0167ı<

©Rƒ∗989.83ß®

Äa = .36ß®©Rƒ

Äj = .60ß®©Rƒ

59

Calculatedtubevelocity:

≈ =

5.78®√;ı< ∗

. 0038Äa

®√; ∗ . 0167ı<

©Rƒ

(∆ ∗ (. 21±< ∗

.0254ı<

2 )8 ∗ 112¥[«R)

= .15Ä©

Calculatedtubeandshellheatflow:

nDEFG = .36ß®©Rƒ

∗ 4066¨ß® ∗ ≠

320.37≠ − 288.15≠ = 47319.81ÆnõbG»» = 20133.71Æ

Calculatedaverageheatflow:

n†T… = 12632.31Æ + 48844.93Æ

2= 33726.76Æ

Calculatedlogmeantemperature:

∆1̀ d = 329.82≠ − 320.37≠ − (321.48≠ − 288.15≠)

ln[329.82≠ − 320.37≠321.48≠ − 288.15≠]

= 18.94≠

Calculatedoverallresistance:

QjT =18.94≠

30738.62Æ= .00062

≠Æ

CalculatedReynoldsnumber:

QR = π π. ∫À{

-∫ ∗.>µ-Ã∗.8>où∗

.ö:sÕ-+.

.rrrµŒÀ{-∗Ã

=1327.71

Calculated >

wG-:

>

wG-=

>

>a8œ.œ>. =0.0032

Wilsonplotconstants(linearregression):

68 = .055Ω

º6> = .0004

Ω

º

Calculatedlocalheattransfercoefficientforoutertube:

ℎj = 1

. 0004≠Æ ∗ .79Ä8

= 3146.56Æ

≠ ∗ Ä8

60

Calculatedlocalheattransfercoefficientforinnertube:

ℎo = 8.65

. 055≠Æ ∗ .67Ä8

= 8170.52Æ

≠ ∗ Ä8

Calculatedoverallheattransfercoefficient:

2 =>

9

9∏ö.s:∑

∂∗-:∗.ª∏-:?

9

∫9Õª.sª∑

∂∗-:∗.∏π-:∗[.œ–Ø:?.qœØ:]

=1085.37 º

Ω∗Ø:

ExperimentDesignExtension

Calculatingvelocityinasingletube:

uóõ = π(0.2±<1

x2.54ƒÄ1±<

x1Ä

2.54ƒÄx12)8 = 2.03x10*µÄ8

v = 12,000ß®

ℎ7x

Äa

993߮x

1(∆/4)(0.00508Ä)8

x1ℎ73600©

x1

400¥[«R©= 0.414m/s

Calculatingpressuredropinthetube:

Re = (993ß®/Äa)(

0.414Ä© )(0.00508Ä)

6.95å10*ÇZ…Ä − ©

= 3.01x10a

Å = 642000

= 3.19x10*8

Å = 0.316(3010)*>/Ç = 4.27x10*8

ΔP = − âäã:

ã9

= Åæ≈8

2¿ âå

ç:

ç9

= 4.27x10*8(993ß®/Äa)(

0.414Ä© )8

2(0.00508)(0.75m − 0m)

= 536.34Pa

Calculatingoverallheattransfercoefficient:

u = ∆0.2±<1

x2.54ƒÄ1±<

x1Ä

2.54ƒÄ)x0.75mx400tubes = 4.788Ä8

< ΔT >`d=(373.15≠ − 358.15≠) − (423.15≠ − 298.15≠)

ln[(373.15≠ − 358.15≠)(423.15≠ − 298.15≠)]

= 51.88K

61

n =12,000ß®

ℎ7å

1ℎ73600©

å(4.184kJ/kg ∗ K)(358.15K– 298.15K) = 836.8kW

2 =836.8ßÆ

(4.788Ä^2)(51.88≠)= 3.369kW/Ä8K

Calculatingsteamflowrate:

Äõ = 2.0039kJ/kg ∗ K(423.15K– 372.75K) + 2257kJ/kg + 4.184kJ/kg

∗ K(372.75K– 373.15K) = 0.355kg/s

ErrorAnalysis

Calculatingconfidenceinterval:

6¢ = 836.36Æ

Ä8 ∗ ≠± 1.96 ∗

61.85Æ

Ä8 ∗ ≠8

6¢ = 836.36Æ

Ä8 ∗ ≠± 42.86

ÆÄ8 ∗ ≠

62

AppendixE–MATLABCodeCo-CurrentOperation(WilsonPlot)clear all clc %For co-current operations Rov = [0.0003831 0.0004170 0.0004068 0.0004968 0.0004075 0.0004965 0.0004687 0.0004272 0.0003870 0.0004088 0.0005044 0.0004919 0.0005403 0.0005391 0.0004841 0.0004787]'; %enters Rov data Re = [1443.69 1334.28 1224.86 1334.28 791.60 1231.43 1006.04 1025.74 901.01 2428.39 1809.12 1809.12 2428.39 2428.39 1809.12 2428.39]'; %Enters Re data

