Experimental Evaluation of a Model Predicting the Performance of a Multiple-Stage Diffusion Based Solar Still

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Title:
Experimental Evaluation of a Model Predicting the Performance of a Multiple-Stage Diffusion Based Solar Still
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1 online resource (125 p.)
Language:
english
Creator:
Espinosa, Gabriel L
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University of Florida
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Gainesville, Fla.
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Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Mechanical Engineering, Mechanical and Aerospace Engineering
Committee Chair:
Ingley, Herbert A
Committee Members:
Lear, William E
Sherif, Sherif A
Pullammanappallil, Pratap C

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Subjects / Keywords:
desalination -- diffusion -- distillation -- solar -- still
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
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Mechanical Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

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Abstract:
Increasing population,industrialization and climate change are likely to drive an increasing demand for freshwater and energy, likely leading to shortages in both. Solar-thermal desalination, especially the solar still, may be used to alleviate these shortages on a small scale.These may become more economical with improved thermal performance. A detailed computer model of a solar still was made in a previous study. The intent was to determine the design parameters with the greatest impact on freshwater production and to predict the performance of a still.  This study focused on testing the accuracy of this model. A lab scale, single-effect still was constructed consisting of two vertical brass plates separated by certain width.  The still was tested at three different widths,and two different heat rates. Analysis of the collected data showed that the model was accurate for predicting average plate temperatures and freshwater production rates, especially at narrow widths and solar-like heat fluxes. The model did poorly at predicting the temperature profiles along the brass plates, especially at the top. The problem was that a critical assumption made in creating the computer model proved to be false. It is believed that the inaccuracies in the temperature profile prediction will have a cascading effect when modelling a multiple-effect still and make the results unusable. A multiple-effect still should be constructed and tested in order to verify this problem.  The model should be edited to correct the false assumption in order to make accurate temperature profile predictions.
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In the series University of Florida Digital Collections.
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Includes vita.
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Includes bibliographical references.
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This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility:
by Gabriel L Espinosa.
Thesis:
Thesis (Ph.D.)--University of Florida, 2012.
Local:
Adviser: Ingley, Herbert A.
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RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2013-08-31

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EXPERIMENTALEVALUATIONOFAMODELPREDICTINGTHEPERFORMANCEOFAVERTICLE-WICKDIFFUSIONBASEDSOLARSTILLByGABRIELL.ESPINOSAADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOLOFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENTOFTHEREQUIREMENTSFORTHEDEGREEOFDOCTOROFPHILOSOPHYUNIVERSITYOFFLORIDA2012

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c2012GabrielL.Espinosa 2

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HaikusareeasyButsometimestheydon'tmakesenseRefrigerator 3

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ACKNOWLEDGMENTS ThankstoeveronewhohelpedmewiththeprojectAtish,Boliang,AlexM.,AlexA.,Andres,Luis,Kemberly,Hansol,Alan,Agneya,andJohnny.Thankstomyfamilyfortheencouragement,Mom,Dad,Nick,Larry,TioandTia.Thankstomycommitteechair,Dr.Ingley,forhisinsight,guidenceandpatience.Thankstotheothermembersofmycommittee:Dr.Pullammanappallil,Dr.Sherif,andDr.Lear.ThankstothestateofFloridaforfundingme.Andthankyouforreadingthis. 4

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TABLEOFCONTENTS page ACKNOWLEDGMENTS .................................. 4 LISTOFTABLES ...................................... 7 LISTOFFIGURES ..................................... 8 ABSTRACT ......................................... 10 CHAPTER 1INTRODUCTIONANDBACKGROUND ...................... 12 1.1Introduction ................................... 12 1.2Background ................................... 13 1.2.1FreshwateravailabilityandNeeds ................... 13 1.2.2WaterUse ................................ 16 1.2.3Desalination ............................... 17 1.3RenewableEnergyDrivenDesalination ................... 20 1.4ResearchObjectives .............................. 23 2SOLARDISTILLATIONFUNDAMENTALSANDLITERATUREREVIEW .... 24 2.1Introduction ................................... 24 2.2DistillationFundamentals ........................... 24 2.3StillperipheralComponents .......................... 28 2.3.1ThermalSupply ............................. 28 2.3.2SalineSupply .............................. 29 2.3.3HeatRejection ............................. 31 3METHODOLOGY .................................. 32 3.1Introduction ................................... 32 3.2ExperimentalDesign .............................. 32 3.2.1Conceptual ............................... 33 3.3EquipmentDescription ............................. 36 3.4DataAcquisition ................................ 37 3.4.1Equipment ................................ 37 3.4.2ErrorAnalysis .............................. 39 3.4.3Procedure ................................ 39 3.5Safety ...................................... 40 4RESULTSANDDISCUSSION ........................... 41 4.1Introduction ................................... 41 4.2PreliminaryResultsandDiscussion ..................... 42 4.2.1Results ................................. 42 5

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4.2.2CoolingWaterFlowsfromToptoBottom ............... 43 4.2.3Discussion ................................ 45 4.2.3.1NarrowVaporSpaceTests ................. 48 4.2.3.2DistillateProduced ...................... 51 4.3MostRecentResults .............................. 52 4.3.1DeterminationoftheGrashofNumber ................ 52 4.3.2Retestofthe12.4mmgap ....................... 54 4.3.3Testsofthe4mmvaporspace .................... 54 4.3.3.1HighFluxTest ........................ 54 4.3.3.2LowerFluxTest ....................... 55 4.3.3.3PolymerWicktest ...................... 55 4.3.3.4GauzeWickTest ....................... 59 4.4Discussion ................................... 63 4.4.1ExplainationoftheSimulation ..................... 63 4.4.2ExplainationoftheData ........................ 65 4.4.3ExplainationoftheDiscrepancy .................... 68 5CONCLUSIONSANDRECOMMENDATIONS ................... 71 5.1Introduction ................................... 71 5.2Conclusions ................................... 71 5.3Recommendations ............................... 72 APPENDIX AENGINEERINGCHECKS .............................. 74 A.1AdjustmentsMadeintheSimulationParameters .............. 74 A.2Tables ...................................... 75 BSOURCECODEANDFLOWCHARTS ....................... 78 B.1SingleSolver .................................. 78 B.2SingleMaster .................................. 92 B.3SolutionOutline ................................. 97 B.4ControlPanel .................................. 108 B.5FlowCharts ................................... 115 REFERENCES ....................................... 122 BIOGRAPHICALSKETCH ................................ 125 6

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LISTOFTABLES Table page 1-1DistillationEnergyConsumption .......................... 20 3-1TableofConclusions/RecommendationsfromMitten[ 1 ] ............. 33 4-1ParametersUsedforNumericalSimulation .................... 42 4-2ChangesGoingfromLargeGaptoSmallGap .................. 50 4-3DistillateProductionRateComparison(allvaluesinmL/sunlessnotedotherwise).LowandHighreferto919W/m2and4290W/m2uxes,respectively ...... 57 4-4DiagramLabelsExplained .............................. 65 4-5GrashofNumberComparison.LowandHighreferto919and4290uxes,respectively ...................................... 66 4-6AverageEvaporatorPlateTemperatureComparison.LowandHighreferto919W/m2and4290W/m2uxes,respectively ................... 67 4-7AverageCondenserPlateTemperatureComparison.LowandHighreferto919W/m2and4290W/m2uxes,respectively ................... 67 A-1Samplewaterelectricalresistance ......................... 75 A-2PerformanceRatioTable.Distillateandenergyvaluesareperdiem ...... 76 A-3PerformanceRatioTable.Distillateandenergyvaluesareperdiem ...... 77 A-4MassBalanceTable(g) ............................... 77 7

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LISTOFFIGURES Figure page 1-1GlobalWaterAvailability ............................... 13 1-2GlobalmapofWaterScarcityIndex ........................ 14 1-3WaterStressCriticality ................................ 15 1-4Multiple-StageFlashPrincipleofOperation .................... 18 1-5Multiple-EffectBoilingPrincipleofOperation .................... 19 1-6Multiple-EffectBoilingPrincipleofOperation .................... 19 1-7VerticalMultiple-EffectStill ............................. 22 2-1Schematicofdistillationcell ............................. 25 3-1ExperimentalApparatus. .............................. 34 3-2InsulationBlockwithdistillate/brinecollector. ................... 34 3-3InternalStillPhoto. .................................. 35 3-4CondenserPlatePicture. .............................. 36 3-5EvaporatorPlate. ................................... 37 3-6Condenserplateassembly. ............................. 38 4-1CondenserPlateTemperaturevsDistancefromtopofCell. ........... 43 4-2EvaporatorPlateTemperaturevsDistancefromtopofCell. ........... 44 4-3CondenserPlateTemperaturevsDistancefromtopofCell,coolingwaterowingfromtoptobottom. .................................. 44 4-4EvaporatorPlateTemperaturevsDistancefromtopofCell,coolingwaterowingfromtoptobottom. .................................. 45 4-5CondenserPlateTemperaturevsDistancefromtopofCell,PredictedandMeasured. ...................................... 46 4-6CondenserPlateTemperaturevsDistancefromtopofCell,PredictedandMeasured. ...................................... 47 4-7Evaporator,narrowgap,comparison. ........................ 49 4-8CondenserPlateTemperaturevsDistancefromtopofCell,Comparison. ... 49 4-9DistillateProducedfor34.9mmGap,Data. .................... 51 8

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4-10CondenserPlateTemperaturevsDistancefromtopofCell,Comparison4mmLowPower. .................................... 56 4-11EvaporatorPlateTemperaturevsDistancefromtopofCell,Comparison4mmLowPower. .................................... 57 4-12CondenserPlateTemperaturevsFeedRateRatio,4mmLowPowerdataset. 58 4-13DistillateProductionvsFeedRateRatio,4mmLowPowerdataset. ...... 59 4-14CondenserPlateTemperaturevsFeedRateRatio,4mmgauzeLowPowerdataset. ........................................ 60 4-15EvaporatorPlateTemperaturevsFeedRateRatio,4mmgauzeLowPowerdataset. ........................................ 61 4-16DistillateProductionvsFeedRateRatio,4mmLowPowergauzedataset. .. 62 4-17EvaporatorandCondeserPlateTemperaturevsFeedRateRatio,4mmLowPowergauzedataset. ................................ 62 4-18Sketchofhowthecodeworks. ........................... 64 4-19EvaporatorPlateTemperatureandBulkSalineTemperature. .......... 69 B-1SingleSolverFlowchart. ............................... 116 B-2SingleMasterFlowchart. .............................. 117 B-3SingleSolutionOutlineFlowchartPart1. ..................... 118 B-4SingleSolutionOutlineFlowchartPart2. ..................... 119 B-5ControlPanelFlowchartPart1. ........................... 120 B-6ControlPanelFlowchartPart2. ........................... 121 9

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AbstractofDissertationPresentedtotheGraduateSchooloftheUniversityofFloridainPartialFulllmentoftheRequirementsfortheDegreeofDoctorofPhilosophyEXPERIMENTALEVALUATIONOFAMODELPREDICTINGTHEPERFORMANCEOFAVERTICLE-WICKDIFFUSIONBASEDSOLARSTILLByGabrielL.EspinosaAugust2012Chair:HerbertA.IngleyIIIMajor:MechanicalEngineeringIncreasingpopulations,industrializationandclimatechangearelikelytodriveanincreasingdemandforfreshwaterandenergy,likelyleadingtoshortagesinboth.Solar-thermaldesalination,especiallythesolarstill,maybeusedtoalleviatetheseshortagesonasmallscale.Thesemaybecomemoreeconomicalwithimprovedthermalperformance.Adetailedcomputermodelofasolarstillwasmadeinapreviousstudy.Theintentwastodeterminethedesignparameterswiththegreatestimpactonfreshwaterproductionandtopredicttheperformanceofastill.Thisstudyfocusedontestingtheveracityofthismodel.Alabscale,single-effectstillwasconstructedconsistingoftwoverticalbrassplatesseparatedbycertainwidthspecied.Thestillwastestedatthreedifferentwidths,andtwodifferentheatuxes.Analysisofthecollecteddatashowedthatthemodelwasaccurateforpredictingaverageplatetemperatures,especiallyatnarrowwidthsandsolar-likeheatuxes.Themodeldidpoorlyatpredictingthetemperatureprolesalongthebrassplates.Themodelgenerallymadebetterpredictionsoffreshwaterproductionasthewidthdecreased.Theproblemwasthatacriticalassumptionmadeincreatingthecomputermodelprovedtobefalse. 10

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Itisbelievedthattheinaccuraciesinthetemperatureprolepredictionwillhaveacascadingeffectwhenmodelingamultiple-effectstillandmaketheresultsunusable.Amultiple-effectstillshouldbeconstructedandtestedinordertoverifythisproblem. 11

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CHAPTER1INTRODUCTIONANDBACKGROUND 1.1IntroductionWaterandenergyarecloselyintertwinedwhenitcomestolife.Itcanbesaidthatwithoutenergyandwatertherewouldbenolifeonthisplanet.Whilethereisnoshortageofwaterontheearth'ssurfacewhenonetakestheoceanintoaccount,theavailabilityoffreshwatertoterrestrialplantsandanimalsshowshightemporalandspacialvariability.Thisvariabilityposesproblemsthatmustbeovercomeforallterrestrialliferangingfromplantstopeople.SincetheancientEgyptiansusedtheoodplainsoftheNile,humanityhasutilizedandadaptedtothevariabilityofavailablefreshwater.Civilizationcontinuestodependonwaternowasitdidthen,butnowitseamsthatourthirstiseverincreasing.Modernindustrialprocessesandagricultureconsumewateronamassivescale.Inaddition,increasingpopulationsdriveanincreasingdemand,andtheworldpopulationisexpectedtoincreasetoover9billionby2050[ 2 ].Theseissuescoupledwiththeshiftingweatherpatternscausedbyglobalclimatechangeindicatethatfreshwatershortages,andconictsarisingfromtheseshortages,arelikelytohappeninthenotsodistantfuture.Asalludedtopreviously,thereisanabundanceofwateronthesurfaceoftheearth.Figure 1-1 showsthatalthoughonly3%oftheword'swaterisfreshwater[ 3 ],vastamountsofsaltwaterareavailable,especiallytocoastalcommunities.Theprocessofdesalinationmaybeusedinordertomakeupforfreshwatershortagesastheyoccurespeciallyinlocationswithaccesstoabundantsaltwater.Theproblemwithdesalinationliesinthefactthatitisenergyintensive,andenergyproductionitselfmaybewaterintensive.Furthermore,thecurrentcommercialtechnologiestendtobeexpensive,limitingtheirapplication. 12

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Apotentialwaytoovercometheenergycostassociatedwithdesalinationistoutilizerenewableenergy,particularlysolarenergy.Solarenergyisfrequentlyavailableinareaswithlowwateravailability,andseasonswithlowwateravailabilitytendtohavehighsolaravailability.Byusingsolarenergy,thedesalinationprocessmayavoidconsumingotherformsofenergy,whichinturnwouldconsumefreshwater. Figure1-1. GlobalWaterAvailibility,originallyfromwbcsd[ 3 ]. 1.2Background 1.2.1FreshwateravailabilityandNeedsWaterisoftenconsideredarenewableresourcebecauseitisassumedthatwhatiswithdrawnfromtheenvironmentwillbereplenished.Thisisnotthecasewhentherateofwaterreplenishedislowerthantherateofwaterwithdrawals.Theuxofwaterthroughtheenvironmentiswhatbecomesimportantforthedeterminationofhowrenewablethewateris.Onewaytodescribethisuxiswiththeresidencetimeofthewaterbody:theaverageamountoftimethatawatermoleculespendsinawaterbody.Insomeplaces,thetimenecessarytorechargegroundwateraquifersissogreatthattheyarecalled`fossil'aquifers[ 4 ].Theowrateofriversversustheirvolumesservesasanotherillustrationastowhytheuxoffreshwaterisabettermeasurementoftheresource.Thetotalvolumeofwatercontainedintheworld'sriversisabout2000km3 13

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[ 3 4 ],andthevolumeofwaterannuallywithdrawnforhumanuseisabout3800km3.Theamountannuallydischargedintotheoceanfromriversisconsiderablylargerat45,000km3/year[ 4 ].Sinceallfreshwateravailableisnotnecessarilyarenewableresource,itisprudenttoestablishwhatfreshwaterresourcesarerenewable.RenewableFreshwaterResources(RFWR)aredenedbyOkiandKanae[ 4 ]asthedifferencebetweenprecipitationandevapotranspiration.Morespecically,thisdifferenceisthemaximumRFRWforagivenregion.Onlyabout10%oftheriverRFWRgoesintogroundwater,withtherestbeingdischargedintotheoceans[ 4 ]. Figure1-2. GlobalmapofWaterScarcityIndex,originallyfrom[ 4 ]. GivenwhatconstitutesRFWR,wemaybegintodenewhatconstituteswaterscarcity.Thereareactuallyanumberofmeasuresofwaterscarcity,butthemostcommonlyusedoneistheFalkenmarkindicatororwaterstressindex[ 5 ].Thisindicatortakesthevalueof1700m3RFWRavailablepercapitaperyearasthethresholdforwaterstress.Whenwatersuppliesfallbelowthisvalueinaregionitissaidtobe 14

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experiencingwaterstress,below1000m3itisdescribedashavingwaterscarcity,andbelow500m3absolutescarcity[ 3 5 ].AlthoughtheFalkenmarkindicatorgivesastraightforwardmeasureforwaterscarcity,itonlypresentswhatrenewablefreshwaterisavailableandmaynotbeanaccuratereectionofthewaterdemandinaregion.Anothermeasureofthescarcityofwatertakesintoaccountthedemandofwaterinanareainsteadofusingaxedvaluepercapita[ 5 ].Thisindextakestheamountofwaterwithdrawnasapercentageoftherenewablewaterresourcesavailabletodeterminethescarcityofwaterinaregion.Whendeterminedinthismanner,itisknownastheWaterResourcesVulnerabilityIndex(orthecriticalityratioifnotgivenasapercent)[ 5 ].Aslightmodicationofthecriticallityratio,calledthewaterscarcityindex,describedbyOkiandKanae[ 4 ]isshownbelow.waterscarcityindex=waterwithdrawals)]TJ /F1 11.955 Tf 11.95 0 Td[(waterfromdesalination annualRFWRWhateverthenameofthisindex,ifthevalueexceeds40%(or0.4)thentheregionisconsideredhighlywaterstressed.AsshownintheFigures 1-2 and 1-3 ,muchofNorthAfricaandWestandCentralAsiaisexperiencingwaterstressorwaterscarcitybyanymeasure. Figure1-3. WaterStressintermsofCriticalityRatio,originallyfrom[ 5 ]. 15

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1.2.2WaterUseThegreatestuserofwaterworldwideisagriculture.Globally,agricultureaccountsfor70%ofthefreshwaterused.Themajorityofthiswaterusedtoirrigateagricultureisconsumedthroughevapotranspiration.Thisisincontrasttootherusesofwater,suchasdomesticconsumption,wherethewastestreammayreturntothewatersystemforfutureuse.Theamountofwaterwithdrawalshavetripledinthelast50yearsinlargepartduetoincreasedagriculturalirrigationworldwide[ 6 ].Thisincreaseinirrigationwasmainlyduetohighfooddemandandagrowthinagriculturebasedeconomies[ 6 ].Waterandenergyarelinked;inthecaseofwaterusedtoprovidefoodcropsthewaterisconsumedtoprovideenergyforpeople.Waterandenergyarealsolinkedinagricultureinthatwatermaybeusedtoproduceenergyviabiofuels.IntheUnitedStates,in2007,27%ofthecorncropwenttowardstheproductionofethanol[ 6 ].Thisstatisticisevenmoreinterestingwhenoneconsidersthat,onaverage,toproduceoneliterofliquidbiofuelittakesasmuchwaterasittakestogrowthecropstofeedonepersonforoneday[ 6 ].Inhigherincomecountriesthepercentageofwaterusedforagricultureislowerthantheglobalgureof70%,andthepercentageofwaterusedforindustrialpurposesismuchgreater[ 3 ].Oneindustrialuseforfreshwaterisasacoolingmediumforelectricpowerplants[ 7 ].IntheUnitedStates,electricpowergenerationfromthermalsources(fossilfuelsornuclearpower)accountsforapproximately39%ofnationalfreshwaterwithdrawals[ 7 ].Whentheplantsuseopenloopcooling,largequantitiesofwaterarewithdrawntocondensesteamandnearlyallofthewaterisreturnedtothesource.Thisreturnedwaterissaidtobeatalowerqualityduetoitshighertemperatureandlowerlevelsofdissolvedoxygen.Additionally,thereturnedwatermayleadtohigherevaporationratesduetotheelevatedtemperature.Powerplantsthat,insteadofopenloopcooling,useevaporativecoolingwithdrawconsiderablylesswater,butnearlyallof 16

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thewaterthatiswithdrawnisconsumedbyevaporation.Thisevaporativecoolingwateraccountsforapproximately3.3%ofthetotalfreshwaterconsumptionoftheUS[ 7 ]. 1.2.3DesalinationOnemethodtodealwiththedemandforfreshwateristodesaltbrackishorsaltwater.Inordertodothis,theremustbeaccesstothenecessaryquantitiesofsaltwaterandtheremustbesufcientenergytodrivethedesalinationprocess.Desalinationconsumesaconsiderableamountofenergy,inthissectionwewillgooverthedifferenttypesofdesalinationtechnologiesandhowmuchenergytheyconsume.Energyconsumptionmayaccountfor35-40%ofthecostofdesalination[ 8 ].Thereareanumberofdesalinationtechnologies,buttheycanbebrokenupintotwomaincategoriesaccordingtohowtheyseparatethewaterfromthedissolvedsalts:phasechangeandmembranes.Membranebasedtechnologiesutilizepressureorelectricitytoforcewaterorsaltmoleculesacrossmembranes.Reverseosmosisdrivesthewateracrossthemembranewithpressureandelectrodialysispullssaltmoleculesacrossthemembranewithelectricpotential(voltage).Phasechangedesalinationworksbyhavingthewatergointoavaporphaseandlaterre-condensingthevapors.Inbothcases,theincomingsaltorbrackishwaterleavesintwostreams;onewithalowersaltconcentrationthantheincomingstream,andonewithahighersaltconcentration[ 9 ].Thethreemostcommonlyuseddesalinationmethods,multiple-stageash,multiple-effectdistillation,andreverseosmosis,willbediscussedindepth.Phasechangeseparationistypicallydistillation.Distillationisaseparationprocessthattakesadvantageofthedifferentvaporpressuresofcomponentsofmixtures.Multiple-StageFlash(MSF)distillationunitsarecomposedofanumberofchambers,calledstages,inseries.TheMSFplantmayhaveupto40stages[ 10 ].Heatedsaltwaterentersastagewhosepressureislowerthanthesaturationpressureofthewater,andashesintosteam.Thissteampassesthroughdemisters,whosepurposeistominimizethecarryoverofbrinedropletsentrainedinthewatervapor,andcondensesonaheat 17

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exchangercalledthecondenser[ 9 11 ].Incomingseawaterisusedasthecoolantinthecondensersothatthecondensingsteamisusedtopreheattheincomingsaltwater.Thebrinethathasnotashedpassesthroughappropriatevalvingintothenextstagewherethepressureislowenoughforittoashagain,andtheprocessisrepeated.Thebrineanddistillatearecascadedfromstagetostage,eachstageatalowerpressureandtemperature,untiltheyarecollectedattheend.Attheend,thebrinemayberejectedasblow-downorsomemayberecirculatedbymixingitwiththeincomingseawater[ 9 11 ]. Figure1-4. Multiple-StageFlashPrincipleofOperation,originallyfrom[ 9 ]. Multiple-effectdistillation(MED)issimilartoMSFinitsuseofmultipledistillationstepsandinrecyclinglatentheat.InMED,multipleevaporationchambers,calledeffects,arearrangedinseries.Inthersteffect,condensingsteamheatsseawateraboveitssaturationtemperaturecausingittoevaporate.Thiswatervaporcondensesinthefollowingeffect,withthelatentheatofcondensationservingastheheatsourceforevaporatingtheseawaterinthiseffect.Thisprocessisrepeatedwiththevaporfromthecurrenteffectcondensinginthefollowingeffectandservingastheheatsourceinthateffect.Thepatternholdsforhowevermanyeffectstheplantmayhave,witheachsubsequenteffectatalowertemperatureandpressurecomparedtothepreviouseffect[ 9 11 ].Themembranebasedprocessmostcommonlyusedforlargescaledesalinationisreverseosmosis.Reverseosmosis(RO)worksbyforcingsaltwaterunderpressurethroughasemi-permeablemembranetoobtainfreshwater.Thisprocessutilizeswater 18

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Figure1-5. Multiple-EffectBoilingPrincipleofOperation,originallyfrom[ 9 ]. atambienttemperatureanduseselectricmotorstodrivehighpressurepumps.InanROplant,waterislteredanddosedwithchemicalsinanefforttominimizethefoulingofthemembranesused.Thewateristhenpumpedtoapressurefrom50-80barandpassesthroughthemembranes[ 9 11 ].Thebrineleavingthemembraneisstillatahighpressureandmayberunthroughaworkexchangerorenergyrecoveryturbineinordertodecreasetheamountofenergyrequired[ 9 12 ]. Figure1-6. Multiple-EffectBoilingPrincipleofOperation,originallyfrom[ 9 ]. PerformanceofMSFandMEDplantsisgivenastheperformanceratio(PR)(orthegainedoutputratio(GOR)[ 12 ])whichistheratioofmassofdistillateoutputoverthemassofsteaminput(kg/kg[ 10 ].PerformanceforROplantsistypciallygivenintermsofkWh/m3.Inordertocomparethesedifferentmethodsonthesamebasis,namelyspecicenergyconsumption,theconversionfactorof627kWh=PRm3 19

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wasusedundertheassumptionthatthesupplyheatwassaturatedsteamat100C.Table 1-1 showsthatonaspecicenergyconsumptionbasis,ROsignicantlyoutperformsthedistillationmethods.However,itshouldbenotedthatthethermaldistillationmethodstakelowavailabilityenergy(steamat100C)whereastheROprocesstakeshighgradeenergyintheformofelectricity. Table1-1. DistillationEnergyConsumptionMethodSpecicEnergy(kWh/3)Source MSF52.3-104.5[ 9 11 ]MED34.8-104.5[ 9 11 ]RO3.5-4.4[ 8 ] 1.3RenewableEnergyDrivenDesalinationSincewaterdesalinationconsumesconsiderableamountsofenergy,itisimportantthatrenewableenergybeusedfordesalination.Althoughthereareafewdesalinationplantsthatutilizerenewableenergy,suchastheseawaterROplantnearPerth,WesternAustralia,thatusesrenewablewindelectricity[ 13 ],thevastmajorityofdesalinationplantsarepoweredbyfossilfuels.Thesunalreadydrivesthewatercycle,soitisanaturalttousesolarenergyforsaltwaterdesalination.Solarenergyinparticularmaybewellsuitedforprovidingtheenergyneedsofdesalinationinwaterstressedregions.Typicallyduringseasonswhenthesunshinesthemostiswhenthereisthegreatestneedforfreshwater.Theenergyintensityofdesalinationmaybeovercomebyusingareadilyavailableandlowcostenergysource,namely,sunshine.Althoughsolarenergymaybeconvertedtoelectricityinordertodrivereverseosmosis,thisconversionisexpensiveandaddscomplexitytothesystem.Fortheareasmostaffectedbywaterscarcity,therobustnessandcostofthesystemmaybemoreimportantthantheenergyefciency,especiallywhenconsideringthevariabilityofsolarenergy.Itisforthisreasonthatthisdiscussiononsolarpowereddesalinationwillfocusonthermallydrivendistillation. 20

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Asisthecasewithdesalinationingeneral,mostMSFplantscurrentlyarepoweredbyfossilfuels.ThisisespeciallytrueinpartsoftheMiddleEastwhereoilfueledboilersprovidethesteamforMSFplants.AlthoughinprincipletheheatrequiredbyanMSFplantcouldbesuppliedbysolarradiation,thepressuredropsacrossthestagesmeanthatthesesystemsneedtimetoreachsteadystate.Sincesolarenergycanbehighlyvariableduringtheday,asolardesalinationsystemusingMSFwouldrequiresignicantthermalstoragetoevenoutthesevariations[ 9 ].MEBplantsaremoresuitedtosolarapplicationsduetotheirbetterloadfollowingability[ 9 ].WhileMEBandMSFmaybesuitedtolargerscaleplants,thedemandsofwaterstressedregionsmaybemorelocalandsmallscale.Oneofthemorepopulardesignsforsolardesalinationisthebasinbasedstill.Thesestillshavethesimplestdesigns;theyconsistofabasininwhichthesaltwatersitsandatransparentcover[ 3 ].Inthisstill,solarradiationpassesthroughthecoverandisabsorbedbythebottomofthebasinheatingupthebasin,which,inturn,heatsupthewater.Waterevaporatesandrisestothecoverofstillwhereitcondenses.Thecondensedwaterthenrunsdownintoatroughthatcollectsthedistillate.Thistypeofstilloffersthesimplestconstructionandonlyrequiresthatsaltwaterbeaddedandthebrinerejected.Whilethebasinstillisveryusefulbecauseofitssimplicity,ithassomeimportantdownsides.Intheformpreviouslydescribed,thebasinstillsuffersfromlowdistillateproductionperunitarea.ThisismainlyduetothefactthatthelatentheatisrejecteddirectlytothesurroundingswithoutbeingrecycledasitisinMEB.Furthermore,thecondensingvapormayobscurethecoverandlimittheamountofsolarradiationthatreachesthebottomofthebasin.Vaporleakagemayalsobeaproblem,especiallyinolderunits[ 14 ].Thesimplebasinstillmaybeimprovedthroughanumberofminoradjustments.Bydecreasingthedepthofthebasin,thedistillateproductionincreases[ 14 ].Adyemaybeaddedtothewaterinordertoincreasetheamountofradiationabsorbed[ 15 ]. 21

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Thestandingwaterinthebasinmaybereplacedbyawick[ 16 ].Oneofthelargestimprovementsinperformancemaycomefromrecyclingthelatentheattocreateamultipleeffectbasinstill.Inthisdesign,thevaporcondensesonthebottomofanotherbasin,whichcausesthewaterinthatbasintoevaporateandproducemorecondensate.BydoingthisthestillbecomesmoreliketheestablishedcommercialmethodsofMSFandMED. Figure1-7. VerticalMultiple-EffectStill,originallyfrom[ 1 ]. Avariationonthisthemeofusingwicksandmultipleeffectsistheverticalmultiple-effectdiffusiondrivenstill,seeninFigure 1-7 .Thistypeofstillwasdevelopedoriginallyasanadd-ontoabasintypestill[ 17 ].Inthisarrangement,theinitialevaporatorplateisheatedfromoneside,whileasalinesoakedwickisattachedontheotherside.Thewaterevaporatesoffofthiswick,crossesasmallairgap,andcondensesonthecondenserplate.Thiscondenserplatemaybethebackofanotherevaporatorplate,thusthelatentheatofcondensationisrecycled.The 22

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verticalarrangementofthestillallowstheairgapbetweentheplatestobedecreasedsubstantially.Thistypeofsolarstillwillbetheresearchfocusofthisdissertation.OfparticularinterestisthepossibilityoflatentheatrecoveryfromthenaleffectandsensibleheatrecoveryfromthebrineandcondensatestreamssuggestedbyMitteninhisdissertation.Manyoftheaforementioneddistillationtechniquesusesomeformofsensibleorlatentheatrecoverytopreheatthefeed-wateranditisintriguingthatthishasnotbeenattemptedforverticalmultiple-effectdiffusiondrivenstills.InMitten'ssimulation,sensibleheatrecoverymadeasignicantimpactontheamountofdistillatethatwouldbetheoreticallyproduced. 1.4ResearchObjectivesTheobjectivesofthisstudyfocusprimarilyonassessingthevalidityofthenumericalmodelofthemultipleeffectdiffusiondrivensolarstillthroughexperimentation.Inparticular,theeffectofheatrecuperation(bothlatentheatandsensibleheat)willbeinvestigated.Integralwiththisaimwillbetheestablishmentofrobustandlowcostfeed-watersupplymethodinordertoachieveorcomeclosetothefeed-waterratiosuggestedbyMitten[ 1 ].Centraltoincreasingtheperformanceofthestillwillbeminimizingthegapspacingbetweenthetwopartitions.Theeffectofpartitiongapspacingwillbeinvestigatedandcomparedtothenumericalmodel. 23

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CHAPTER2SOLARDISTILLATIONFUNDAMENTALSANDLITERATUREREVIEW 2.1IntroductionDistillationhasafewfundamentalprocessesandattributesthatarethesamenomatterthemethodofdistillation,andsomeprocessesandattributesthatarespecictothedesalinationmethod,whetheritisMSF,MED,orasolarstill.Solarstillsareaparticularapplicationofdesalinationthatistypicallyusedfordesalinationatasmallscale.Thedevelopmentoftheverticalwickdiffusiondrivensolarstillfromthetraditionalsolarstillwasdescribedinthelastchapter,sothatwillnotbetreatedhere.Instead,thischapterwillfocusonwhatiscommonamongthermaldesalinationsystemsandwhatisparticulartothesolarstill,especiallytheverticalwickmultiple-effectsolarstill.Inthissection,areviewoftheprinciplesinvolvedinthesolarstillandhowchangingthemaffectstheoutputofthestillwillbediscussed.Thefocuswillbeonthedistillationcell,aconceptualprocessthatisuniversaltoalldistillationsystems,andtheperipheralcomponentsofthediffusiondrivensolarstill. 2.2DistillationFundamentalsThemostfundamentalprocessinthermaldesalination(distillation)istheheatandmasstransferthatoccursinthedistillationcell,showninFigure 2-1 .Thedistillationcell,oreffect,consistsof3parts:heattransfersurfaces(anevaporatingsurfaceandacondensingsurface),vaporspace,andtheliquidlmsontheevaporatingandcondensingsurfaces.Heatpassesthroughtheevaporatingsurfaceandistransferredtothesalinewater.Theheatincreasesthesalinetemperature,raisingthevaporpressureofthewaterandcausingsomewatertoevaporate.Thewatervapordiffusesacrossthevaporgapandcollectsonalmofcondensedwaterordirectlyonthecondensingsurface.Heatpassesthroughthewaterlmandthroughthecondensingsurfacetoeitherthenexteffect,ortoberejectedtotheambient. 24

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Figure2-1. Schematicofdistillationcell,OriginallyfromMitten[ 1 ]. Amajorobjectiveofsolardistillationunitsistomaximizetheamountofdistillateproducedperunitofheatinput.AmetricthatcapturesthisobjectivewasdescribedbyMitten[ 1 ]astheperformanceratio(PR)andISGIVenbyEquation 2 ,wherehlvisthelatentheatofvaporizationofwater.Theamountofdistillateproducedperunitheatinputisadirectproductoftheheatpassingthroughthestill.Theheatpassingthroughthestillmaybedividedintotwoportions,asensibleheatportionandalatentheatportion.qtotal=qsensible+qlatentThelatentheatportionoftheheattransferredcomesfromthemasstransferofwatervapor.Thus,theactofmaximizingthedistillateproductionofthestillmaybethoughtofasthemaximizingofthelatentheattransfer.Inordertomaximizelatentheattransfer,themaximumamountofheatshouldreachthesalinewaterandtheminimumamountofsensibleheatshouldbetransferredacrossthevaporgap. PR=_mtotaldistillatehlv qsupplied(2)Therstcomponentstoevaluateinthedistillationcellaretheheattransfersurfaces(theevaporatorandcondensersurfaces).Heattransferthroughthesesurfacesis 25

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governedbytheconductionequation:q00partition=kpartition@T @x=kpartitionT xAssumingtheheattransferthroughthepartitionqpartitionisxed,thenthechangeintemperatureacrossthesurfaceTwillbedirectlydependentonthethickness(x)andthermalconductivityofthepartitionmaterial(kpartition).Thus,thehighertheconductivityofthepartitionmaterialandthethinnerthematerial,themoreheatmaybetransferredthroughthematerial.Usingthinnerheattransfermaterialalsohastheaddedeffectofloweringthematerialcostofthestill.Thedecreaseincostduetothinnerpartitionsshouldnotbeoverlooked;forcommercialplantsthematerialsmaycontribute25%ofthecostoftheplant[ 18 ].ThisisreectedintheliteraturesincemanyMEDunitsusealuminumorcopperalloys[ 18 ],whichhavehighthermalconductivity.Anotherconcernthatwillinuencethematerialchoiceinastillistheresistancetocorrosionandscaling.Scalingandcorrosionwillleadtolowerheattransferandpossiblymaterialfailureofthestillcomponents.ScalingandcorrosionaredealtwithinMEDandMSFplantsbyusingcorrosionresistantmaterialssuchastitaniumandstainlesssteel[ 18 ],operatingatalowertemperature,ortreatingtheincomingwaterwithananti-scalingchemical.Thenextcomponentofthedistillationcellisthevaporspacebetweentheevaporatorandcondenser.Thedimensionofthevaporspacewillhaveasubstantialeffectoftheoutputofthestill.Sincetheretypicallyisnoactivemixinginthestill,masstransfermayonlyoccurduetoconvectionordiffusion.Ifthedimensionbetweentheevaporationandcondensingsurfaceissmallenough,thenconvectionmaybeneglectedandonlydiffusionistakingplace.Itisimportanttonotethatunlessthecellisevacuatedpriortodistillation,thediffusionofwatervaporisthroughanon-condensiblegas(air).Forthediffusiondrivenstill,themasstransferisrelatedtotheheattransferaccordingtoqlatent=hvg_mdiusion 26

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andthediffusionbasedmasstransferisgivenby_mdiusion=DAB@c @xTheliquidlmsontheevaporatingandcondensingsurfacesarethenalcomponentofthedistillationcell.Theliquidlmsneedtobemanipulatedtomaximizeheattransferthroughthem.Thisimpliesdropwiseorthinlmcondensationonthecondenser,andathinlmontheevaporatorside.Athinlmontheevaporatorsidewillleadtoincreasedheattransfer[ 18 ].Thethicknessoftheliquidlmhasadirecteffectonhoweasilyheatistransferredthroughthatlm,thatiswhybasinstillswithshallowerbasinstendtohavebetterperformance.Insomesolarstills,theevaporatormayhaveawickinordertoensureevenwettingacrossthesurface.Inthiscase,thethermalconductivityoftheevaporatorplaysanimportantroleintheheattransferintothesalineinthewick.Thematerialandthicknessofthewickwillhaveasimilareffectontheheattransferthroughthewick.Thewicksmaybemadeofavarietyofmaterialsfromporousgauzetoblackenedjute[ 19 20 ].Onewaytoensureathinlmofwateristogiveasuperwettingsurfacetreatmenttotheheattransfersurfaces.Ifdropwisecondensationmaybemaintained,itcanresultinanorderofmagnitudehigherheattransfercoefcientcomparedtothanlmcondensationforsimilarsituations[ 21 ].Theorientationofthestillcankeepaliquidlayerfrombuildingupbyhavingthestillsitatanangleclosetoorequalto90degrees.Surfacetreatmentmayalsohelpinthiscasetoensurethatthedropsdonotbecometoolargeindiameterandbecomereabsorbedintotheevaporatorwick.Theliquidlmsonthecondenserandevaporatormustalsobeabletotransfertheuid.Thismeansthatthewickmustwickwelltoensureanevendistributionofsalineontheevaporatorsurface.Theporositywillalsoaffecttheheattransferredthroughthewickbyconvectioninadditiontoinuencingthemassuxofsaline.Onthecondenser,ifcondensationoccursindrops,thedropsmustnotbesolargethattheybridgethe 27

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gapandarere-absorbedbythewickontheevaporatorside,whichwoulddecreasetheamountofdistillateproducedandcauseaconsiderableportionoflatentheattobetransferedthroughthecellwithoutdoinganyusefulwork. 2.3StillperipheralComponentsAlthoughalldistillationunitssharetheprocessthatoccursinthedistillationcell,theydifferintheperipheralsassociatedwiththecell.PeripheralsmaybethoughtofastheinputsandoutputsnecessaryforthecelltofunctionandareillustratedinFigure 2-1 .Thermalenergymustbesuppliedtothecell,anditmaybesupplieddirectlyorindirectly.Salinewatermustbesuppliedtothestill.Thewaterneedstobepumpedorotherwisetransferredfromitssourcetothedistillationunit,anditmayormaynotneedtobepretreatedtoremovesedimentorbiologicalcontaminants.Finally,thewatermustbemeteredandbroughttothewick.Distillateandbrinemustbecollected,andthebrinemustbedisposedofinsomefashion.Heatmustberejectedfromthestill.Thisheatmayberecycledbypreheatingtheincomingsalinewater.Thelatentheatmaybeusedtoevaporatewaterinanothereffectaswell.Inanycase,theremustbesomeheatthatisrejectedtotheambient.Theseperipheralsvarywiththestilldesignandwillbeinvestigatedintherestofthechapter. 2.3.1ThermalSupplyThermalenergy,inthiscasefromthesun,mustbesuppliedtothestill.Solarenergysupplymaybecategorizedasdirectorindirect.Directsolarenergysupplyiswhendistillationoccursinthesolarenergycollector.Alternatively,thesolarstillmayconsistoftwosubsystems,oneservingasastillandtheotherasasolarenergycollector,whichisknownasindirectsolarenergysupply[ 9 22 23 ].Themostbasicdirectsolarstillisthetraditionalsolarstill.Thisconsistsoftransparentmaterialcoveringashallowbasinofsaltwater.Thesunpassesthroughthetransparentmaterial(glassorplastic),throughthesaltwaterandisabsorbedbythebottomofthebasin,heatingupthewateranddrivingthedistillationprocess.Solarstills 28

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ofthisdesignaresuitablewheredemandislessthan200m3/day[ 9 ].Directsolarsupplyisnotlimitedtothetraditionalbasinstill,butisapplicabletowickingstills,diffusionstills,ormultipleeffectstills[ 22 ].Inaddition,directthermalsupplymaybeaugmentedbyusingmirrorstoreectmoresunlighttothestillleadingtoincreasedperformancethroughsolarconcentratingeffects[ 20 24 ].Directsolarstillshavetheaddedsimplicityoftheintegratedsolarcollector,andbecauseofthis,theymayhavealowerinitialcostcomparedtoindirectlysuppliedstills.However,theperformanceoftraditionalsolarstillsisimprovedwhenoperatingonindirectlysuppliedsolarenergy.RaiandTiwari[ 25 ]founda24%increaseindistillateproductionwhenthebasinstillwascoupledwithaatplatecollector,andananalyticalsimulationbyKumarandSinha[ 26 ]foundanincreaseinbasinproductionwhenusingaconcentratingsolarcollector.Inlightofthis,theappropriatenessofdirectorindirectthermalsupplyforasolarstillwouldneedtobedeterminedonacasebycasebasistodeterminethemostlife-cyclecosteffectivemodeofoperation.Sincethesolarenergycollectionisdecoupledfromthedistillationprocess,indirectlysuppliedsolardesalinationunitsmaybesetuplikeconventionaldesalinationplants(MSFandMED)orlikesolarstills.Thetypeofsolarcollectoruseddependsonthedesiredtemperatureofthestill,withthecostofthecollectorsincreasingwiththetemperaturethatcanbeproducedbythecollector[ 22 ].Solarcollectorsmaybeatplate,evacuatedtube,solarponds,orparabolictroughtypes,withQiblaweyandBanat[ 22 ]givingamorethoroughdescriptionofeachcollector.Descriptionsofconventionalstyleplantssuppliedbysolarthermalenergymaybefoundin[ 23 ]and[ 22 ],butadirectcomparisonwithconventionaldesalinationplantsisnoteasilydonesincethemetricmostoftenquotedisthem3/daytheplantmakes. 2.3.2SalineSupplySalinewatermustalsobesuppliedtothestill.Salinewatermustbepumpedorotherwisebroughttothestillfordesalination,thusmoststillsarebuiltasclosetothe 29