63

j=1; %creates index variable j for i = 0.01:.01:1 p = polyfit(1./(Re.^i),Rov,1); %linearly regresses orginal Wilson equation yfit = polyval(p,1./(Re.^i)); %applies statistics to find Rsquared values ymean = mean(Rov); SSR = sum((yfit-ymean).^2); SST = sum((Rov-ymean).^2); m = polyfit(log(Re),log(1./(Rov-p(2))),1); %linearly regresses modified wilson equation if(p(2)>=0) %condition assuring that C1 is positive diff(j,1) = abs(m(1)-i); %finds the absolute value between the two m values diff(j,3) = i; %places the applied m value in an array diff(j,2) = SSR/SST; %calculates Rsquared and places it in array j=j+1; end end [a b] = min(diff(:,1)); %finds the minimum difference figure %plots Difference vs M valuse hold on plot(diff(:,3),diff(:,1)); title('Optimization of m for Co-Current Operations') ylabel('Difference (between m original and calculated)') xlabel('m values') hold off fprintf('Optimized m value: \n m = %2.2f \n RSquared = %2.2f \n', diff(b,3), diff(b,2)) %reports optimal value

64

Counter-CurrentOperation(WilsonPlot)clear all clc %For counter current operations Rov = [0.000562 0.000679 0.000630 0.000682 0.000650 0.000639 0.000712 0.000667 0.000465 0.000496 0.000560 0.000550 0.000566 0.000544 0.000570]'; %enters Rov data Re = [1327.71 800.35 1220.49 1336.46 1003.85 1001.67 914.14 682.19 2428.39 2428.39 2428.39 1809.12 2428.39 1809.12 1809.12]'; %Enters Re data j=1; %creates index variable j for i = 0.01:.01:1

65

p = polyfit(1./(Re.^i),Rov,1); %linearly regresses orginal Wilson equation yfit = polyval(p,1./(Re.^i)); %applies statistics to find Rsquared values ymean = mean(Rov); SSR = sum((yfit-ymean).^2); SST = sum((Rov-ymean).^2); m = polyfit(log(Re),log(1./(Rov-p(2))),1); %linearly regresses modified wilson equation if(p(2)>=0) %condition assuring that C1 is positive diff(j,1) = abs(m(1)-i); %finds the absolute value between the two m values diff(j,3) = i; %places the applied m value in an array diff(j,2) = SSR/SST; %calculates Rsquared and places it in array j=j+1; end end [a b] = min(diff(:,1)); %finds the minimum difference figure %plots Difference vs M valuse hold on plot(diff(:,3),diff(:,1)); title('Optimization of m for Counter-Current Operations') ylabel('Difference (between m original and calculated)') xlabel('m values') hold off fprintf('Optimized m value: \n m = %2.2f \n RSquared = %2.2f \n', diff(b,3), diff(b,2)) %reports optimal value

66

NTU3DScatterPlotclear all clc X=[9.52 7.47 5.91 3.34 6.47 8.45 5.38 9.46 9.95 10.11 7.54 2.80 5.14 2.84 5.15]' %shellside Y=[5.78 3.49 5.32 5.82 4.37 4.36 3.98 2.97 10.11 10.11 10.15 7.92 10.14 7.87 7.84]' %tubeside Z=[0.28 0.406976744 0.280487805 0.223404255 0.329411765 0.325 0.348314607 0.471264368 0.188403908 0.187535285

67

0.237068511 0.434219315 0.312662801 0.428403161 0.288942299]' figure scatter3(X,Y,Z) grid on xlabel('Shell Side Flow Rates (gpm)') ylabel('Tube Side Flow Rates (gpm)') zlabel('Effectiveness') title('Optimal Flow Rates for Counter-Current Operation') legend('Trials','Location','ne')

68

Co/Counter-CurrentOverallHeatTransferCoefficientvs.FlowRatesclc clear all X1=[2.43 3.31 4.32 9.99 8.49 8.92 7.44 5.97 5.88 5.16 7.55 9.95 2.78 2.78 9.95 7.55]' %shellside Y1=[6.29 5.81 5.34 5.81 3.45 5.36 4.38 4.47 3.92 10.58 7.88 7.88 10.58 10.58 7.88 10.58]' %tubeside Z1=[1418.54 1303.45 1335.89 1093.95 1333.57 1094.52 1159.51 1272.28 1404.49

69

1329.33 1077.45 1104.80 1005.85 1008.14 1122.65 1135.26]' %Coefficients X2=[9.52 7.47 5.91 3.34 6.47 8.45 5.38 9.46 9.95 7.55 2.78 5.16 2.78 5.16 5.16]' %shellside Y2=[5.78 3.49 5.32 5.82 4.37 4.36 3.98 2.97 10.58 10.58 10.58 7.88 10.58 7.88 7.88]' %tubeside Z2=[967.66 800.79 863.25 797.29 836.32 850.89 763.27

70

814.57 1169.57 1094.97 970.10 988.68 959.87 999.32 952.95]' %Coefficients figure hold on scatter3(X1,Y1,Z1,'filled') scatter3(X2,Y2,Z2,'filled','markerfacecolor',[1 0 0]) hold off grid on xlabel('Shell Side Flow Rates (gpm)') ylabel('Tube Side Flow Rates (gpm)') zlabel('Overall Heat Transfer Coefficient (W/m^2*K)') title('Optimal Flow Rates for Co/Counter-Current Operation') legend('Co-Current','Counter-Current','Location','ne')

71

AppendixF–CalibrationCurves

Figure16.ShellSideFlowrateCalibrationCurve

Figure17.TubeSideFlowrateCalibrationCurve

y=1.0243x+0.2145

Calib

ratedFlow

rate(G

PM)

MeasuredFlowrate(GPM)

ShellSideCalibrationCo/Countercurrent

72

AppendixG–AdditionalDataCo-CurrentandCounter-CurrentOperationTemperatureProfiles

73

74

75

76

77

78

TableofParametersandConstants

Table14.CalculationConstantsandProperties

Table15.DesignExtensionConstants

79

ExperimentTimeLog

Table16.OperationTimeLog