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thesourceofsalinesupplyaspossible.Dependingonthequality,thesalinewatermayneedpretreatmentpriortobeingprocessedinthestillinordertoremovesediment,biologicalagents,ortoreducescalinginthestill[ 27 ].Theextentandfocusofthetreatmentdependsonthedesalinationprocesstobeemployed,withROrequiringpretreatmenttopreventmembranefoulingandthethermalmethods(MSFandMED)requiringtreatmenttopreventscaling.Bycomparison,solarstillsrequirelittlepretreatment,generallyonlyrequiringltrationforpretreatment[ 1 ].Finally,salinewaterneedstobesuppliedtothewick:andthemethodforsalinesupplytotheevaporatorplatemayhaveasubstantialeffectontheefcacyofthestill.Thesalinewaterwillneedtobebroughttothewickandtheowratetothewickneedstobecontrolled.AreviewofsolarstillsbyFath[ 16 ]illustrateshowsalineissuppliedforsingleandmultiplestagebasinandwick-typestills.Forthemultiplewickstill,salinewaterissuppliedtothewicksthroughamanifoldwithholesinthetubestodripwateroneachwick.Theauthoralsoshowsthatlowerowrateofsalinethroughthewickresultsinhigherproduction.SupplyofsalinetothewicksofamultipleeffectstillwasaccomplishedbyTanakaetal.[ 17 ]byusinga50mmdeeptroughconnectedtoeacheffect,witheachtroughbeingfedbyacapillarytube.Thesalinefeedratetothewickwillhaveapronouncedeffectonthedistillateproduction,withalowerowrateresultinginhigherdistillateproductionaccordingto[ 1 16 28 ].Inremoteorunderdevelopedregions,electricityforpumpstosupplythesalinemaybeoutofthequestion.Iftheystillareusable,thentheywilladdanothercomponentthatcouldpossiblyfail.Theproductsofsaltwaterdistillation,thebrineanddistillate,mustbecollectedafterrunningthroughaneffect.Thebrineanddistillatemustbecollectedandkeptseparated.Insomestills,suchasthetraditionalsolarstill,thisisstraightforward.Fortheverticalwickmultipleeffectstill,thesmallvaporgapimposeshandlingproblems,suchaspotentialcrossoverofdistillatetothesalineside.Oncethestreamshavebeen 30

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separatedandcollected,theconcentratedbrinemustbedisposedof,typicallythisisdonebyreturningittothesource,oftenthesea. 2.3.3HeatRejectionAttheendofthedistillationprocesstheheatthathaspassedthroughthestillmustberejectedtotheambient.Thisprocessmayoccurafteroneormorestagesofheatrecycling.Thelatentheatofvaporizationmayberecycledbyusingmultipleeffectssuchthatthelatentheatrejectedfromoneeffectisusedtodriveevaporationinthefollowingeffect.ThisisthedrivingprinciplebehindbothlargescaleMEDplantsandmultipleeffectsolarstills.ThelatentheatofcondensationmayalsobeusedtopreheattheincomingsalinewaterasisdoneinMSFsystems[ 9 11 ].Thesensibleheatofthebrineandordistillatemayberecycledaswellbyusingittopreheatincomingsaline.Finally,someheatmustberejectedtotheenvironment.Thisistypicallydonebyleavingthebackofthestillexposedtoair,orrejectingtheheattotheincomingseawater.InEl-Sebaii[ 29 ]itwasfoundthathigherwindtemperaturesincreaseddaytimeproductivityinabasinstillbyincreasingthetemperaturedifferencebetweentheglassandthewater.Ithasalsobeenfoundthatadecreaseintheambienttemperaturefrom30to25Ccausedanincreaseinstillproductionforaircooledstills[ 30 ]. 31

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CHAPTER3METHODOLOGY 3.1IntroductionThepurposeofthenumericalmodelistodecreasetheamountoftimetestingdesigns.Byusingacomputertosimulatetheconditionsofasolarstill,thetimeintensiveprocessesofstillconstructionandtestingisavoided.Amyriadofdifferentsolarstillarrangementsandsolaruxconditionsmaybesimulatedinamatterofminutesweretheconstructionandtestingofallthesestillswouldtakemonthstoyears.Thepurposeofthisnumericalmodelofamultipleeffectverticalwickstillwastotestdifferentparametersandtheiraffectondistillateproduction.Withtheinsightgained,appropriateareasforrenementofthevertical-wickdiffusion-drivensolarstillcouldbefoundandpursued.Numericalsimulationsareveryusefultoolsforminimizingthetimeandeffortnecessarytooptimizethedesignofaproject.Itiscriticalthattheaccuracyofthenumericalmodelbeknown,andthatthisaccuracybeashighasnecessary.Iftheresultsofasimulationdonotreectreality,thenthesimulationhasnovalue.Themorecloselyasimulationisabletopredictrealworldeventsthemorevaluableitisduetoitstimesavingability.Therefore,thetestingofanumericalmodelagainstempiricaldataisnecessarytorenethemodelandmakeitmoreaccurateandbetteratprediction.Furthermore,ifadesignissimulatedandhasgoodresults,itdoesnotmeanthatthedesignwillbeeasytoproduceintherealworld.Thisisanotherimportantreasonforexperimentalvalidationofasimulation,becauseevenifasimulatedresultlookspromising,ifitcannotbeconstructedeasilyandatlowcost,thanitisnotaveryhelpfulresult. 3.2ExperimentalDesignTodeterminewhichcongurationstotest,itwasnecessarytolookatthemostprominentresultsfrom[ 1 ].Themostbasicassumptionofthemodelshouldbe 32

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Table3-1. TableofConclusions/RecommendationsfromMitten[ 1 ] ImprovementforStillComment/RecommendationbyMitten[ 1 ] MaximizingtheheatrateSuggestsimprovingthesolarcollector,butthiscanbedonebychangingthepowertotheheaterDecreasingthethermalenergyforheatingtheincomingsalinesupplyLowerFRtojustbeforetheonsetofdry-outofthewickLoweringthetemperaturedropsthrougheachcomponentLowerthegapspacingandusepartitionsandwickswithlowthermalresistancesDecreasingtheresistancetoevaporativeheattransferthroughthevaporspaceIncreasethetemperatureofthecell,diffusioncoefcientgoesupwithtemperatureRecyclinglatentheatPrimarilydonebyaddingeffects evaluatedextensively.Namely,thesingleeffect(thedistillationcell)wastestedinvariouscongurationstoensurethatthefundamentalphysicsandassumptionsofthemodelwerewellfounded.Inthemajorconclusionsofhisthesis,Mitten[ 1 ]divideduptheimprovementsthatcouldbemadetothestillintermsofthematerialaspects,geometricaspects,feedrateratio(FR),andheatrecuperation(HR).Materialaspectsrefertowhatmaterialsmakeupthecomponentsofthestill.Geometricaspectsrefertothegeometryinherenttothestillsuchasthevaporgapspacingsorthicknessofthepartitions.Feedrateratio(FR)istheratioofsalinesuppliedtodistillateproduced.Heatrecuperation(HR)ishowtheheat,bothlatentandsensible,isreusedtoincreasedistillateproduction.ToimprovetheperformanceratioherecommendsvariousactionslistedinTable 3-1 .Someofthesearemoreeasilymanipulatedinanexperimentthanothers. 3.2.1ConceptualSinceallofthesuggestedimprovementsexceptforaddingdistillationeffectstothestillmaybecarriedoutinasingledistillationcell,thiswillbetheinitialfocusoftheexperiment.Withasinglecellthemodelwastestedundervariouscombinationsofgapspacing,FR,andheatux.Theempiricaldatafortemperaturealongtheevaporatorand 33

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Figure3-1. ExperimentalApparatus.A)SalineReservoir.B)Scaffolding.C)Coolingwatertubes.D)Distillatecollectingcylinder.E)Brinecollectingcylinder. condenserplateandtheowrateofdistillateandbrinewererecordedandcomparedwiththedataproducedbythemodelunderthesameconditions. Figure3-2. Distillate/Brinecollectorblock.A)Styrofoaminsulationblock.B)6.35mm(1/4)tubetocollectthedistillateorthebrine. Thevariousparametersforthedifferenttrialsforthesinglecellaregiveninthefollowingtable.Arunwascompletedbyheatingupthesystemuntilitreachedsteadystate.Steadystatewasdeterminedtobewhentheaveragetimerateofchangeofthetemperaturesapproachedzero.Thetimetoreachsteadystatewasdeterminedbyexaminingdatacollectedduringafewpracticeruns.Afterthedatawascollected,the 34

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timeneededtoreachsteadystatewasdeterminedtobeabout25minutesforthehighheatuxtestandapproximately70minutesforthelowuxtests.Atotalof6runswereconductedforeachcongurationinordertoallowforstatisticalanalysisofthedata.Solarenergyisabundant,butitisalsointermittentandcontinuouslychangingthroughouttheday.Duetothesereasons,theexperimentwasperformedindoorswithanelectricalheatertosimulatesolarux.Thiswasdonebecausetheheaterwouldprovideasteadyandrepeatableheatux,whichwasnecessarytotesttheresultsofthenumericalsimulation,sincethenumericalmodelonlypredictsvaluesforsteadystate.Thus,usingactualsolarlightwouldhavegivenresultsthatwouldbedifculttocomparetothenumericalmodel. Figure3-3. InternalPhotooftheapparatus.A)Evaporatorwick.B)Condenserwithdistillatedroplets.C)Brineanddistillatecollectiontubes. Theowrateofsalineintothewickwasmanipulatedbyadjustingtheheightofthesalinereservoirabovetheentrancetothestill.Preliminarytestswereconductedtoensurethattheheightofthesalinereservoirproducedthedesiredmassowratethroughthewick.Thegapspacingwasadjustedbymovingtheinsulationblockswiththetubesonthemandputtingadifferentspaceratthetopofthestill.Theseblockswereplacedcloseenoughtogethersothattheplateswere34.9mm,12.4mm,and4.2mmapartfromeachother.Afterasingleeffectwastestedthoroughly,theempiricaldatawerecomparedtothesimulationandthesimulation. 35

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3.3EquipmentDescription Figure3-4. CondenserPlatePicture.Thecircleshighlightthethermocouplelocations. Theexperimentusedverticalmetalplatesmadeofbrass3/8thickastheevaporatingandcondensingplates.Onthebackofoneofthebrassplates,anelectricheaterwasplacedtosupplytheheatuxsimulatingsolarinput.Notchesweremachinedintotheplatestohousethethermocouplesandwiressothatthesurfaceoftheplateswouldbesmoothandnotimpedetheowofwaterdowntheirfaces.Anotherplatewasmachinedwithmatchingholeswiththecondenserplateandapocket10mm76.2mm304.8mmwasmachinedintoitaswellasthroughholesforwaterinletandexit.Thisplatewasxedtothebackofthecondenserplateandservedtoprovidecoolingtothecondenser. 36

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Figure3-5. Thecondenserplatehassimilardimensionsandmachining.Dimensionsareinmillimeters. Ascaffoldingofextrudedaluminumwasmadetosupportthetwoplatesverticallywhiletheapparatuswasoperating.Expandedpolyethylenewascuttosizeandusedasinsulationforthecell.Wicksofcottongauzewereusedtoensureevenwaterdistributionalongtheevaporatorplateandtoensurethatthedistillatewaschanneledawayfromthecell.Brineanddistillatewerecollectedusing6.35mm(1/4)plastictubeswithslotscutintothemandoneoftheendssealed.ThesetubesweregluedintoStyrofoamblocksthatservedtoinsulatethebottomoftheplates. 3.4DataAcquisition 3.4.1EquipmentTheexperimentusedT-typethermocouplesinordertomeasurethetemperaturealongthebrassplatesthatactedastheevaporatorandcondensersideofthedistillationcell.ApairofInstruNetdataacquisitionunitswereusedtomeasureandrecordthetemperaturesalongtheplates.Theinitialowrateofsalinethroughthewick,anddistillateandbrinecollectedafterthesystemhadreachedsteadystateweremeasured 37

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Figure3-6. Showscondenserandthebackingplatewiththewaterjacketmachinedintoit. 38

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usinggraduatedcylindersandastopwatch.Arota-meterwasusedtocontrolandmeasurethewaterthatowedthroughthecondensercoolingwaterjacket. 3.4.2ErrorAnalysisAcalibrationexperimentwasdonetominimizeerrors.Biaserrorswouldbeminimizedthroughcalibrationbyestablishingoffsetsassociatedwitheachthermocouple.Statisticaldataaboutthenoiseassociatedwithaconstanttemperaturewastaken.Theoffsetswereeliminatedfromsubsequentdatathatweretakenandthestatisticaldataforthesteadystatetemperatureswerecomparedtothecalibrationstatistics.Todeterminetheerrorassociatedwitheachofthecomponents,theerrorswerecombinedusingtherootsumsquaresmethodtoestablishanoverallerrorfortheexperiment. 3.4.3ProcedureTheprocedurefortheexperimentsfollowsbelow.PleaserefertoFigures 3-1 3-2 3-3 ,and 3-4 forclarication. 1. Firstthewickwassoakedinthesalinesolution.Thenitwaslaidalongtheevaporatorplatewithasmallamountofwickingmaterialprotrudingfromthebottom. 2. TheevaporatorplatewasthenplacedonaStyrofoaminsulatingblockwithabuiltincollectortube.Thesmallamountofwickingmaterial(describedinthepreviousstep)wasthentuckedintothecollectortube. 3. Another,separatesmallpieceofwickingmaterialwassoaked.Thisstripofwickwasadheredtothecondenserplatesurfaceviasurfacetensionandthebottomendwastuckedpartiallyintothedistillatecollectortube. 4. Thecondenserplatewasthenbroughtintothescaffold(whichwasaframemadeofextrudedaluminumusedtosupportthestill)andsetontotheStyrofoamblockwiththeembeddedcollectortube.Theendofthewickthatwasprotrudingfromthetubewasplacedagainstthecondenserplatewhereitadheresduetosurfacetension. 5. Theplatesarethenarrangedattheappropriatevaporgapdistanceandthetopofcellwasplacedontheplates.Thepolyethylenefoaminsulationwasplacedaroundthedistillationcellandsecuredusingstring. 39

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6. Typicallythescaffoldwasusedtoensurethatthecellstaysuprightanddoesnottipover.Thewickwasdippedinthesalinetrough.Throughacombinationofcapillaryactionandgravitythesalineisdrawnfromthetroughandthroughthewick.Theheightoftheshelfthatheldthetroughwasadjustedsothatthedesiredowratewasestablished. 7. Thecoolingwaterowratewassetat500ccmandthedataacquisitionunitwasturnedon.Afterrecordingabout90secondsofdatafortheunheatedcell,theheaterwasturnedon.TheDAQrecordsanddisplaysthetemperaturedataandafterabout25minutes,steadystatewasreached.Aftersteadystatewasreached,therecordeddatawassavedandanewsetofdatawererecorded.Thesedataweretakenasthesteadystatetemperaturesofthestill.Thesedatawereaveragedinordertoeliminaterandomnoiseinthethermocouplereadings. 8. Thewaterowrateswererecordedoncethesystemhadreachedsteadystatebyusinggraduatedcylindersandastopwatch.Aftersufcientowratedatahadbeentakenthenewsetofdatawererecorded,theheaterwasturnedoffandthesystemwasallowedtocool. 3.5SafetyTheexperimentdealswithwateratnearboilingtemperatures.Becauseofthisitwasimportanttowearsafetyglassesandwaituntilthestillcoolsdownbeforetouchingit.Enoughtime(approximately15to20minutes)wasallowedtopassbeforethestillwashandledwithbarehands. 40

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CHAPTER4RESULTSANDDISCUSSION 4.1IntroductionComputersimulationshaveleadtocountlessadvancesinthetwentiethcenturyandwillundoubtedlyleadtocountlessmoreinthetwenty-rst.However,theresultsofanumericalsimulationareonlyusefuliftheyaccuratelyreectreality.Thegoalofasimulationisinsight,notnumbers.Itiswiththisinmindthattheexperimentalresultsofthevertical-wicksolarstillwerecomparedwiththeresultsofthenumericalsimulation.Oneshouldnotethataftertherstsetofexperimentswereconcluded,itwasdiscoveredthatthedirectionthecoolingwaterowinginthebackofthecondenserwasnotconsistentwiththecomputermodelsimulation.Thewaterowedfromthetoptothebottominthemodelandfrombottomtotopintheexperiment.Thealternateowdirectionwascorrectedafteritwasfoundanddatameasurementswerealreadytaken,byreversingtheowdirectionintheexperimentandsothatitcoincidedwiththesimulation.Allsubsequentexperimentshadthecoolingwaterowinginthesamedirectionastheexperiment.Aftertestingattheinitalvaporspacegapwidthof34.9mm,atestatawidthof12.4mmwasattempted,buthadtobeaborted.Afterthe12.4mmvaporspacegapwassuccesfullyretested,anewsetoftestswereperformedatagapspacingof4mm.Thesetestsweredoneatthepreviousheatuxof4290W/m2,andataheatuxthatmorecloselyapproximatedsolarinputof919W/m2.Twodifferentwickswereusedinthe4mmgaptests;onemadeofcottongauzeandtheothermadeofpolyesterclothfromamoisturewickingundershirt.TheGrashofnumberfortheverticalenclosurewiththeverticalwallsattwodifferenttempratureswascalculatedtodeterminetheeffectofbuoyantconvectioninthestill.Thevariousnumericalpredictionsandexperimentallycollecteddatawerecompared. 41

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4.2PreliminaryResultsandDiscussionThedatathatfollowconsistoftemperaturesanddistillationratestakenbothbeforeandafteritwasdiscoveredthattheowdirectionofthecoolingwaterwasoppositethedirectionedassumedinthenumericalsimulation.Thesimulationdidnotlenditselftoreversingthedirectionofowofthecoolingwater,sotheowdirectionintheexperimentwasreversed.Theaccidentalreversaloftheowdirectionhelpedprovidemoreinsightintotheworkingsofthedistillationcell.Thetemperatureanddistillateproductionpatternsaresimilarforbotharrangementsandpointtoimportantgeneraltrends. Table4-1. ParametersUsedforNumericalSimulation ParameterValue qsupply4290Height76.2mmWidth304.8mmEffects1GapSpacing12.7mmFeedrateRatio(FR)2Partition9.525mmbrassWick0.5mmCoolingWaterFlowRate500ccm(8.310)]TJ /F8 7.97 Tf 6.59 0 Td[(3m3/s)AmbientTemperature25CHeatRecuperationno 4.2.1ResultsThefollowingresultswerefromtheexperimentsdonebeforerealizingthatthecoolingwaterwasnotowinginthesamedirectionassumedinthesimulation.Table 4-1 givesthedimensionsthatwereusedinthenumericalsimulation.Thesurfacetemperatureofthecondenserdecreasedgoingfromthetoptothebottomofthecondenser,quicklyatrstthenapproachingalinearfashionasseeninFigure 4-1 .Thiswastobeexpectedsince,inthiscase,thecoolingwaterforthecondenserentersfromthebottom.Therefore,thecoldesttemperatureforthecondensershouldbeatthebottom.Thefactthatthetemperaturehadasuddenjumptowardsthetopofthedistillationcell,maybeduetohotwatervaporaccumulatingatthetopofthecelldueto 42

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buoyancyeffects.Alsonoteworthywasthesmallspreadofthedatapointsatthetopofthecell,exceptforonedatapointfromtherstthermocouplethatservedasanout-lier. Figure4-1. CondenserPlateTemperaturevsDistancefromtopofCell. Thesurfacetemperatureoftheevaporator,goingfromtoptobottom,rstincreasedtoamaximumsoonafterthesalineinletandthenbegantodecreaseasseeninFigure 4-2 .Thevariabilityofthetemperatureoftherstthermocouplewashighest,duetoit'sproximitytothesalineinlet.Anyvariationinthetemperatureofthesalineinletwouldbemostapparentinthereadingoftherstthermocouple.Itwasinterestingtonotethatwhileitmayappearthattherewasalargespreadinthetemperaturemeasurementsfortherestofthethermocouplesintheevaporatorplate,thespreadinrecordedtemperatureswascomparabletothecondenserplate. 4.2.2CoolingWaterFlowsfromToptoBottomThefollowingtestswereperformedaftercorrectingthedirectionofthecoolingwaterowonthebackofthecondenserplate.Theowdirectionwasreversedsothatitmatchedtheowdirectioninthenumericalmodel.Thecondensertemperaturesinthis 43

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Figure4-2. EvaporatorPlateTemperaturevsDistancefromtopofCell. Figure4-3. CondenserPlateTemperaturevsDistancefromtopofCell,coolingwaterowingfromtoptobottom. 44

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secondsetweregenerallylowerthantherstsetofdata.Thedatastilldisplaythesamegeneraltrend:thehighesttemperatureoccurringatthetopoftheplateandthelowestoccurringatthebottom.Figure 4-3 showsthattherealsoseemstobeanintermediatetemperaturepeakatthemiddleoftheplate,nearthe150mmmark.Theevaporatorplatealsohadlowertemperaturesinthesecondsetofdatacomparedtotherst.Furthermore,thescatterinthesecondsetofdatafromtheevaporatorplatewassmallerthantherst.Thetrendofthedatawassimilartothestsetofdata.Thetemperatureincreasedfromthetopoftheplatetoamaximumvaluebeforethemiddleoftheplate,thenitdecreasedallthewaydown.ThiscanbeseeninFigure 4-4 .Again,thescatterinthedatawashighestatthetopoftheplatewheretheinletwaterwasfedin. Figure4-4. EvaporatorPlateTemperaturevsDistancefromtopofCellcoolingwaterowingfromtoptobottom. 4.2.3DiscussionThemeasuredtemperaturesanddistillateproductionrateshadnoticeablediscrepanciescomparedtothepredictedvalues.Thepredictedtemperaturesofthe 45

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evaporatorplatehadhighervaluesthanwhatwasexperimentallyobserved.Thenumericallypredictedandexperimentallyobservedtrendsintheevaporatorplatetemperaturedidnotmatch.Forthecondenserplate,theexperimentallyobservedtemperaturesweregenerallylowerandfollowedtheexactoppositetrendofthepredictedtemperatures.Ingeneralthesimulationoverpredictedthetemperatureandunderpredictedthedistillateproduction. Figure4-5. ComparisonBetweenPredictedandMeasuredTemperaturesontheCondenserPlate34.9mm AscanbeseeninFigure 4-5 ,thereversaloftheowdirectionofthecoolingwaterhadasubstantialeffectonthetemperatureproleofthecoolingplate.Thetemperatureatthetopofthetopoftheplatedroppedbynearly10C.However,theexperimentallyobservedtemperaturesdidnotmatchthenumericalpredictionsregardlessofthedirectionofthecoolingwaterow,especiallytowardsthetopoftheplate.Thereversalofthedirectionofcoolantowhadanegligibleeffectonthetemperatureproleoftheevaporatorplate,bothintermsofmagnitudeandshape.Figure 4-6 showsthat,withtheexceptionofthetopthermocouple,theaveragemeasuredtemperatureof 46

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theevaporatorplatewasnearlyunchangedbythedirectionoftheowofcoolingwater.Clearly,thetrendoftheexperimentallydetermineddatadidnotmatchthenumericallypredictedtemperatures.Thenumericalpredictionforthissetofparameterstendstogrowliketheresponseofarstordersystemtoastepinput,theexperimentalresultsdonot.Instead,theexperimentalresultsriserapidlytoapeaktemperaturethatoccursinthetophalfoftheplate,andslowlydecreasedintemperaturefromtheretothebottom.AscanbeseeninFigure 4-6 theexperimentaltemperatureclimbsfasterthanpredictedbythesimulation.Therstthermocoupletemperaturepointsweregreaterthanwhatwaspredictedbythesimulation. Figure4-6. ComparisonBetweenPredictedandMeasuredTemperaturesontheEvaporatorPlate34.9mm Bothofthesegraphspointtothesimulationnotaccuratelyreectingreality.Thiswasmostlikelyduetoincorrectassumptionsinherentinthenumericalsimulation.Themostlikelyfaultyassumptioninthesimulationmaybeassumingthatitwasapurelydiffusionbasedprocess.Sincetheplateswereover3centimetersapart,whatwasverylikelyhappeningwasthatanaturalconvectioncellhadformedinsidethedistillation 47

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cell.ThiswouldaccountfortheexperimentallydeterminedtemperatureproleofthecondenserplateinFigure 4-5 .Thehighertemperatureatthetopoftheplateindicatedthatthehottestwatervaporwascollectingatthetopofthecell.Furthermore,thedramaticdecreaseinsurfacetemperatureofthecondenserplatethatoccurredwhenthecoolingwaterenteredatthetopoftheplatelendsfurtherevidencetothisconjecture.Thecoolerwaterenteringthecondenserleadtocoolertemperatures.Ifthehotvaporwasrisingandpreferentiallycondensingatthetopofthecell,itwouldleadtoalowervaporpressure(relativehumidity)atthebottomofthecell,whichcouldaccountforthelowertemperaturesatthebottomoftheevaporatorplate.Thisconvectioncurrentwouldincreasethemasstransferofwatervaporandleadtohigherdistillateproductionthanpredictedbythenumericalsimulation,whichwaswhattheexperimentssofarhaveshown.Allthisevidencedemonstratedthattheassumptionthatwatervapordiffusedfromtheevaporatortothecondenserdirectlyacrossthevaporgapwasnotvalidforthegapdistanceselectedinthiscongurationoftheexperimentaldistillationcell. 4.2.3.1NarrowVaporSpaceTestsThreeexperimentaltestswererunusinganarrowergapinbetweentheevaporatorandcondenserplate(thegapspacingwasapproximately12.4mm)comparedtosixtestsfortheearlier,widergap(34.9mm)conguration.Thiswasbecausethetestingequipmentfailedpriortocompletionofallsixtests.Thenarrowgapresultsfortheevaporatorplateshowbetteragreementbetweenthepredictedandexperimentalvalues.Figure 4-7 showsthattheexperimentalvaluesare,atbest,withinapproximately7Cofthepredictedvalues.Thetrendoftheexperimentalvaluesstilldidnotmatchthesimulationtrend.Thenarrowgapresultsforthecondenserplateshowthatthecondenserplatetemperaturedidnotfollowthepredictionofthenumericalsimulationeither.Thecondenserplatetemperatureswerelowerforthe12.4mmgaptest,asseeninFigure 4-8 .Thedifferencesintemperaturebetweenthe 48

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Figure4-7. ComparisonBetweenPredictedandMeasuredTemperaturesontheEvaporatorPlate,12.4mmgap. Figure4-8. ComparisonBetweenPredictedandMeasuredTemperaturesontheCondenserPlate,narrow(12.4mm)gap. 49

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thermocouplesalongthecondenserplatewerealsosmaller,exceptforthesecondthermocouple,whichwasmalfunctioning.Thismeantthatthehottestandcoldesttemperatureswereclosertogetherthanintheexperimentswithalargergap.Theevaporatortemperaturesforthe12.4mmand34.9mmvaporspacegapappeartohavesimilarmagnitudes,butthecondenserplatetemperatureswerenoticeablylowerforthe12.4mmgap.Thepredictedevaporatorplatetemperaturesforthe12.4mmgapwerelowerthanthatofthe34.9mmgap,whichresultsinthepredictedandmeasuredtemperaturescomingmoreintolinewitheachotherforthe12.4mmgaptestandthecorrespondingsimulation.Thisoccursbecausethesmallerdiffusiondistanceinthenarrowergapresultsinalowerresistancetomasstransferwhichresultedinalowerresistancetoheattransfer.Asthevaporgapdistancedecreased,theagreementbetweentheaverageevaporatorplatetemperaturesthatwereexperimentallyobservedandnumericallypredictedimproved.Table 4-2 illustratesthecontrastsbetweenwhatwasexpectedandwhatwasobservedgoingfromavaporgapof34.9mmto12.4mm. Table4-2. ChangesGoingfromLargeGaptoSmallGap NumericallyPredictedExperimentallyMeasured EvaporatorplatetemperaturedecreasedEvaporatorplatetemperaturedidnotchangeCondenserplatetemperaturedidnotchangeCondenserplatetemperaturedecreasedDistillateproductionincreasesDistillateproductionremainsthesame Itbearsmentioningthattheheatuxoftheexperimentwasnearly5timesthatofthesolaruxandthatthismaybethecauseofthediscrepancysincethesimulationwasdesignedforastillwithoutsolarconcentration.Thehigherheatuxwouldleadtoavarietyofissuesthatwerenotanticipatedinthecreationofthemodel.Forexample,themodelwasbasedonevaporativeheattransfer,andiftheheatuxintothestillwashighenoughboilingwouldoccurwhichwasnotpartofthenumericalmodel.Thiserroneous 50

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extrapolationisseeninFigure 4-6 ,wherethemodelpredictsatemperaturesignicantlyabove100C. 4.2.3.2DistillateProducedThedistillateproductionpredictedbythenumericalmodelwasclosertowhatwasobservedexperimentallythanthepredictedtemperatures.Figure 4-9 showsthenumericallypredicteddistillateproductionvaluesandtheaverageexperimentallymeasuredvaluesforcoolingwaterowingfrombottomtotopandfromtoptobottom.Bothexperimentalaveragesweregreaterthanthevaluepredictedbythenumericalmodel,withthetoptobottomcase(whichfollowstheowdirectioninthemodel)havingthehighervalue. Figure4-9. DistillateProducedfor34.9mmGap,forbothpredictedandmeasuredvalues.Experimental1CorrespondstothecoolingwaterowingfromBottomtoTop. 51

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4.3MostRecentResultsThemostrecentresultsincludetheretestofthe12.4mmvaporspacegapandthetestingof4.2mmvaporspacegap.The4.2mmgaptestswereconductedatthe4290W/m2heatuxcommontotheprevioustests,andataheatuxmoremorerepresentativeofsolarapplicationsof919W/m2.Inthe12.4mmretestsandthe4.2mmhighuxtest,polyesterclothfromamoisturewickingundershirtwasusedexclusivelyasthewick.Forthelowux4.2mmtests,bothgauzeandpolymerwicksweretested. 4.3.1DeterminationoftheGrashofNumberSincethepreliminarydatashowedthataconvectivecellwaslikelydevelopinginthe34.9mmgap,theGrashofnumberforboththe34.9mmand12.4mmgapwascalculated.TheGrashofnumberistheratioofbuoyantforcesoverviscousforces,anditmaybeusedtodeterminewhenthebuoyancyeffectsofaowmaybeneglected.Equation 4 (Incropera[ 31 ],eqn9.12)isvalidforauidsuchasdryairwhosecompositiondoesnotchangewiththetemperature.Fortheairwater-vapormixturefoundinthesolarstill,thecompositionchangesdependingonthetemperature.Therefore,analternativeequation,basedonthedensityoftheair-watermixture,mustbeused. Gr=buoyancyforce viscousforce=g(Ts)]TJ /F6 11.955 Tf 11.95 0 Td[(T1)L3 2.(4)Forexample,usingthepreviousequationfortheGrashofnumberandthevalueofthegapdimensionL=0.0124m(or12.4mm),wegetGr=257.Thiswasoutsideoftherealmofnaturalconvectioninanenclosure,butthisGrashofnumberwasbasedontheassumptionofsinglecomponentgas,suchasdryairornitrogen.Inreality,thevaporspaceofthestillwascomposedofamixtureofairandwatervapor.Equation 4 isabetter(ormoregeneral)equationfortheGrashofnumberthattakesintoaccountthechangeindensityoftheuid(eqn9.65,Incropera[ 31 ]). Gr=g( )L3 2=g(s)]TJ /F7 11.955 Tf 11.95 0 Td[(1)L3 2.(4) 52

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InordertousethisGrashofnumber,thedensityofthemixturemustbedetermined.TheidealgaslawmaybeusedsuchthatPv=mRmixTand100%saturationwasassumed.Notingthattheratioofmassovervolumeisthedensity,theequationmayberearrangedasfollows. =P RmixTRmix=R MmixMmix=Pv PtotMv+Pa PtotMa,Combiningtheseequationstogethergives: =PMmix RT,(4)UsingEquations 4 and 4 andndingthevaporpressureofwaterat80Cand40CresultedinGr=20857.ThiswasfarpastthethresholdvalueofGr1000[ 31 ],fornaturalconvectionandputstheenclosureeasilyinthenaturalconvectionregime.TheGrashofnumberpredictedbyusingtherstequationwastwoordersofmagnitudelower.Thisvastunder-predictionoftheGrashofnumbermayexplainwhytheresultssopoorlymatchedthepredictionsforthe12.4mmand34.9mmvaporspacegaps.Usingtheaboveequations,afunctionwasconstructedinMATLABthatwoulddeterminetheGrashofnumberinthestillenclosureaccordingtotheaveragetemperaturesoftheevaporatorandcondenserplatespredictedbythenumericalmodel.TheGrashofnumberscalculatedbythatfunctionforafewstillcongurationsaregiveninTable 4-5 .Ascanbeseeninthetable(anditcanalsobeinferredfromthegoverningequations)anarrowervaporspaceand/oralowerheatrate(whichlowersthetemperaturedifferencebetweenthetwoplates)resultsinalowerGrashofnumber,whichimpliedlesslikelihoodthattherewillbebuoyantconvection. 53

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4.3.2Retestofthe12.4mmgapThe12.4mmgapwastestedagaintoafrmthepreviousresults.Theretesteddataconrmedtheresultsfromthetruncateddataset.Thepredictionswereclosertotherecordeddatathanthe34.9mmtest,buttherewasconsiderabledifferencebetweenthepredictedandmeasuredtemperatures.Sincethedatafollowedasimilartrenditwaspostulatedthatadjustingtheparametersfedintothesimulationsothattheybetterreectthetestconditionswouldyieldbetterresults.ThedetailsontheadjustmentoftheinputstothenumericalmodelisdetailedinAppendix A 4.3.3Testsofthe4mmvaporspaceSinceanarrowervaporspacewouldbemorelikelytoinhibitbuoyantconvection,thestillwassetupandtestedwitha4mmvaporspace.The4mmvaporspacetestsconsistedoftwoparts,atestattheheatuxofalltheprevioustests(4290W/m2)andatestat919W/m2,whichisclosertoatypicalsolarheatux(800W/m2).Thetestatthelowerheatrateresultedinacorrespondingdecreaseinthedistillateproductionrate,whichfurtherresultedinaconsiderableincreaseinthetimeittooktoconductthetest. 4.3.3.1HighFluxTestThestillwastestedwitha4mmgapandaheatuxconsistentwiththepreviousstilltestsof4290W/m2.Thedatafollowsatrendseeninthepreviousgures,withtheshapeofthetemperaturedatabeingsimilar.Likethepreviousgraphscomparingthepredictedevaporatortemperaturewiththeempiricallymeasuredvalues,thepredictedtemperatureswerehigherthantherecordedtemperatures,andtheyfollowaslightlydifferenttrend,particularlyatthetopofthestill.Forthisvaporgapsettingthepredictionswereclosertotherecordeddatathanprevioustests,establishingadenitetrendofbetteragreementbetweenthesimulationandexperimentasthedimensionofthevaporspacedecreases.Thedisagreementbetweenthecondenserpredictionandtheexprimentalobservationalsoheldforthistest.Oncemoretherewasamismatch 54

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withthetrendsshownbythesimulationandtheexperiment.Althoughthetrendsdidnotagree,thetemperatureswerecloserthanforpreviousvaporspacesettings. 4.3.3.2LowerFluxTestDecreasingthevaporspacegapresultedinamoreaccuratesimulation,atrendthatcontinuedfromthe35mmgapthroughthe4mmgap.Alongwiththedecreasingvaporspacedistance,acorrespondingdecreaseintheGrashofnumberoccurredinboththeexperimentandtheprediction.Takentogether,theseresultsmakesensebecausetheGrashofnumberforthisvaporspacegapandheatuxwaslower.Thismeansthatbuoyanteffectswerelesspronounced.Thisalsomeansthattheassumptionofdiffusiveheattransfer,whichwascriticaltotheoperationofthesimulation,hasgreatervalidity.Inorderforthesimulationtobemoreaccurate,theGrashofnumbermustbedecreasedevenfurther.Thiswasdonebyloweringtheheatuxto919W/m2,whichagreedmorecloselywithatypicalsolarheatuxof800W/m2.Thevaporspacedistanceof4mmwasmaintainedforthefollowingtests,buttwodifferentwickswereused. 4.3.3.3PolymerWicktestThistestwasconductedusingthesamepolymerwickthatwasusedintheretestofthe12mmgapandthe4mmtestathighux.Figure 4-10 showsthatatthedecreasedheatux,thepredictedandexperimentalresultshavemuchcloseragreementthanthepreviousgraphs.Theexperimentalandsimulatedtemperaturesevenshowedcloserqualitativeagreement;thepredictedcondensersurfacetemperatureshaveadecreasedslope.Thelargeuncertaintybarsillustratedthattherewasconsiderablescatterinthissetofdata,butuponcloseinspection,onewillnoticethatthedifferencebetweenthepredictedandmeasuredtemperatureswaslessthat2C.Theevaporatorplatetemperaturesforthe4mmvaporspacegapalsoshowedbetteragreementbetweenthesimulationandexperimentforthereducedheatux.Figure 4-11 showsthebetteragreementbetweentheexperimentandthesimulation,withthepredictedtemperaturescomingwithin5Cofallofthemeasureddata.The 55

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Figure4-10. ComparisonBetweenPredictedandMeasuredTemperaturesontheCondenserPlate,4mmgap,919W/m2. trendsinthedatastilldidnotmatchtheprediction.Thepredictedtemperatureshadthesamecharacteristicshapeofarapidriseintemperaturefromthetopoftheplate,andthemeasuredvalueshadamorehorizontalshape.Table 4-3 showsthedistillateproducedforthevariousstillteststhatwereconducted.Italsoshowsthattheactualdistillateproductionratewaslessthantheamountpredicted.Thelargesdiscrepencywasapproximately11%.Thegeneraltrendinthetableisanimprovementinpredictingabilitiesofthemodelastheheatuxandvaporspacegapdecreased.Note:thepercentdifferenceisgivenby100%actual)]TJ /F6 11.955 Tf 11.96 0 Td[(predicted predictedWhilethenumericalsimulationmayhavebeenabletoholdthefeed-rateratio(FRR)constant,thisdidnotoccurintheexperiment.Duringthelowpower,4mmwidevaporspaceexperimentstherewassignicantscatterintheFRR.Inordertodeterminewhateffectthismighthavehadontheexperimentalresults,aseriesofcomparisonsbetweenthepredictedandmeasuredavergeplatetemperaturesofbothplatesandthedistillateproductionrateswasmade.Inalloftheseguresthereweresomecommontrends. 56

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Figure4-11. ComparisonBetweenPredictedandMeasuredTemperaturesontheEvaporatorPlate,4mmgap,919W/m2. Table4-3. DistillateProductionRateComparison(allvaluesinmL/sunlessnotedotherwise).LowandHighreferto919W/m2and4290W/m2uxes,respectively Test_mmeasured(mL s)_mpredicted(mL s)%Difference 4mmgauzeLow0.005690.00585-2.814mmpolymerLo0.005620.00575-2.274mmpolymerHigh0.02820.0309-9.3812mmpolymerHigh0.02650.0292-10.2034.9mmgauzeHigh0.02690.0279-3.86 Therstwasthesignicantscatterinthecollecteddatawhichmadeinferenceoftrendsdifcult.ThesecondwasthesmalleffecttheFRRhadonthevaluespredictedbythesimulation.Forexample,inalltheplatetemperatureversusFRRgures,thepredictedchangeinaverageplatetemperaturewaslessthan1C,whileinsomeplotsthespreadintheaverageplatetemperatureswasgreaterthan5C. 57

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Figure4-12. EvaporatorandCondenserPlateTemperaturevsFeedRateRatio,4mmpolymerwick,LowPowerdataset.R2valuesaregivenfortheevaporatorandcondenser,respecively Figure 4-12 showsthechangesintheaveragetemperatureofthecondenserandevaporatorplatesasafunctionofthefeedrateratio.AscanbeseeninFigure 4-12 ,thepredictedtemperatureswere,onaverage,slightlyhigherthantheexperimentallyrecordedaveragecondensertemperatures.ThenumericalmodelclearlypredictedthatastheFRRincreased,theaveragecondenserwouldtemperaturedecreaseslightly.TherecordedaveragesshowedatrendofincreasingtemperaturewithincreasingFRRaccordingtothetrend-line,butthelowR2valueofthetrend-linemeansthatthistislikelynotsignicant.Figure 4-12 alsoshowsthechangeinaveragetemperatureoftheevaporatorplateasversustheFRR.Oncemore,thenumericalmodelpredictsadecreaseintemperatureforanincreaseintheFRR.Therewasconsiderablescatterintheobservedtemperatures,withaspreadofnearly8Cinaverageplatetemperatures.Thetrend-lineforthemeasuredtemperaturesshowsdecreasingtemperatureswithincreasingFRR, 58

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whichmatchedthepredictedtrend,butagainthelowR2valueofthetrend-linemeansthatthistislikelynotsignicant.Finally,Figure 4-13 showsthedistillateproductionasafunctionoftheFRR.Again,thenumericalmodelpredictsthathigherFRRwillresultinlowerdistillateproductionrate.Thefactthatmostofthedistillateproductionvaluesweregreaterthantheirpredictedvalueswasalsonoteworthy.Thetrend-linefortherecordeddata,however,showsanincreasingdistillateproductionwithincreasingFRR.ThiswascounterintuitivesincethehigherFRRmeansthatmoresalinepassedthroughthewickperunitofdistillateproduced.Thishigherowrateshouldresultinacoolingeffectofthestillandthusleadtoadecreaseddistillateproductionrate.OnceagainthelowR2valueofthetrend-lineindicatesthatthislineofbesttislikelynotsignicant. Figure4-13. DistillateProductionRatevsFeedRateRatio,forthe4mmLowPowerdataset. 4.3.3.4GauzeWickTestThe4mmvaporspacegaptestwasrepeatedoncemoreatheatratesapproximatingtypicalsolarux,butthistimethewickwascottongauze;thesamematerialusedduring 59

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the34.9mmvaporgaptest.Ascanbeseeninthefollowinggures,thetrendswerecomparabletopreviouscollecteddata.Theaverageobservedtemperaturesforthegauzewickwereallhigherthanthetemperaturesobservedforthepolymerwick.Thistrendheldforboththecondenserandevaporatorplates.Thisdifferencewaslikelyduetothedifferenceinaveragesalineinlettemperatureforthedaysthegauzeandpolymertestswereconducted.Thedifferencecouldalsohavebeenduetothethicknessorthermalconductivityofthewicks,butthisisunlikelysincethepolymerandgauzewickswere0.4mmand0.5mmthick,respectively. Figure4-14. CondenserPlateTemperaturevsFeedRateRatio,4mmgauzeLowPowerdataset. Figure 4-14 showsthetemperaturespredictedbythenumericalmodelforthecondenserplatepassingthroughtheerrorbarsoftheexperimentallyobservedtemperatures.Thisgureshowsverygoodagreementbetweenthepredictionandthecollecteddata.Thedifferencebetweenthedataandthenumericalpredictionislessthan1Cforallofthedatapoints. 60

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Figure4-15. EvaporatorPlateTemperaturevsFeedRateRatio,4mmgauzeLowPowerdataset. Theevaporatorplatetemperatures,showninFigure 4-15 alsoshowlessspreadintheerrorbarscomparedtothedatacollectedwiththepolymerwickinFigure 4-10 .Thecollecteddatacontinuetofollowadifferenttrendthanthepredictedtemperatures.Itisinterestingtonotethatthemodelpredictsasteepincreaseintemperatureatthetopoftheplate,andthattrendwasnotseeninanyofthedatarecorded.Thehighgradientspredictedbythemodelwerenotseeninthedata.Thegauzewickdatawasalsoexaminedtodeterminetheeffectthefeedrateratio(FRR)hadontheexperimentalresults.ThedataforthedistillateproductionrateasafunctionoftheFRRhadconsiderablescatterascanbeseeninFigure 4-16 .Thereappearstobeageneraltrendofdecreasingdistillateproductionwithincreasingfeedrateratioasseeninthetrend-line.ThelowR2valueof0.026impliesthatthetrendillustratedbythetrend-linemaynotbereal.Thisgeneraldownwardtrendmatchedthetrendpredictedbythenumericalmodel,andtheaveragedistillateproductionobservedwasclosetothevaluepredictedbythemodel. 61

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Figure4-16. DistillateProductionRatevsFeedRateRatio,forthe4mmLowPowergauzedataset. Figure4-17. CondenserPlateTemperaturevsFeedRateRatio,4mmgauzewick,LowPowerdataset.R2valuesaregivenfortheevaporatorandcondenser,respecively. 62

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ThemeasuredcondenserplatetemperaturesversustheFRRalsoshowssomescattercomparedtothepredictedvaluesasFigure 4-17 illustrates.Itshouldbenotedthattheactualspreadinaveragemeasuredcondenserplatetemperatureswasonlyabout2C.Again,R2valuesmaketheinterpretationofthetrend-lineunreliable.Theslighteffectofdecreaseintemperaturepredicedbythemodelmaynotbedetectableduetothenoiseinthedata.Figure 4-17 showsthattheevaporatorplatetemperatureversusFRRdatahadatrend-linewithapositiveslope.ThepositiveslopeimpliedthattheplatetemperaturewouldincreasewithanincreaseinFRR,whichcontradictsthetrendsseenintheothergures.However,theR2valuewasrelativelylowfromastatisticalstandpoint.Furthermore,thedatashowssomestraticationaboutthreetemperaturelevelsofroughly43C,43.9C,and44.2Cwhichindicatedthatthetemperatureoftheevaporatorplatevariedduringdifferenttestdates.Ifthiswerethecase,theaveragetemperaturemaybefollowingthepredictedtrendduringaparticulartestdate,butthiswouldnotmanifestitselfintheoveralltrendforallofthedata. 4.4Discussion 4.4.1ExplainationoftheSimulationThenumericalsimulationwasbasedonsomesimplifyingassumptions.Themostcriticalassumptionmadeinordertocreatethesimulationisthatheattransferintheverticaldirectionmaybeneglected.Withthisassumptioninplacethemodelofthestillmaybedividedintohorizontalsections.Theheattransferequationsforthesectionaresetupandthetemperaturesatvariouspointsinasectionaredeterminedusinganonlinearsystemofequationsolver(fsolve)thatisbuilt-intoMATLAB.Thesectionsarecoupledviathesalineanddistillatestreams.Thetemperatureofthedistillateandbrinestreamintheprevioussectionisusedforthedeterminationofthetemperaturesinthecurrentsection.Inthismannerthesimulationsolvesforthetemperaturesofeachhorizontalsection,goingfromthetoptothebottomofthestill. 63

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Figure4-18. Sketchofhowthecodeworks. Figure 4-18 showsasketchofatypicalsection.Thenumbersshowninthediagramcorresponttolocationsinthesectionwherethecodesolvesfortemperature.ThelabelsforthenumbersarefoundinTable 4-4 .Abriefdescriptionoftheenergybalancethroughthesectionfollows,foramoreexhaustiveexplanationpleaserefertothedissertationbyMitten[ 1 ].Proceedingfromlefttorighttheheatowsthroughtthestillandouttotheambient.Firsttheincidentheatuxgoesfromglazingtoabsorber.Theenergyabsorbedbytheglazingplustheenergyconductedandradiatedfromtheglazingtotheabsorbersurface(1!2)isequaltotheenergyradiatedandconvectedfromtheglazingtotheambient.Thenetengergyabsorbedbytheabsorbersurfaceisequaltotheradiationandconductionfromabsorbertoglazing(1!2)plustheconductionthroughpartition(2!3).Theenergyconductedthroughtheabsorber(2!3)isequaltotheenergyconductedintothewick(3!4).Atthewickthesituationiscomplicatedbytheheatandmasstransferintoandoutofthesectionduetothesalineandthemasstranferacrossthevaporspaceduetoevaporation.Theenergyconductedintowickfrompartition(3!4)plustheenthalpy 64

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owintowickfromtheprevioussection(salinein)isequaltotheenergyevaporated,radiated,andconductedoutofwickacrossvaporspace(4!5)plustheenthalpyowoutofwickintothefollowingsection(salineout).Theenergyconducted,radiated,andcondensedintothecondensinglmfromthevaporspace(4!5)plustheenthalpyowintocondensinglmfromtheprevioussection(distillatein)isequaltotheenergyconductedthroughthecondensinglm(5!6)plustheenthalpyowoutofcondensinglmintothefollowingsection(distillateout).Finally,theheatmustberejectedtotheambient.Theenergyconductedthroughcondensationlm(5!6)isequaltotheenergyconductedthroughthepartition(5!6).Theenergyconductedthroughthepartition(5!6)isequaltotheenergyconvectedintotheambient(qout). 4.4.2ExplainationoftheData Table4-4. DiagramLabelsExplained NumberCorrespondsWith 1Glazing2AbsorberSurface(EvaporatorPlate)3Absorer/WickInterface4Wick/VaporSpaceInterface5VaporSpaceInterface/CondensingFilm6CondensingFilm/CondensingPlateInterface7CondensingPlate/HeatRejectionInterface ThemainassumptioninthesynthesisofthenumericalmodelbyMitten[ 1 ]wasthatofdiffusionbasedheattransferinthehorizontaldirection.Implicitinthisassumptionwastheassumptionthattherewouldbenegligibleheattransferintheverticaldirection.ThisimplicationwascloselyexaminedinthevaporspaceofthestillthroughtheanalysisoftheGrashofnumber.ThereasoningwasthatiftheGrashofnumberwaslowerthanthethresholdthatpredictedconvectioninanenclosure,thentheheattransferinthevaporspacecouldbeassumedtobediffusionbased.Thediffusionbasedmassandheattransferthroughthevaporgapcouldbeassumedtotakeplaceonlyinthe 65

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verticaldirectionsinceairisapoorconductorofheat,andbecausethewatervaporconcentrationgradientwaslowerintheverticaldirectionthaninthehorizontaldirection. Table4-5. GrashofNumberComparison.LowandHighreferto919and4290uxes,respectively TestMeasuredGrPredictedGr%Difference 4mmgauzeLow6.271027.29102-16.24mmpolymerLow6.611028.13102-22.94mmpolymerHigh1.431031.79103-25.112mmpolymerHigh4.511046.32104-40.334.9mmgauzeHigh1.131061.70106-50.6 Table 4-5 showstheGrashofnumbersfortheaverageplatetemperaturesmeasuredduringtheexperimentsandpredictedbythenumericalmodel.TheGrashofnumberwasdeterminedusingtheaverageevaporatorandcondenserplatetemperaturesinthestillandpassingthemintotheMATLABfunctionthatcalculatestheGrashofnumberpreviouslymentioned.ThisfunctioncalculatedthevapordensitiesbasedontheaverageplatetemperaturesaccordingtoEquation 4 .ItcanbeobservedfromTable 4-5 thatthenumericalmodelconsistentlyoverestimatedtheGrashofnumberinthedistillationcell.Themodelgetsmoreaccurateasthesizeofthevaporspacegapdecrease,andaswhentheheatuxwaslowered.Themostaccurateestimatesstillhadapercentdifferencegreaterthan15%.Table 4-5 alsoshowsthatthetwotestsat4.2mmand919W/m2werebelowthethresholdofGr=1000.Thisindicatesthatbothofthosetestwereintheconductionheattransferregime.AscanbeseeninTable 4-6 ,therewasevencloseragreementbetweenpredictedandmeasuredaverageevaporatorplatetemperaturesthanthecomparisonbetweenpredictedandmeasuredGrashofnumbers.Theerrorwaslessthan10%differenceforallcases.Thegeneraltrendwasthatthesmallerthedimensionofthevaporspaceandthelowertheheatux,thebettertheagreementbetweenthetwoaverageplatetemperatures.Thisaffectmayhavebeenenhancedbytheuseofabsolutetemperature 66

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Table4-6. AverageEvaporatorPlateTemperatureComparison.LowandHighreferto919W/m2and4290W/m2uxes,respectively TestMeasuredT(K)PredictedT(K)%Difference 4mmgauzeLow317319-0.6804mmpolymerLow315318-0.8084mmpolymerHigh344350-1.7912mmpolymerHigh349365-4.3734.9mmgauzeHigh351374-6.73 todeterminethepercentdifferencebetweenthetwotemperatures.Inanytemperaturescale,thepredictedandmeasuredvaluesforthelowux4mmgapwereveryclose.Thistrendoflowpercentdifferencebetweenpredictedandmeasuredaverageplatetemperatureswasmaintainedforthecondenserplateaswell.AscanbeseeninTable 4-7 ,theagreementbetweenthepredictedandmeasuredaveragecondenserplatetemperatureswasexceptional.Lessthan1.5%differenceseparatedallcases.Itmustbenotedthattheseweretheaverageplatetemperatures.Whiletheaverageswereincloseagreement,thetrendswerenot. Table4-7. AverageCondenserPlateTemperatureComparison.LowandHighreferto919W/m2and4290W/m2uxes,respectively TestMeasuredT(K)PredictedT(K)%Difference 4mmgauzeLow3013010.1544mmpolymerLow2992970.4284mmpolymerHigh3073040.87612mmpolymerHigh3053030.52834.9mmgauzeHigh3013009.7910)]TJ /F8 7.97 Tf 6.58 0 Td[(2 ThegeneraltrendseeninTable 4-3 wasadecreaseinthepercentdifferencebetweenthepredictedandmeasureddistillateproductionvaluesasthevaporspacedimensionandheatuxdecrease.Anotableexceptionisthe34.9mmgaptest,whichhadcloseragreementwiththeprediction.Thiswaslikelyduetotheconvectivecellinthestillenhancingmasstransfer,whichwouldincreasethedistillateproducedbythe 67

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still.Ingeneral,themodelaccuratelypredicteddistillateproductionforallofthetest,withthehighestpercentdifferencebeingabout10%.Themodelalsopredictedtheincreaseindistillateproductionrateasaresultoftheincreaseinheatux.Overallthisindicatesthatthemodeliseffectiveforpreliminaryestimationoftheperformanceofasingle-effect,vertical-wicksolarstill. 4.4.3ExplainationoftheDiscrepancyItwasnotuntilthedatawereplottedforseveralexperimentsthatthetemperaturegradientsintheverticaldirectioncouldbeexamined.Theexperimentaldatashowedsmalltemperaturegradientsintheverticaldirection,whilethenumericalmodelpredictedhightemperaturegradients.Thelargetemperaturegradientsintheverticaldirectionthatwerepredictedbythenumericalsimulation,especiallyontheevaporatorplate,wouldtendtodriveheattransferintheverticaldirection.Inordertodeterminewhetheritwasreasonabletoassumeconductionthroughthewickonlyinthehorizontaldirection(x-direction),Mitten[ 1 ]usedadirectionalscaleanalysis.Inasimilarmannerascaleanalysisofthegradientsofthepredictedevaporatortemperatureswasmade.Theplatethickness(x=9.5310)]TJ /F8 7.97 Tf 6.59 0 Td[(3)andtheverticalsegmentlengthwerefound.y=platelength numberofslices=0.3048 30=1.101610)]TJ /F8 7.97 Tf 6.59 0 Td[(2.Thegradientwasapproximatedasfollows@T @xT x,Thepeakgradientspredictedinthe4mmevaporatorplatewithagauzewickwerefoundtobeT x=17.1K/mandT y=482K/m.Thisshowsthatthegradientinthey-directionwasanorderofmagnitudegreaterthanthatofthex-direction.Agradientof 68

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thismagnitudewoulddrivesignicantheattransferintheverticaldirection.Thismadetheassumptionofpurelyhorizontalheattransferinvalid.Thisalsoexplainswhythecharacteristicshapeofthepredictedevaporatortemperaturesdidnotcomparewellwiththeexperimentallyobservedtemperatures.Inordertoexaminethethistemperaturegradientmoreclosely,therstfewmillimetersatthetopoftheevaporatorplateareexamined.Thebulktemperatureofthewick,Tb,isanaveragetemperatureoftheuidinthewick.Thistemperaturewillvaryalongthewickasheatfromtheplategoesintoincreasingthetemperatureofthewick.Intheserstfewmillimetersatthetopofthewick,themajorityoftheheattransferedthroughtheplategoestowardincreasingthetemperatureofthesalineinthewick.Athisprocesswasmodeledandcomparedtothenumericalpredictionusedforthestillandtheexperimentalvaluesrecorded.Inordertopredictthebulktemperatureinthewickattheverytopofthewick,heattransferthroughthewickwasignored,andallheatleavingtheplatewenttowardheatingthewick. Figure4-19. EvaporatorPlateTemperatureandBulkSalineTemperature. 69

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Figure 4-19 showsthedifferentpredictedandobservedtemperaturesatthetopoftheevaporatorplate.Ascanbeseeninthegure,thebulktemperatureincreasesatafasterratethanthenumericalmodelofthestill.Thishighgradient,again,impliesthattherewouldbesignicantheattransferintheverticaldirectionalongtheplate,atleastattheverytopofthestill.ThishigherrateoftemperatureincreasebettermatchesthedatapointthatwasexperimentallyobservedasshowninFigure 4-19 70

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CHAPTER5CONCLUSIONSANDRECOMMENDATIONS 5.1IntroductionTheresultshaveshownthattherearenoticeablediscrepanciesbetweenthenumericallypredictedandempiricallymeasuredtemperaturevalues.Thepredictedtemperaturevalueswerehigherfortheevaporatorandslightlylowerforcondenserplatethanwhatwasobserved.Furthermorethetrendsobservedinthedata,specicallytherelativelyattemperaturedistributionalongthelengthoftheplate,didnotmatchtherapidtemperatureriseseeninthenumericalprediction.However,theaverageplatetemperatureswereincloseagreementforthenarrowestvaporgapsettingof4.2mm.Theobservedandpredictedvalueswerealsoincloseagreementregardingthedistillateproductionresults.Thelargestdifferencebetweenthepredictedandobserveddistillateproductionhadapercentdifferencelessthanof11%. 5.2ConclusionsDespitetheseshortcomings,thecodewasabletopredictaverageplatetemperatureswell.Theover-predictionoftheaverageevaporatorplatetemperaturelikelyledtotheoverestimationoftheGrashofnumberprediction.ThepredictedGrashofnumberswereaccurateenoughtousetodetermineifthestillwouldoperateintheconductionheattransferregime.Finally,thepredicteddistillateproductionrateswereclosetotheobservedrates.Withthehighestpercentdifferenceofslightlyover10%,thevaluesprovidedcouldbeusefulforinitialroughestimation.Thegreatestdisappointmentinthepredictionswasthat,althoughtheaverageplatetemperatureswerepredictedwell,thetrendobservedintheplatetemperatureprolewasnotcaptured,especiallyattheverytopoftheplate.Thisproblemmayhavebeenoverlookedforasingle-effectstill,butthetemperatureprolemayneedtobemoreaccuratetopredicttemperaturesanddistillateproductionratesfromamultiple-effectstill.Theerrorinthepredictedtemperatureprolefromasingleeffect 71

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maybecompoundedthrougheacheffectinamultipleeffectstillsimulation.Thisaddederrorcouldleadtosuchlargeinaccuraciesastomakethepredictionunusable.Theonlywaytodetermineifthisisthecasewouldbetotestamultipleeffectstillandcomparethepredictiontotheexperimentalresults.Themostlikelyreasonforthediscrepanciesbetweenthesimulationandexperimentalresultswasthatthemainassumptionusedincreatingthecode,theassumptionofheattransferinthehorizontaldirectiononly,wasinvalid.Bydoingadirectionalscaleanalysisonthepredictedtemperaturesoftheevaporatorplate,itwasdemonstratedthatthehighestverticaltemperaturegradientwasmorethananorderofmagnitudegreaterthanthegreatesthorizontaltemperaturegradient.Thisimpliesthattheconductionintheverticaldirectioninthesimulationcannotbeignored,andthusrenderedthebasicassumptionofthenumericalsimulationinvalid.Ifheatdidtransferupthewick,itwouldresultinmorerapidheatingofthewickatthetopoftheplateandalargerareaofnearlyconstanttemperaturealongtherestoftheplate.Thelatterphenomenonisdirectlyobservedinthedata,andthepriorphenomenonmaybeinferredfromit. 5.3RecommendationsWiththeconclusionsmade,thefollowingrecommendationsaresuggested.1)Performanexperimentonamultipleeffectapparatusandcomparetheresultswiththosepredictedbythenumericalmodel.Thiswouldconrmorrefutetheconcernthattheerrorsinpredictingthetemperatureprolewouldcascadethroughamultipleeffectpredictionandrendertheresultsuseless.2)Investigatesomewaytocorrectforthelackofverticalheatconduction.Morethermocouplescouldbeplacedintherstcentimeteroftheevaporatorplateinordertodetermineifalargetemperaturegradientexistsinthisregion.Perhapsthemodelcouldbealteredtotakeintoaccountthe`averaging'effectthattheverticalplateconductionhas.3)Performtheexperimentwithalargerbenchscalestill.Oneoftheissuesthatcameupintheexperimentwastheamountofscatterthatwasfoundinthedata.Thedistillateproducedinthisstillwasintermittent 72

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becausethedistillatewouldbuildupinthecollectiontubeuntilenoughdistillatewasaccumulatedtobreakthesurfacetensioninthetube.Alargerstillwouldprovidealargerdistillateproductionratewhichwouldovercometheintermittencyoftheoutpouringofthedistillate. 73

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APPENDIXAENGINEERINGCHECKS A.1AdjustmentsMadeintheSimulationParametersSinceallofthetestswerenotconductedinthesamemonth,thedatawerereviewedtoinvestigateiftheambientconditionswereconstant.Uponreviewingthecollecteddata,itwasfoundthattheinitialtemperatureofthestill,priortoheataddition,wasnotconstant.Thenumericalsimulationprovidedanumberofoptionsforchangingtheseinitialtemperatures.Therewerethreetemperaturevariablesthatmaybesetinthesimulation.T_infsetstheambientairtemperature,andwasusedwhenheatwasrejectedtotheenvironmentvianaturalconvection.T_surrwasthetemperatureofthesky,whichwasusedtodetermineradiationlossesfromtheabsorberandtheheatrejectiontotheambient.T_sourcewasthetemperatureofthesalinewater,andthereforetheinlettemperatureofthesalinewater.Oftheenvironmentaltemperatures,T_sourcehadthegreatestinuenceonthepredictedstilltemperatures.Anincreaseof5CinT_sourceresultedinanalmostuniformincreaseinthecondenserandevaporatorofapproximately4.9Cand3Crespectively.WhilemanipulatingT_surranddeterminingit'saffectsonradiantheattransferitwasnoticedthatthecodewasstillsetuplikeasolarstillandnotlikeintheexperiment.Thenitwasdeterminedthattheradiationheattransferportionofthecodewasstillassumingthatthesolaruxwasgoingthroughacollector.Becauseanelectricheaterwasusedintheexperiment,mostoftheenergyintheexperimentshouldhavepassedthroughthestill.Tocorrectforthisdiscrepancywiththesimulation,thelossesthroughthesimulatedsolarcollectorwereminimized.Todothis,thefollowingchangesweremadetoabsorptivityoftheglassg=0.1!0.01,theabsorptivityoftheabsorberplatep=0.9!0.99,andthetransmissivityoftheglassg=0.9!0.99.Oncethesechangesweremade,therewasamoremeaningfulchangeintheplatetemperatures,especiallytheevaportatortemperature.Withthesechangesanincrease 74

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inthecondenserandevaporatorplatesof0.2-0.7Cand2.3Cwasobserved.Withthediscoveriesmade,thesimulationwasrunagainwithincreasedradiationabsorptionandwithT_sourcematchingtheambienttemperatureforthetest. A.2TablesThefollowingtablesareusedtocheckthevalidityofvariouscomponentsoftheexperiment.Theelectricalresistancewasusedasananalogforthesaltconcentration.Therelationshipbetweensaltconcentrationandconductivityisnonlinear,sothevaluesgivenherearestrictlyforaqualitativecomparison.ThevaluesweretakenusinganCraftsmanProfessionalMultimeterwiththeelectrodesseparatedbyadistanceof8.41mm.Table A-1 showsthatthedistillateproducedwasnotexactlyaspureasdistilledwater,butitwasmorepurethantapwater.Alikelyexplanationforthedecreasedresistivityofthedistillateisthatbrassmayhaveleachedintothedistillate,addingasmallamountofdissolvedsolids. TableA-1. Samplewaterelectricalresistance SampleAverageelectricalresistance(ink) DistilledWater3300DistillateWater2000TapWater1300SalineWater187 Theequationfortheperformanceratio(PR)isgivenbelow.Thedistillateproductionrate,_mdistillate,istypicallygivenintermsofintheliterature.Thelatentheatofvaporization,hlv,wastakentobe2400J/ginthecalculationoftheperformanceratiofromtheexperimentaldata.Theheatsuppliedtothestill,qsupply,net,wasnotalwaysclearlycitedinthesolarstillliterature,butitisnecessaryforcomparisonofperformanceofstillsindifferentlatitudes.ThePRisusedtocomparetheefcacyofvariousstillsregardlessoftheircongurationornumberofeffects.ofvarioussolarstillsisgiveninTable A-2 below. 75

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Forthestillswithmultipleeffectsanadditionaltableisgiventoshowtheperformanceratiopereffect.PR=1Pe=1_mdistillate,ehlv,e qsupply,netPRobserved=0.2451g s2400J g 918.8J m2s=0.64HeatFlux=21.34W 0.0023226m2=918.8W m2HighestDistillateRate=0.005693g s 0.0023226m2=0.2451g msHighHeatFlux=99.64W 0.0023226m2=4290W m2 TableA-2. PerformanceRatioTable.Distillateandenergyvaluesareperdiem NumberofEffects_mdistillatekg/m2qsupply,netMJ/m2PRSource 12.06518.560.264VarolandYazar[ 32 ]14.8822.550.513Cooper[ 33 ]1118.722.41.978Tanakaetal.[ 30 ]613.520.21.584Tanakaetal.[ 34 ]1130.020.03.554Mitten[ 1 ]15.4419.80.650Mitten[ 1 ]15.2919.80.632Experiment ThemassbalanceoftheentiresystemisshowninTable A-4 below.Themissingmasswasthedifferencebetweeninitialsalinemassandthesumofthemassesofthesaline,distillate,andbrineattheendoftheexperiment.Thetableshowsthatthemissingmassissmallwhencomparedtoinitialamountofsalineusedfortheexperiment.Whenitiscomparedtothetotalmasscollected,whichisthesumofthe 76

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TableA-3. PerformanceRatioTable.Distillateandenergyvaluesareperdiem NumberofEffects_mdistillatekg/m2qsupply,netMJ/m2PRpereffectSource 12.06518.560.264VarolandYazar[ 32 ]14.8822.550.513Cooper[ 33 ]1118.722.40.180Tanakaetal.[ 30 ]613.520.20.264Tanakaetal.[ 34 ]1130.020.00.323Mitten[ 1 ]15.4419.80.650Mitten[ 1 ]15.2919.80.632Experiment massesofdistillateandbrinecollected,themissingmassismoresubstatial,comparingtoapproximately22%ofthecollectedmassforonecase. TableA-4. MassBalanceTable(g) TestInitialSystemMassMassCollectedMissingMass June1250026731June2249924242June5-1250024254June5-2200018030 77

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APPENDIXBSOURCECODEANDFLOWCHARTSInthisappendix,thesourcecodeforthenumericalsimulationandtheowchartsforthiscodearepresented. B.1SingleSolverThisrstscriptisv3_sngl_solvr.manditisthecodethattakesinanumberofvariablesandsolvedforthetemperatureinthestill. %f %+++++++++++++++++++++++++++++++++++++++++++++++++++++++++REJECTIONTOAIR function[T,fval]=v3 sngl solvr(N,alpha g,Q supply,tau g,... alpha p,A,sigma,eps p1,eps g,k a j,t ag,T surr,u a,T inf,k p,t p,... Nu w1,k w j,t w,k g,mdot w j,Cp br j,T w in j,h lv j,D ab j,P,R,... T m vs j,a,b,c,d,e,f,g,h,k,S j,eps w,eps cf,k ha j,t vs,k l j,... t cf j,mdot cf j,Cp l j,T cf in j,eps p,T0);%withrejectiontoair %g %f function[T,fval]=v3 sngl solvr(alpha g,Q supply,tau g,... alpha p,A,sigma,eps p1,eps g,k a,t ag,T surr,u a,T inf,k p,t p,Nu w1,... k w j,t w,k g,mdot w j,Cp br j,T w in,h lv j,D ab j,P,R,T m vs j,... 78

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a,b,c,d,e,f,g,h,k,S j,eps w,eps cf,k ha j,t vs,mdot cf j,Cp l j,... k l j,t cf j,T cf in,eps p,T0); %g %[T,fval]=fsolve(@nestedfun,T0); % %%Nestedfunctionthatcomputestheobjectivefunction %functiony=nestedfun(T) %++++++++++++++++++++++++++++++++++++++++++++++++++++++HEATRECOUPERATION function[T]=v3 sngl solvr(N,alpha g,Q supply,tau g,... alpha p,A,sigma,eps p1,eps g,k a j,t ag,T surr,u a,T inf,k p,t p,Nu w1,... k w j,t w,k g,mdot w j,Cp br j,T w in j,h lv j,D ab j,P,R,T m vs j,a,b,... c,d,e,f,g,h,k,S j,eps w,eps cf,k ha j,t vs,k l j,t cf j,mdot cf j,... Cp l j,T cf in j,Nu hr,D,k br j,T lhr j,eps p,T0);%withrejectiontoheatrecuperator func=@(T)nestedfun(N,alpha g,Q supply,tau g,... alpha p,A,sigma,eps p1,eps g,k a j,t ag,T surr,u a,T inf,k p,t p,Nu w1,... k w j,t w,k g,mdot w j,Cp br j,T w in j,h lv j,D ab j,P,R,T m vs j,a,b,... 79

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c,d,e,f,g,h,k,S j,eps w,eps cf,k ha j,t vs,k l j,t cf j,mdot cf j,... Cp l j,T cf in j,Nu hr,D,k br j,T lhr j,eps p,T); %[T,fval]=fsolve(@(T)nestedfun,T0); [T,fval]=fsolve(func,T0); end %Nestedfunctionthatcomputestheobjectivefunction functiony=nestedfun(N,alpha g,Q supply,tau g,... alpha p,A,sigma,eps p1,eps g,k a j,t ag,T surr,u a,T inf,k p,t p,Nu w1,... k w j,t w,k g,mdot w j,Cp br j,T w in j,h lv j,D ab j,P,R,T m vs j,a,b,... c,d,e,f,g,h,k,S j,eps w,eps cf,k ha j,t vs,k l j,t cf j,mdot cf j,... Cp l j,T cf in j,Nu hr,D,k br j,T lhr j,eps p,T) n=N; fori=1:n;%equationbuilder GC=alpha g(Q supply)+(((Asigma)/(1/eps p1+1/eps g)]TJ /F1 11.955 Tf 9.69 0 Td[(1))(T(2)4)]TJ /F1 11.955 Tf 9.55 0 Td[(T(1)4))... +((Ak a j/t ag)(T(2))]TJ /F1 11.955 Tf 8.53 0 Td[(T(1))))]TJ /F1 11.955 Tf 9.56 0 Td[((sigmaeps gA(T(1)4)]TJ /F1 11.955 Tf 11.17 0 Td[(T surr4))... )]TJ /F1 11.955 Tf 9.57 0 Td[((A(5.7+3.8u a)(T(1))]TJ /F1 11.955 Tf 10.53 0 Td[(T inf)); 80

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%f GC=alpha g(Q supply)/(tau galpha p)... +(((Asigma)/(1/eps p1+1/eps g)]TJ /F1 11.955 Tf 9.7 0 Td[(1))(T(2)4)]TJ /F1 11.955 Tf 9.55 0 Td[(T(1)4))... +((Ak a j/t ag)(T(2))]TJ /F1 11.955 Tf 8.53 0 Td[(T(1))))]TJ /F1 11.955 Tf 9.56 0 Td[((sigmaeps gA(T(1)4)]TJ /F1 11.955 Tf 11.17 0 Td[(T surr4))... )]TJ /F1 11.955 Tf 9.57 0 Td[((A(5.7+3.8u a)(T(1))]TJ /F1 11.955 Tf 10.53 0 Td[(T inf));%Tanakamodel %g %Q r p1g(j,:)=((Asigma)/(1/eps p1+1/eps g)]TJ /F1 11.955 Tf 9.7 0 Td[(1))(T(2)4)]TJ /F1 11.955 Tf 9.55 0 Td[(T(1)4); %Q d p1g(j,:)=(Ak a/t ag)(T(2))]TJ /F1 11.955 Tf 8.52 0 Td[(T(1)); %Q r ga(j,:)=sigmaeps gA(T(1)4)]TJ /F1 11.955 Tf 11.16 0 Td[(T surr4); %Q c ga(j,:)=A(5.7+3.8u a)(T(1))]TJ /F1 11.955 Tf 10.53 0 Td[(T inf); AB=(Q supplytau galpha p)... )]TJ /F1 11.955 Tf 18.16 0 Td[((((Asigma)/(1/eps p1+1/eps g)]TJ /F1 11.955 Tf 9.69 0 Td[(1))(T(2)4)]TJ /F1 11.955 Tf 9.55 0 Td[(T(1)4))... )]TJ /F1 11.955 Tf 17.89 0 Td[(((Ak a j/t ag)(T(2))]TJ /F1 11.955 Tf 8.52 0 Td[(T(1))))]TJ /F1 11.955 Tf 17.89 0 Td[(((k pA/t p)(T(2))]TJ /F1 11.955 Tf 15.7 0 Td[(T(3))); %f AB=(Q supply))]TJ /F1 11.955 Tf 18.16 0 Td[((((Asigma)/(1/eps p1+1/eps g)]TJ /F1 11.955 Tf 9.69 0 Td[(1))(T(2)4)]TJ /F1 11.955 Tf 9.55 0 Td[(T(1)4))... )]TJ /F1 11.955 Tf 17.89 0 Td[(((Ak a j/t ag)(T(2))]TJ /F1 11.955 Tf 8.52 0 Td[(T(1))))]TJ /F1 11.955 Tf 17.89 0 Td[(((k pA/t p)(T(2))]TJ /F1 11.955 Tf 15.7 0 Td[(T(3)));%TanakaModel %g %Q d(j,1)=(k pA/t p)(T(2))]TJ /F1 11.955 Tf 15.7 0 Td[(T(3)); P1 e(i,:)=((k l j(i)A/t cf j(i)))(T(4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+5))]TJ /F1 11.955 Tf 8.52 0 Td[(T(4(i)]TJ /F1 11.955 Tf 9.69 0 Td[(1)+6))... )]TJ /F1 11.955 Tf 10.15 0 Td[(((k pA/t p)(T(4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+6))]TJ /F1 11.955 Tf 15.7 0 Td[(T(4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+7))); 81

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%P1 e(1)=((k l j(i).A/t cf j(i)))(T(6))]TJ /F1 11.955 Tf 8.53 0 Td[(T(7)))]TJ /F1 11.955 Tf 10.15 0 Td[(((k gA/t p)(T(7))]TJ /F1 11.955 Tf 15.7 0 Td[(T(8))); %f P1 e(2)=((k l j(i).A/t cf j(i)))(T(11))]TJ /F1 11.955 Tf 8.53 0 Td[(T(12)))]TJ /F1 11.955 Tf 10.15 0 Td[(((k gA/t p)(T(12)... )]TJ /F1 11.955 Tf 8.53 0 Td[(T(13))); %g %Q cf(j,i)=((k l j(i)A/t cf j(i)))(T(4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+5))]TJ /F1 11.955 Tf 8.53 0 Td[(T(4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+6)); %Q d(j,i)=((k pA/t p)(T(4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+6))]TJ /F1 11.955 Tf 15.69 0 Td[(T(4(i)]TJ /F1 11.955 Tf 9.69 0 Td[(1)+7))); P2 e(i,:)=((k pA/t p)(T(4(i)]TJ /F1 11.955 Tf 9.69 0 Td[(1)+2))]TJ /F1 11.955 Tf 15.7 0 Td[(T(4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+3)))... )]TJ /F1 11.955 Tf 10.15 0 Td[(((Nu w1k w j(i)A/t w)(T(4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+3))]TJ /F1 11.955 Tf 8.53 0 Td[(T(4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+4))); %P2 e(1)=((k pA/t p)(T(2))]TJ /F1 11.955 Tf 15.69 0 Td[(T(3))))]TJ /F1 11.955 Tf 10.15 0 Td[(((Nu w1.k w j(i).A/t w)(T(3))]TJ /F1 11.955 Tf 8.53 0 Td[(T(4))); %P2 e(2)=((k pA/t p)(T(7))]TJ /F1 11.955 Tf 15.69 0 Td[(T(8))))]TJ /F1 11.955 Tf 10.15 0 Td[(((Nu w1.k w j(i).A/t w)(T(8))]TJ /F1 11.955 Tf 8.53 0 Td[(T(9))); %Q w(j,i)=((Nu w1k w j(i)A/t w)(T(4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+3))]TJ /F1 11.955 Tf 8.52 0 Td[(T(4(i)]TJ /F1 11.955 Tf 9.69 0 Td[(1)+4))); P2 en=((k pA/t p)(T(4(n)]TJ /F1 11.955 Tf 9.69 0 Td[(1)+6))]TJ /F1 11.955 Tf 15.7 0 Td[(T(4(n)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+7)))... )]TJ /F1 11.955 Tf 17.89 0 Td[(((Nu hrk br j(n)A)/D)(T(4(n)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+7))]TJ /F1 11.955 Tf 10.88 0 Td[(T lhr j); %withrejectiontoheatrecuperator %f %======================================================== P2 en=((k pA/t p)(T(4(n)]TJ /F1 11.955 Tf 9.69 0 Td[(1)+6))]TJ /F1 11.955 Tf 15.7 0 Td[(T(4(n)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+7)))... 82

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)]TJ /F1 11.955 Tf 17.36 0 Td[((A(5.7+3.8u a)(T(4(n)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+7))]TJ /F1 11.955 Tf 10.53 0 Td[(T inf))... )]TJ /F1 11.955 Tf 17.36 0 Td[((sigmaeps pA(T(4(n)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+7)4)]TJ /F1 11.955 Tf 11.16 0 Td[(T surr4)); %withrejectiontoambientairfromTanaka %======================================================== %g W(i,:)=((Nu w1k w j(i))A/t w)(T(4(i)]TJ /F1 11.955 Tf 9.69 0 Td[(1)+3))]TJ /F1 11.955 Tf 15.7 0 Td[(T(4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+4))... )]TJ /F1 11.955 Tf 16.98 0 Td[(mdot w j(i)Cp br j(i)(T(4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+4))]TJ /F1 11.955 Tf 17.6 0 Td[(T w in j(i))... )]TJ /F1 11.955 Tf 10.54 0 Td[((((Ah lv j(i)D ab j(i)P)/(Rt vsT m vs j(i)))... log((P)]TJ /F1 11.955 Tf 10.22 0 Td[((10000010(a+b/T(4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+5)... +((c(T(4(i)]TJ /F1 11.955 Tf 9.69 0 Td[(1)+5)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g))/T(4(i)]TJ /F1 11.955 Tf 9.69 0 Td[(1)+5))(10(d(T(4(i)]TJ /F1 11.955 Tf 9.69 0 Td[(1)+5)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g)2))]TJ /F1 11.955 Tf 9.62 0 Td[(1)... +e10(f(617.27)]TJ /F1 11.955 Tf 10.03 0 Td[(T(4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+5))1.25))))/(P)]TJ /F1 11.955 Tf 10.22 0 Td[((10000010(a+b/T(4(i)]TJ /F1 11.955 Tf 9.69 0 Td[(1)+4)... +((c(T(4(i)]TJ /F1 11.955 Tf 9.69 0 Td[(1)+4)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g))/T(4(i)]TJ /F1 11.955 Tf 9.69 0 Td[(1)+4))(10(d(T(4(i)]TJ /F1 11.955 Tf 9.69 0 Td[(1)+4)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g)2))]TJ /F1 11.955 Tf 9.62 0 Td[(1)... +e10(f(617.27)]TJ /F1 11.955 Tf 10.03 0 Td[(T(4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+4))1.25)+hS j(i)+kS j(i)2)))))... )]TJ /F1 11.955 Tf 11.06 0 Td[(((1/((1/eps w)+(1/eps cf))]TJ /F1 11.955 Tf 9.62 0 Td[(1))Asigma(T(4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+4)4)]TJ /F1 11.955 Tf 9.55 0 Td[(T(4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+5)4))... )]TJ /F1 11.955 Tf 10.15 0 Td[(((Ak ha j(i)/t vs)(T(4(i)]TJ /F1 11.955 Tf 9.69 0 Td[(1)+4))]TJ /F1 11.955 Tf 8.53 0 Td[(T(4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+5))); CF(i,:)=(((A(h lv j(i)+Cp br j(i).(T(4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+4))]TJ /F1 11.955 Tf 8.52 0 Td[(T(4(i)]TJ /F1 11.955 Tf 9.69 0 Td[(1)+5)))... D ab j(i)P)/(Rt vsT m vs j(i)))... log((P)]TJ /F1 11.955 Tf 10.22 0 Td[((10000010(a+b/T(4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+5)... 83

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+((c(T(4(i)]TJ /F1 11.955 Tf 9.69 0 Td[(1)+5)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g))/T(4(i)]TJ /F1 11.955 Tf 9.69 0 Td[(1)+5))(10(d(T(4(i)]TJ /F1 11.955 Tf 9.69 0 Td[(1)+5)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g)2))]TJ /F1 11.955 Tf 9.62 0 Td[(1)... +e10(f(617.27)]TJ /F1 11.955 Tf 10.03 0 Td[(T(4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+5))1.25))))/(P)]TJ /F1 11.955 Tf 10.22 0 Td[((10000010(a+b/T(4(i)]TJ /F1 11.955 Tf 9.69 0 Td[(1)+4)... +((c(T(4(i)]TJ /F1 11.955 Tf 9.69 0 Td[(1)+4)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g))/T(4(i)]TJ /F1 11.955 Tf 9.69 0 Td[(1)+4))(10(d(T(4(i)]TJ /F1 11.955 Tf 9.69 0 Td[(1)+4)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g)2))]TJ /F1 11.955 Tf 9.62 0 Td[(1)... +e10(f(617.27)]TJ /F1 11.955 Tf 10.03 0 Td[(T(4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+4))1.25)+hS j(i)+kS j(i)2)))))... +((1/((1/eps w)+(1/eps cf))]TJ /F1 11.955 Tf 9.62 0 Td[(1))Asigma(T(4(i)]TJ /F1 11.955 Tf 9.69 0 Td[(1)+4)4)]TJ /F1 11.955 Tf 9.55 0 Td[(T(4(i)]TJ /F1 11.955 Tf 9.69 0 Td[(1)+5)4))... +((Ak ha j(i)/t vs)(T(4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+4))]TJ /F1 11.955 Tf 8.53 0 Td[(T(4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+5)))... )]TJ /F1 11.955 Tf 17.36 0 Td[((k l j(i)A/t cf j(i))(T(4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+5))]TJ /F1 11.955 Tf 15.69 0 Td[(T(4(i)]TJ /F1 11.955 Tf 9.69 0 Td[(1)+6))... )]TJ /F1 11.955 Tf 17.51 0 Td[(mdot cf j(i)Cp l j(i)(T(4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+5))]TJ /F1 11.955 Tf 10.9 0 Td[(T cf in j(i)); %includesuperheatandheatingofCFflow end y=[GC; AB; P1 e; P2 e; P2 en; W; CF]; end end 84

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%f %T g=T(1) %T p1(1)=T(2) %T p2(1)=T(3) %T w(1)=T(4) %T cf(1)=T(5) %T p1(2)=T(6) %T p2(2)=T(7) %T w(2)=T(8) %T cf(2)=T(9) %T p1(3)=T(10) %T p2(3)=T(11) %g %Energybalanceequations %f %Balanceonglasscover(T inf,T surr,T(1),T(2)) %Equation:alpha g(Q supply)/(tau galpha p)+Q rad p1g+Q d p1g %)]TJ /F1 11.955 Tf 16.07 0 Td[(Q rad ga)]TJ /F1 11.955 Tf 16.6 0 Td[(Q c ga=0 %Q supply=Q supply %Q rad p1g=((Asigma)/(1/eps p1+1/eps g)]TJ /F1 11.955 Tf 9.7 0 Td[(1))(T(2)4)]TJ /F1 11.955 Tf 9.56 0 Td[(T(1)4) %Q d p1g=(Ak a/t ag)(T(2))]TJ /F1 11.955 Tf 8.52 0 Td[(T(1)) %Q rad ga=sigmaeps gA(T(1)4)]TJ /F1 11.955 Tf 11.17 0 Td[(T surr4) %Q c ga=A(5.7+3.8u a)(T(1))]TJ /F1 11.955 Tf 10.53 0 Td[(T inf) 85

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%Plugin %GC=alpha g(Q supply)/(tau galpha p)+(((Asigma)/(1/eps p1+1/eps g)]TJ /F1 11.955 Tf 9.7 0 Td[(1))(T(2)4)]TJ /F1 11.955 Tf 9.55 0 Td[(T(1)4))+((Ak a/t ag)(T(2))]TJ /F1 11.955 Tf 8.53 0 Td[(T(1))))]TJ /F1 11.955 Tf 9.56 0 Td[((sigmaeps gA(T(1)4)]TJ /F1 11.955 Tf 11.17 0 Td[(T surr4)))]TJ /F1 11.955 Tf 9.57 0 Td[((A(5.7+3.8u a)(T(1))]TJ /F1 11.955 Tf 10.53 0 Td[(T inf)) %P1(e=1)CSbalance)]TJ /F1 11.955 Tf 15.66 0 Td[(Cap(T(1),T(2),T(3)) %Equation:Q supply)]TJ /F1 11.955 Tf 16.7 0 Td[(Q rad p1g)]TJ /F1 11.955 Tf 16.48 0 Td[(Q d p1g)]TJ /F1 11.955 Tf 16.08 0 Td[(Q d %Q supply=Q Supply %Q rad p1g=((Asigma)/(1/eps p1+1/eps g)]TJ /F1 11.955 Tf 9.7 0 Td[(1))(T(2)4)]TJ /F1 11.955 Tf 9.56 0 Td[(T(1)4) %Q d p1g=(Ak a/t ag)(T(2))]TJ /F1 11.955 Tf 8.52 0 Td[(T(1)) %Q d=(k pA/t p)(T(2))]TJ /F1 11.955 Tf 15.7 0 Td[(T(3)) %Plugin % %f P1 e1=(Q supply))]TJ /F1 11.955 Tf 18.16 0 Td[((((Asigma)/(1/eps p1+1/eps g)]TJ /F1 11.955 Tf 9.69 0 Td[(1))(T(2)4)]TJ /F1 11.955 Tf 9.55 0 Td[(T(1)4))... )]TJ /F1 11.955 Tf 17.89 0 Td[(((Ak a/t ag)(T(2))]TJ /F1 11.955 Tf 8.52 0 Td[(T(1))))]TJ /F1 11.955 Tf 17.89 0 Td[(((k pA/t p)(T(2))]TJ /F1 11.955 Tf 15.7 0 Td[(T(3))) %g %P1(e=n)CSbalance %Equation:Q cf)]TJ /F1 11.955 Tf 16.54 0 Td[(Q d 1 %Q cf=(k l(j,1)A/t cf(j,1))(T(6))]TJ /F1 11.955 Tf 8.52 0 Td[(T(7)); %Q d=(k gA/t p)(T(7))]TJ /F1 11.955 Tf 15.7 0 Td[(T(8)); %Plugin %((k l(j,1)A/t cf(j,1))(T(6))]TJ /F1 11.955 Tf 8.52 0 Td[(T(7))))]TJ /F1 11.955 Tf 10.15 0 Td[(((k pA/t p)(T(7))]TJ /F1 11.955 Tf 15.7 0 Td[(T(8)))=0 86

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%P2(e=1)CSbalance %Equation:Q d)]TJ /F1 11.955 Tf 15.73 0 Td[(Q w1=0 %Q d=(k pA/t p)(T(2))]TJ /F1 11.955 Tf 15.7 0 Td[(T(3)) %Q w1=(Nu w1k w(j,1)A/t w)(T(3))]TJ /F1 11.955 Tf 8.52 0 Td[(T(4)) %Plugin %((k pA/t p)(T(2))]TJ /F1 11.955 Tf 15.69 0 Td[(T(3))))]TJ /F1 11.955 Tf 10.15 0 Td[(((Nu w1k w(j,1)A/t w)(T(3))]TJ /F1 11.955 Tf 8.52 0 Td[(T(4)))=0 %P2(e=2)CSbalance %Equation:Q d)]TJ /F1 11.955 Tf 15.73 0 Td[(Q w1=0 %Q d=(k pA/t p)(T(7))]TJ /F1 11.955 Tf 15.7 0 Td[(T(8)) %Q w1=(Nu w1k w 2A/t w)(T(8))]TJ /F1 11.955 Tf 8.52 0 Td[(T(9)) %Plugin %((k pA/t p)(T(7))]TJ /F1 11.955 Tf 15.69 0 Td[(T(8))))]TJ /F1 11.955 Tf 10.15 0 Td[(((Nu w1k w 2A/t w)(T(8))]TJ /F1 11.955 Tf 8.52 0 Td[(T(9)))=0 %P2(e=3)CSbalance %Equation:Q d)]TJ /F1 11.955 Tf 15.73 0 Td[(Q w1=0 %Q d=(k pA/t p)(T(12))]TJ /F1 11.955 Tf 15.69 0 Td[(T(13)) %Q w1=(Nu w1k w 3A/t w)(T(13))]TJ /F1 11.955 Tf 8.53 0 Td[(T(14)) %Plugin %((k pA/t p)(T(12))]TJ /F1 11.955 Tf 15.7 0 Td[(T(13))))]TJ /F1 11.955 Tf 10.15 0 Td[(((Nu w1k w 3A/t w)(T(13))]TJ /F1 11.955 Tf 8.52 0 Td[(T(14)))=0 %P2(e=4)CSbalance %Equation:Q d)]TJ /F1 11.955 Tf 15.73 0 Td[(Q w1=0 87

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%Q d=(k pA/t p)(T(17))]TJ /F1 11.955 Tf 15.69 0 Td[(T(18)) %Q w1=(Nu w1k w 4A/t w)(T(18))]TJ /F1 11.955 Tf 8.53 0 Td[(T(19)) %Plugin %((k pA/t p)(T(17))]TJ /F1 11.955 Tf 15.7 0 Td[(T(18))))]TJ /F1 11.955 Tf 10.15 0 Td[(((Nu w1k w 4A/t w)(T(18))]TJ /F1 11.955 Tf 8.52 0 Td[(T(19)))=0 %Wick(e=1)CVbalance %Equation:Q w1)]TJ /F1 11.955 Tf 16.91 0 Td[(Q f)]TJ /F1 11.955 Tf 15.73 0 Td[(Q w2=0 %Equation:Q w1+Q m w(j)]TJ /F1 11.955 Tf 9.69 0 Td[(1))]TJ /F1 11.955 Tf 15.65 0 Td[(Q m w)]TJ /F1 11.955 Tf 15.73 0 Td[(Q w2=0 %Q w1=(Nu w1k w(j,1)A/t w)(T(3))]TJ /F1 11.955 Tf 8.52 0 Td[(T(4)); %Q m w in=mdot w(j,1)Cp br(j,1)T w(j,1); %Q f=mdot w(j,1)Cp br(j,1)(T(5))]TJ /F1 11.955 Tf 16.08 0 Td[(T w(j,1)); %g %f Q m w out=(mdot w(j,1))]TJ /F1 11.955 Tf 10.54 0 Td[((((Ah lv(j,1)D ab(j,1)P)/(Rt vsT m vs(j,1)))... log((P)]TJ /F1 11.955 Tf 10.22 0 Td[((10000010(a+b/T(6)+((c(T(6)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g))/T(6))(10(d(T(6)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g)2))]TJ /F1 11.955 Tf 9.61 0 Td[(1)... +e10(f(617.27)]TJ /F1 11.955 Tf 10.03 0 Td[(T(6))1.25))))... /(P)]TJ /F1 11.955 Tf 10.21 0 Td[((10000010(a+b/T(5)+((c(T(5)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g))/T(5))(10(d(T(5)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g)2))]TJ /F1 11.955 Tf 9.62 0 Td[(1)... +e10(f(617.27)]TJ /F1 11.955 Tf 10.03 0 Td[(T(5))1.25)+hS(j,1)+kS(j,1)2)))))/h lv(j,1))Cp br(j,1)T(4); %g 88

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%f %Q w2=(Nu w2k w(j,1)A/t w)(T(4))]TJ /F1 11.955 Tf 15.7 0 Td[(T(5)); %mdot w 1=(mdot w(j,1))]TJ /F1 11.955 Tf 18.16 0 Td[((((Ah lv 1D ab 1P)/(Rt vsT m vs 1))log((P)]TJ /F1 11.955 Tf 10.22 0 Td[((10000010(a+b/T(6)+((c(T(6)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g))/T(6))(10(d(T(6)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g)2))]TJ /F1 11.955 Tf 9.61 0 Td[(1)+e10(f(617.27)]TJ /F1 11.955 Tf 10.02 0 Td[(T(6))1.25))))/(P)]TJ /F1 11.955 Tf 10.22 0 Td[((10000010(a+b/T(5)+((c(T(5)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g))/T(5))(10(d(T(5)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g)2))]TJ /F1 11.955 Tf 9.62 0 Td[(1)+e10(f(617.27)]TJ /F1 11.955 Tf 10.03 0 Td[(T(5))1.25)+hS 1+kS 12)))))/h lv 1)mdot w 1issolvedimplicity %bythepreviousmdot wandmdot evap %Plugin %((Nu w1k w(j,1)A/t w)(T(3))]TJ /F1 11.955 Tf 8.52 0 Td[(T(4)))+(mdot w(j,1)Cp br(j,1)T m w(j,1)))]TJ /F1 11.955 Tf 17.89 0 Td[(((mdot w(j,1))]TJ /F1 11.955 Tf 18.15 0 Td[((((Ah lv(j,1)D ab(j,1)P)/(Rt vsT m vs(j,1)))log((P)]TJ /F1 11.955 Tf 10.22 0 Td[((10000010(a+b/T(6)+((c(T(6)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g))/T(6))(10(d(T(6)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g)2))]TJ /F1 11.955 Tf 9.62 0 Td[(1)+e10(f(617.27)]TJ /F1 11.955 Tf 10.03 0 Td[(T(6))1.25))))/(P)]TJ /F1 11.955 Tf 10.21 0 Td[((10000010(a+b/T(5)+((c(T(5)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g))/T(5))(10(d(T(5)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g)2))]TJ /F1 11.955 Tf 9.61 0 Td[(1)+e10(f(617.27)]TJ /F1 11.955 Tf 10.02 0 Td[(T(5))1.25)+hS(j,1)+kS(j,1)2)))))/h lv(j,1))Cp br(j,1)T(4)))]TJ /F1 11.955 Tf 17.89 0 Td[(((Nu w2k w(j,1)A/t w)(T(4))]TJ /F1 11.955 Tf 15.7 0 Td[(T(5))) %W(e=1)CSbalance %Equation:Q w2)]TJ /F1 11.955 Tf 16.08 0 Td[(Q e)]TJ /F1 11.955 Tf 15.25 0 Td[(Q m)]TJ /F1 11.955 Tf 16.74 0 Td[(Q r)]TJ /F1 11.955 Tf 16.25 0 Td[(Q s=0 %Q w2 1=(Nu w2k w(j,1)A/t w)(T(4))]TJ /F1 11.955 Tf 15.69 0 Td[(T(5)); 89

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%Q e 1=((Ah lv(j,1)D ab(j,1)P)/(Rt vsT m vs(j,1)))log((P)]TJ /F1 11.955 Tf 10.22 0 Td[((10000010(a+b/T(6)+((c(T(6)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g))/T(6))(10(d(T(6)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g)2))]TJ /F1 11.955 Tf 9.62 0 Td[(1)+e10(f(617.27)]TJ /F1 11.955 Tf 10.03 0 Td[(T(6))1.25))))/(P)]TJ /F1 11.955 Tf 10.21 0 Td[((10000010(a+b/T(5)+((c(T(5)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g))/T(5))(10(d(T(5)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g)2))]TJ /F1 11.955 Tf 9.62 0 Td[(1)+e10(f(617.27)]TJ /F1 11.955 Tf 10.03 0 Td[(T(5))1.25)+hS(j,1)+kS(j,1)2)))); %(donotinclude)Q m 1=Cp l j(1)T(5)((AD ab j(1)P)/(Rt vsT m vs j(1)))log((P)]TJ /F1 11.955 Tf 10.21 0 Td[((10000010(a+b/T(6)+((c(T(6)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g))/T(6))(10(d(T(6)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g)2))]TJ /F1 11.955 Tf 9.62 0 Td[(1)+e10(f(617.27)]TJ /F1 11.955 Tf 10.03 0 Td[(T(6))1.25))))/(P)]TJ /F1 11.955 Tf 10.22 0 Td[((10000010(a+b/T(5)+((c(T(5)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g))/T(5))(10(d(T(5)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g)2))]TJ /F1 11.955 Tf 9.62 0 Td[(1)+e10(f(617.27)]TJ /F1 11.955 Tf 10.03 0 Td[(T(5))1.25)+hS j(1)+kS j(1)2)))); %Q r 1=(1/((1/eps w)+(1/eps cf))]TJ /F1 11.955 Tf 9.62 0 Td[(1))Asigma(T(5)4)]TJ /F1 11.955 Tf 9.56 0 Td[(T(6)4); %Q s 1=(Ak ha(j,1)/t vs)(T(5))]TJ /F1 11.955 Tf 8.52 0 Td[(T(6));%orfromMcBain %Plugin %((Nu w2k w(j,1)A/t w)(T(4))]TJ /F1 11.955 Tf 15.7 0 Td[(T(5))))]TJ /F1 11.955 Tf 18.16 0 Td[((((Ah lv(j,1)D ab(j,1)P)/(Rt vsT m vs(j,1)))log((P)]TJ /F1 11.955 Tf 10.22 0 Td[((10000010(a+b/T(6)+((c(T(6)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g))/T(6))(10(d(T(6)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g)2))]TJ /F1 11.955 Tf 9.62 0 Td[(1)+e10(f(617.27)]TJ /F1 11.955 Tf 10.03 0 Td[(T(6))1.25))))/(P)]TJ /F1 11.955 Tf 10.22 0 Td[((10000010(a+b/T(5)+((c(T(5)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g))/T(5))(10(d(T(5)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g)2))]TJ /F1 11.955 Tf 9.62 0 Td[(1)+e10(f(617.27)]TJ /F1 11.955 Tf 10.03 0 Td[(T(5))1.25)+hS(j,1)+kS(j,1)2))))))]TJ /F1 11.955 Tf 18.15 0 Td[(((1/((1/eps w)+(1/eps cf))]TJ /F1 11.955 Tf 9.62 0 Td[(1))Asigma(T(5)4)]TJ /F1 11.955 Tf 9.55 0 Td[(T(6)4)))]TJ /F1 11.955 Tf 17.89 0 Td[(((Ak ha(j,1)/t vs)(T(5))]TJ /F1 11.955 Tf 8.53 0 Td[(T(6))) %CF(e=1)CSbalance %Equation:Q e+Q m+Q r+Q s+Q m cf(j)]TJ /F1 11.955 Tf 9.7 0 Td[(1))]TJ /F1 11.955 Tf 16.6 0 Td[(Q m cf)]TJ /F1 11.955 Tf 16.92 0 Td[(Q cf=0 90

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%Q e=((Ah lv(j,1)D ab(j,1)P)/(Rt vsT m vs(j,1)))log((P)]TJ /F1 11.955 Tf 10.22 0 Td[((10000010(a+b/T(6)+((c(T(6)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g))/T(6))(10(d(T(6)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g)2))]TJ /F1 11.955 Tf 9.62 0 Td[(1)+e10(f(617.27)]TJ /F1 11.955 Tf 10.03 0 Td[(T(6))1.25))))/(P)]TJ /F1 11.955 Tf 10.21 0 Td[((10000010(a+b/T(5)+((c(T(5)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g))/T(5))(10(d(T(5)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g)2))]TJ /F1 11.955 Tf 9.62 0 Td[(1)+e10(f(617.27)]TJ /F1 11.955 Tf 10.03 0 Td[(T(5))1.25)+hS(j,1)+kS(j,1)2)))); %(donotinclude)Q m=Cp l j(1)T(5)((AD ab j(1)P)/(Rt vsT m vs j(1)))log((P)]TJ /F1 11.955 Tf 10.21 0 Td[((10000010(a+b/T(6)+((c(T(6)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g))/T(6))(10(d(T(6)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g)2))]TJ /F1 11.955 Tf 9.62 0 Td[(1)+e10(f(617.27)]TJ /F1 11.955 Tf 10.03 0 Td[(T(6))1.25))))/(P)]TJ /F1 11.955 Tf 10.22 0 Td[((10000010(a+b/T(5)+((c(T(5)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g))/T(5))(10(d(T(5)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g)2))]TJ /F1 11.955 Tf 9.62 0 Td[(1)+e10(f(617.27)]TJ /F1 11.955 Tf 10.03 0 Td[(T(5))1.25)+hS j(1)+kS j(1)2)))); %Q r=(1/((1/eps w)+(1/eps cf))]TJ /F1 11.955 Tf 9.61 0 Td[(1))Asigma(T(5)4)]TJ /F1 11.955 Tf 9.55 0 Td[(T(6)4); %Q s=(Ak ha(j,1)/t vs)(T(5))]TJ /F1 11.955 Tf 8.53 0 Td[(T(6)); %Q m cf(j)]TJ /F1 11.955 Tf 9.7 0 Td[(1)=mdot cf(j,1)Cp l(j,1)T cf(j,1); %Q m cf=(mdot cf(j,1)+(((Ah lv(j,1)D ab(j,1)P)/(Rt vsT m vs(j,1)))log((P)]TJ /F1 11.955 Tf 10.21 0 Td[((10000010(a+b/T(6)+((c(T(6)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g))/T(6))(10(d(T(6)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g)2))]TJ /F1 11.955 Tf 9.62 0 Td[(1)+e10(f(617.27)]TJ /F1 11.955 Tf 10.03 0 Td[(T(6))1.25))))/(P)]TJ /F1 11.955 Tf 10.22 0 Td[((10000010(a+b/T(5)+((c(T(5)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g))/T(5))(10(d(T(5)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g)2))]TJ /F1 11.955 Tf 9.62 0 Td[(1)+e10(f(617.27)]TJ /F1 11.955 Tf 10.03 0 Td[(T(5))1.25)+hS(j,1)+kS(j,1)2)))))/h lv(j,1)))Cp l(j,1)T(6); %Q cf=(k l(j,1)A/t cf(j,1))(T(6))]TJ /F1 11.955 Tf 15.7 0 Td[(T(7));%accountformeantemperatureofcondenserfluid? %Plugin 91

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%(((Ah lv(j,1)D ab(j,1)P)/(Rt vsT m vs(j,1)))log((P)]TJ /F1 11.955 Tf 10.22 0 Td[((10000010(a+b/T(6)+((c(T(6)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g))/T(6))(10(d(T(6)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g)2))]TJ /F1 11.955 Tf 9.62 0 Td[(1)+e10(f(617.27)]TJ /F1 11.955 Tf 10.03 0 Td[(T(6))1.25))))/(P)]TJ /F1 11.955 Tf 10.21 0 Td[((10000010(a+b/T(5)+((c(T(5)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g))/T(5))(10(d(T(5)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g)2))]TJ /F1 11.955 Tf 9.62 0 Td[(1)+e10(f(617.27)]TJ /F1 11.955 Tf 10.03 0 Td[(T(5))1.25)+hS(j,1)+kS(j,1)2)))))+((1/((1/eps w)+(1/eps cf))]TJ /F1 11.955 Tf 9.61 0 Td[(1))Asigma(T(5)4)]TJ /F1 11.955 Tf 9.55 0 Td[(T(6)4))+((Ak ha(j,1)/t vs)(T(5))]TJ /F1 11.955 Tf 8.52 0 Td[(T(6)))+(mdot cf(j,1)Cp l(j,1)T cf(j,1)))]TJ /F1 11.955 Tf 17.89 0 Td[(((mdot cf(j,1)+(((Ah lv(j,1)D ab(j,1)P)/(Rt vsT m vs(j,1)))log((P)]TJ /F1 11.955 Tf 10.21 0 Td[((10000010(a+b/T(6)+((c(T(6)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g))/T(6))(10(d(T(6)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g)2))]TJ /F1 11.955 Tf 9.61 0 Td[(1)+e10(f(617.27)]TJ /F1 11.955 Tf 10.02 0 Td[(T(6))1.25))))/(P)]TJ /F1 11.955 Tf 10.22 0 Td[((10000010(a+b/T(5)+((c(T(5)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g))/T(5))(10(d(T(5)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g)2))]TJ /F1 11.955 Tf 9.62 0 Td[(1)+e10(f(617.27)]TJ /F1 11.955 Tf 10.03 0 Td[(T(5))1.25)+hS(j,1)+kS(j,1)2)))))/h lv(j,1)))Cp l(j,1)T(6)))]TJ /F1 11.955 Tf 17.89 0 Td[(((k l(j,1)A/t cf(j,1))(T(6))]TJ /F1 11.955 Tf 15.7 0 Td[(T(7))) %g B.2SingleMasterThisscriptisv3_sngl_master.manditisthecodethattakescalculatesthetemperaturedependentpropertiesofthesalineandthevaporsspaceinthestill. T temp(j,:)=T; n=N; fori=1:n %Temperatureguessesforpropertycalculation)]TJ /F1 11.955 Tf 17.45 0 Td[(calculatesT wandT cf %vectorsasT tempvectorasinput T w(j,i)=T temp(j,4(i)]TJ /F1 11.955 Tf 9.69 0 Td[(1)+4); z w(j,i)=T w(j,i))]TJ /F1 11.955 Tf 17.05 0 Td[(273.16; 92

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T w j(i)=T temp(j,4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+4); T cf(j,i)=T temp(j,4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+5); z cf(j,i)=T cf(j,i))]TJ /F1 11.955 Tf 17.05 0 Td[(273.16; T cf j(i)=T temp(j,4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+5); T m vs(j,i)=(T temp(j,4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+4)+T temp(j,4(i)]TJ /F1 11.955 Tf 9.69 0 Td[(1)+5))/2; T m vs j(i)=(T temp(j,4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+4)+T temp(j,4(i)]TJ /F1 11.955 Tf 9.69 0 Td[(1)+5))/2; end T m a(j,1)=(T temp(j,1)+T temp(j,2))/2; T m a j(1)=(T temp(j,1)+T temp(j,2))/2; %Airgapconstants k a(j,:)=0.000851+0.00009555.T m a(j,:))]TJ /F1 11.955 Tf 10.04 0 Td[(0.0000000375.T m a(j,:).2; %thermalconductivityofairinairgap(W/mK) k a j=k a(j,:); %Film/Wickconstants Cp br(j,:)=3958)]TJ /F1 11.955 Tf 17.47 0 Td[(52.3.(S(j,:)..1)+0.837.T w(j,:); Cp br j=Cp br(j,:); k br(j,:)=(577+1.522.(T w(j,:))]TJ /F1 11.955 Tf 10.05 0 Td[(273.16)... )]TJ /F1 11.955 Tf 17.15 0 Td[(0.00581.(T w(j,:))]TJ /F1 11.955 Tf 10.06 0 Td[(273.16).2).10.()]TJ /F1 11.955 Tf 10.79 0 Td[(3);%(W/mK) %thermalconductivityofliquidwithinmatrix(sourceShalabhpg67) k br j=k br(j,:); k w(j,:)=(1)]TJ /F1 11.955 Tf 11.01 0 Td[(phi).k s+phi.k br(j,:);%(W/mK) %effectiveconductivityofparalletheattransferthroughwickmatrix %andliquid 93

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k w j=k w(j,:); %rho br(j,:)=1000(1+0.805(S(j,:)1000))]TJ /F1 11.955 Tf 10.04 0 Td[(0.0000065(T w(j,:))]TJ /F1 11.955 Tf 9.75 0 Td[(4+220(S(j,:)1000))2): %notusedyet(Holzbecher) %Latenttransferconstants D ab(j,:)=0.000000000187.T m vs(j,:).(2.072);% D ab j=D ab(j,:); R=461.5;%(J/kgK) h lv(j,:)=1000.(3146)]TJ /F1 11.955 Tf 17.26 0 Td[(2.36.T w(j,:));%(J/kg)latentofvaporization %atwicktemperature h lv j=h lv(j,:); a=5.432368;%constantsforcalculationofpartialpressure b=)]TJ /F1 11.955 Tf 10.12 0 Td[(2005.1; c=0.00013869; d=0.000000000011965; e=)]TJ /F1 11.955 Tf 10.12 0 Td[(0.0044; f=)]TJ /F1 11.955 Tf 10.05 0 Td[(0.0057148; g=293700; h=)]TJ /F1 11.955 Tf 10.05 0 Td[(0.0002169; k=)]TJ /F1 11.955 Tf 10 0 Td[(0.00000035012; sigma=0.0000000567;%W/m2K4 %CondensationFilmconstants mu l(j,:)=0.001(10.()]TJ /F1 11.955 Tf 10.5 0 Td[(10.2158+1792.5./T cf(j,:)+0.01773.T cf(j,:)... 94

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)]TJ /F1 11.955 Tf 16.78 0 Td[(0.000012631.T cf(j,:).2));%(mNs/m2) %dynamicviscosityofliquidwater(Shalabh) %z cf=T cf)]TJ /F1 11.955 Tf 17.06 0 Td[(273.16; rho l(j,:)=(999.83952+16.945176.(T cf(j,:))]TJ /F1 11.955 Tf 10.05 0 Td[(273.16))]TJ /F1 11.955 Tf -371.73 -23.91 Td[(0.0079870401.... (T cf(j,:))]TJ /F1 11.955 Tf 10.05 0 Td[(273.16).2)]TJ /F1 11.955 Tf 10.35 0 Td[(0.000046170461.(T cf(j,:))]TJ /F1 11.955 Tf 10.06 0 Td[(273.16).3... +0.00000010556302.(T cf(j,:))]TJ /F1 11.955 Tf 10.05 0 Td[(273.16).4)./(1+0.016879850.... (T cf(j,:))]TJ /F1 11.955 Tf 10.05 0 Td[(273.16));%(kg/m3)densityofliquidwater(Shalabh) gv=9.81;%(m/s2)gravity P cf(j,:)=100000.10.(a+b./T cf(j,:)... +((c.(T cf(j,:).2)]TJ /F1 11.955 Tf 10.47 0 Td[(g))./T cf(j,:)).(10.(d.(T cf(j,:).2)]TJ /F1 11.955 Tf 10.47 0 Td[(g).2))]TJ /F1 11.955 Tf 9.61 0 Td[(1)... +e.10.(f.(617.27)]TJ /F1 11.955 Tf 11.9 0 Td[(T cf(j,:)).1.25));%(N/m2) %partialpressureofwatervaporofcondensorfilmsurfacewithx(T) %andy(T)pluggedin P w(j,:)=100000.10.(a+b./T w(j,:)... +((c.(T w(j,:).2)]TJ /F1 11.955 Tf 10.47 0 Td[(g))./T w(j,:)).(10.(d.(T w(j,:).2)]TJ /F1 11.955 Tf 10.46 0 Td[(g).2))]TJ /F1 11.955 Tf 9.62 0 Td[(1)... +e.10.(f.(617.27)]TJ /F1 11.955 Tf 10.67 0 Td[(T w(j,:)).1.25)+h.S(j,:)+k.S(j,:).2); P m vs(j,:)=(P cf(j,:)+P w(j,:))./2; rho ha(j,:)=(352.6(1)]TJ /F1 11.955 Tf 10.51 0 Td[(0.378.P cf(j,:)/P))./T cf(j,:);%(kg/m3) %densityofhumidairusedformomentumbalanceoncondenserfilm(Tanaka) t cf(j,:)=((3.mdot cf(j,:).mu l(j,:))./(gvW.rho l(j,:).(rho l(j,:)... 95

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)]TJ /F1 11.955 Tf 9.76 0 Td[(rho ha(j,:)))).(1/3); %thicknessofcondenserfilmbasedonmassflowrateandlaminar %condensingfilmassumptions(source:Carey) t cf j=t cf(j,:); Cp l(j,:)=1000.(4.2174)]TJ /F1 11.955 Tf 16.92 0 Td[(0.003720283.(T cf(j,:))]TJ /F1 11.955 Tf 10.05 0 Td[(273.16)... +0.0001412855.(T cf(j,:))]TJ /F1 11.955 Tf 10.06 0 Td[(273.16).2... )]TJ /F1 11.955 Tf 16.82 0 Td[(0.000002654387.(T cf(j,:))]TJ /F1 11.955 Tf 10.05 0 Td[(273.16).3... +0.00000002093236.(T cf(j,:))]TJ /F1 11.955 Tf 10.06 0 Td[(273.16).4);%(kJ/kgK) %specificheatofliquidwater(Source:Shalabh) Cp l j=Cp l(j,:); k l(j,:)=)]TJ /F1 11.955 Tf 9.79 0 Td[(0.2758+0.004612.T cf(j,:))]TJ /F1 11.955 Tf 16.75 0 Td[(0.0000055391.T cf(j,:).2; %(W/mK)thermalconductivityofliquidwater(Source:Shalabh) k l j=k l(j,:); %Vaporspacethermalconductivitycalculation k v(j,:)=)]TJ /F1 11.955 Tf 10.06 0 Td[(0.003537+0.0000654755.T m vs(j,:)+0.000000017446.T m vs(j,:).2; k a2(j,:)=0.000669881+0.0000942482.T m vs(j,:)... )]TJ /F1 11.955 Tf 10.01 0 Td[(0.0000000327450.T m vs(j,:).2; mu v(j,:)=)]TJ /F1 11.955 Tf 10 0 Td[(0.00000097494+0.0000000359061.T m vs(j,:)... +0.000000000000241612.T m vs(j,:).2; mu a(j,:)=0.00000143387+0.0000000656244T m vs(j,:)... )]TJ /F1 11.955 Tf 9.99 0 Td[(0.000000000029905.T m vs(j,:).2; X v(j,:)=(0.622.(P m vs(j,:)./(P)]TJ /F1 11.955 Tf 8.89 0 Td[(P m vs(j,:))))./... 96

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(0.62197058+(0.622.(P m vs(j,:)./(P)]TJ /F1 11.955 Tf 8.89 0 Td[(P m vs(j,:))))); X a(j,:)=1./(1+1.607793.(0.622.(P m vs(j,:)./(P)]TJ /F1 11.955 Tf 8.89 0 Td[(P m vs(j,:))))); G v(j,:)=0.277609.(1+1.12605.(mu v(j,:)./mu a(j,:)).0.5).2; G a(j,:)=0.2189366.(1+0.8880603.(mu a(j,:)./mu v(j,:)).0.5).2; k ha(j,:)=k v(j,:)./(1+G v(j,:).(X a(j,:)./X v(j,:)))... +k a2(j,:)./(1+G a(j,:).(X v(j,:)./X a(j,:))); k ha j=k ha(j,:); %McBain: %rho v(j,:)=1./((460.5.T m vs(j,:))./P w(j,:))]TJ /F1 11.955 Tf 10.11 0 Td[(0.02);%Shalabh rho v(j,:)=0.0022P w(j,:)./T m vs(j,:); Cp v(j,:)=3399.476)]TJ /F1 11.955 Tf 10.13 0 Td[(10.83929.T m vs(j,:)+0.01916667.T m vs(j,:).2;%Tanaka Le v(j,:)=k v(j,:)./(rho v(j,:).Cp v(j,:).D ab(j,:)); w cf(j,:)=0.622.(P cf(j,:)./(P)]TJ /F1 11.955 Tf 9.65 0 Td[(P cf(j,:))); w w(j,:)=0.622.(P w(j,:)./(P)]TJ /F1 11.955 Tf 8.39 0 Td[(P w(j,:))); B(j,:)=(w w(j,:))]TJ /F1 11.955 Tf 9.89 0 Td[(w cf(j,:))./(w cf(j,:))]TJ /F1 11.955 Tf 9.62 0 Td[(1); Nu vs(j,:)=log((P)]TJ /F1 11.955 Tf 9.66 0 Td[(P cf(j,:))/(P)]TJ /F1 11.955 Tf 8.38 0 Td[(P w(j,:)))... .(1./(Le v(j,:).(((P)]TJ /F1 11.955 Tf 9.66 0 Td[(P cf(j,:))/(P)]TJ /F1 11.955 Tf 8.39 0 Td[(P w(j,:))).(1./(Le v(j,:))))]TJ /F1 11.955 Tf 9.62 0 Td[(1))); %McBainmodifierofconduction B.3SolutionOutlineThisrstscriptisv3_sngl_soln_outline.manditisresponsibleforintegratingtheSolverandMastertogether,andforconvergingonthedesiredfeedrateratio. 97

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n=N;%%numberofeffects delta y=L/m;%%incrementsize A=Wdelta y;%%areaofincrement Q supply=q fluxA;%%Watt%s T guess(1:4(n)]TJ /F1 11.955 Tf 9.69 0 Td[(1)+7)=25+273.16;%298.16;%%(K)firsttemperatureguessforfsolveoriginally303.16 mdot cooling=0.000833;%kg/s=500ccm %Latentheatrecuperationfromthefinalcondenser forq=1:1%mustbeatleast4ortheheataddedbyLHRisoverestimatedand %mmustbeatleast5 ifq==1 T lhr out=25.6+273.16;%T source else T lhr out=real((Q lhr(m,n)/((sum(mdot supply final))Cp br j(n))+T lhr(m,1)));% %calculatesthefinalLHRtempbasedonthepreviousT lhrandQ lhr %thisisusedtodeterminethetemperatureofthesalinesuppliedtothestill %thisisn'timportantunlessq>1 end T lhr out temp(q,:)=T lhr out;%%showsiterationsofT lhr out %SensibleheatrecuperationiterationofT supplyfromenergyrejectedin %massstreams(p=3issuggestedforconvergence) 98

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forp=1:1 ifp==1 T shr out(1:n)=T lhr out;% else ifSHR==1% T shr out(1:n)=... (eff.(sum(mdot w(m+1,:).Cp br(m,:).(T w(m,:))]TJ /F1 11.955 Tf 10.47 0 Td[(T lhr out))... +sum(mdot cf(m+1,:).Cp l(m,:).(T cf(m,:))]TJ /F1 11.955 Tf 10.46 0 Td[(T lhr out)))... +sum(mdot supply final).Cp br(1,1).T lhr out)... ./(sum(mdot supply final).Cp br(1,1));%%thermalmixingofalleffects elseifSHR==2% T shr out=... (eff.(mdot w(m+1,:).Cp br(m,:).(T w(m,:))]TJ /F1 11.955 Tf 10.46 0 Td[(T lhr out)+... mdot cf(m+1,:).Cp l(m,:).(T cf(m,:))]TJ /F1 11.955 Tf 10.47 0 Td[(T lhr out))+... mdot supply final.Cp br(1,1).T lhr out)... ./(mdot supply final(1,:).Cp br(1,1));% %thermalmixingateacheffectseperately end end T shr out temp(p,:)=T shr out;%%showiterationsofT shr out %mdot supplyiterationbasedonFR(mustbehigherforlowvertical %resolution/suggestvalueofatleast4forconvergence) forl=1:6 ifq==1&&p==1&&l==1 99

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fori=1:n%initialguessform dotsupply mdot supply(l,i)=0.00035)]TJ /F1 11.955 Tf 10.03 0 Td[((i1.10.00002);%%(kg/s) end elseifl==1%butsystemhasalreadybeensolvedforqorp mdot supply(l,:)=FR.mdot evap sum temp(l,:);% else mdot supply(l,:)=FR.mdot evap sum temp(l)]TJ /F1 11.955 Tf 10.62 0 Td[(1,:);% end %ydirectionstepthrough forj=1:m% ifj==1% T(j,:)=T guess;% %T(j,4(n)]TJ /F1 11.955 Tf 9.69 0 Td[(1)+7)=T shr out(n); mdot w(j,:)=mdot supply(l,:);% mdot cf(j,1:n)=0.000000001;% t cf(j,1:n)=0.000001;%%usefunctioncallforrestofequation S(j,1:n)=S supply;% T w in(j,:)=T shr out;% T cf in(j,:)=T shr out;% T lhr(j,1)=T source;% %ifq==1 %T lhr(j,1)=T source; %guessataveragerejectiontemperatureoffirstelementsoasto %notoverpredicttheheatintotherecuperator 100

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%else %T lhr(j,1)=T source+((T lhr temp(2,q)]TJ /F1 11.955 Tf 9.69 0 Td[(1))]TJ /F1 11.955 Tf 10.04 0 Td[(T lhr temp(1,q)]TJ /F1 11.955 Tf 9.7 0 Td[(1))/2); %guessbasedonprevioustemperaturerisesacrossrecuperator %end else %mdot evapneedscalculatedinj)]TJ /F1 11.955 Tf 8.76 0 Td[(1results mdot w(j,:)=mdot w(j)]TJ /F1 11.955 Tf 10.62 0 Td[(1,:))]TJ /F1 11.955 Tf 16.54 0 Td[(mdot evap(j)]TJ /F1 11.955 Tf 10.62 0 Td[(1,:);% mdot cf(j,:)=mdot cf(j)]TJ /F1 11.955 Tf 10.63 0 Td[(1,:)+mdot evap(j)]TJ /F1 11.955 Tf 10.63 0 Td[(1,:);% t cf(j,:)=0.000001;% S(j,:)=S(j)]TJ /F1 11.955 Tf 10.62 0 Td[(1,:).mdot w(j)]TJ /F1 11.955 Tf 10.63 0 Td[(1,:)./(mdot w(j)]TJ /F1 11.955 Tf 10.63 0 Td[(1,:))]TJ /F1 11.955 Tf 9.36 0 Td[(mdot evap(j)]TJ /F1 11.955 Tf 10.62 0 Td[(1,:));% T w temp(j,:)=T sol(j)]TJ /F1 11.955 Tf 10.63 0 Td[(1,:);% T cf temp(j,:)=T sol(j)]TJ /F1 11.955 Tf 10.63 0 Td[(1,:);% T lhr(j,1)=(Q lhr(j)]TJ /F1 11.955 Tf 9.75 0 Td[(1,n)/((mdot cooling)Cp br j(n))+T lhr(j)]TJ /F1 11.955 Tf 9.7 0 Td[(1));% fori=1:n% T w in(j,i)=T w temp(j,4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+4);% T cf in(j,i)=T cf temp(j,4(i)]TJ /F1 11.955 Tf 9.69 0 Td[(1)+5);% end end mdot w j=mdot w(j,:);% T w in j=T w in(j,:);% T cf in j=T cf in(j,:);% T lhr j=T lhr(j,1);% mdot cf j=mdot cf(j,:);% 101

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S j=S(j,:);% t cf j=t cf(j,:);% %T test=T %l %disp('jlT') %disp([j,l,T]) %pause %Temperaturedependentpropertyconvergence forconverj=1:3 v3 sngl master%%propertiesaresolvedatT tempatj T0=T;%%Startingpointforfsolve %T0=T;%Startingpointforfsolve %options=optimset('Display','iter')%Optiontodisplayoutput %%runsolver(takespropertiesatT temp,T0,mdot w(j,:),mdot cf(j,:), %%t cf,andSandgivesnewT [T]=v3 sngl solvr(N,alpha g,Q supply,tau g,alpha p,A,sigma,... eps p1,eps g,k a j,t ag,T surr,u a,T inf,k p,t p,Nu w1,k w j,t w,k g,... mdot w j,Cp br j,T w in j,h lv j,D ab j,P,R,T m vs j,a,b,c,d,e,f,g,... h,k,S j,eps w,eps cf,k ha j,t vs,k l j,t cf j,mdot cf j,Cp l j,... T cf in j,Nu hr,D,k br j,T lhr j,eps p,T0);% %f [T]=v3 sngl solvr(N,alpha g,Q supply,tau g,alpha p,A,sigma,... 102

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eps p1,eps g,k a j,t ag,T surr,u a,T inf,k p,t p,Nu w1,k w j,t w,... k g,mdot w j,Cp br j,T w in j,h lv j,D ab j,P,R,T m vs j,a,b,c,d,e,... f,g,h,k,S j,eps w,eps cf,k ha j,t vs,k l j,t cf j,mdot cf j,Cp l j,... T cf in j,eps p,T0);%withrejectiontoambient %g %rejectiontoamientorheatrecoup %systemissolvedwithpropertiesatT tempatjtogivenewT %T test(converj+1,:)=T %pause end T sol(j,:)=real(T);%%savethefinalTforjintoT solmatrix T temp(j,:)=T;% fori=1:n%locationtemperatures T g(j,i)=real(T(4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+1));% T p1(j,i)=real(T(4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+2));% T p2(j,i)=real(T(4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+3));% T w(j,i)=real(T(4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+4));% T cf(j,i)=real(T(4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+5));% T m vs(j,i)=real((T(4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+4)+T(4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+5))/2);% end 103

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mdot evap(j,:)=real(((A.D ab(j,:).P)./(R.t vs.T m vs(j,:)))... .log((P)]TJ /F1 11.955 Tf 10.58 0 Td[((100000.10.(a+b./T cf(j,:)+((c.(T cf(j,:).2)]TJ /F1 11.955 Tf 10.46 0 Td[(g))./T cf(j,:))... .(10.(d.(T cf(j,:).2)]TJ /F1 11.955 Tf 10.47 0 Td[(g).2))]TJ /F1 11.955 Tf 9.61 0 Td[(1)+e.10.(f.(617.27)]TJ /F1 11.955 Tf 11.9 0 Td[(T cf(j,:)).1.25))))... ./(P)]TJ /F1 11.955 Tf 10.58 0 Td[((100000.10.(a+b./T w(j,:)+((c.(T w(j,:).2)]TJ /F1 11.955 Tf 10.46 0 Td[(g))./T w(j,:))... .(10.(d.(T w(j,:).2)]TJ /F1 11.955 Tf 10.47 0 Td[(g).2))]TJ /F1 11.955 Tf 9.62 0 Td[(1)+e.10.(f.(617.27)]TJ /F1 11.955 Tf 10.66 0 Td[(T w(j,:)).1.25)... +h.S(j,:)+k.S(j,:).2)))));% fori=1:n%heatfluxcomponents(forHHR's) ifi==1% Q c ga(j,i)=real(A(5.7+3.8u a)(T(1))]TJ /F1 11.955 Tf 10.53 0 Td[(T inf));% Q r ga(j,i)=real(sigmaeps gA(T(1)4)]TJ /F1 11.955 Tf 11.17 0 Td[(T surr4));% Q d p1g(j,i)=real((Ak a j/t ag)(T(2))]TJ /F1 11.955 Tf 8.52 0 Td[(T(1)));% Q r p1g(j,i)=real(((Asigma)/(1/eps p1+1/eps g)]TJ /F1 11.955 Tf 9.69 0 Td[(1))(T(2)4)]TJ /F1 11.955 Tf 9.55 0 Td[(T(1)4));% end Q d(j,i)=real((k pA/t p)(T(4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+2))]TJ /F1 11.955 Tf 15.69 0 Td[(T(4(i)]TJ /F1 11.955 Tf 9.69 0 Td[(1)+3)));% Q w f(j,i)=real((mdot w j(i)Cp br j(i)(T(4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+4))]TJ /F1 11.955 Tf -378.51 -23.91 Td[(T w in j(i))));% Q cf f(j,i)=real((mdot cf j(i)Cp l j(i)(T(4(i)]TJ /F1 11.955 Tf 9.69 0 Td[(1)+5))]TJ /F1 11.955 Tf -385.22 -23.9 Td[(T cf in j(i))));% Q w(j,i)=real((Nu w1k w j(i)A/t w)(T(4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+3))]TJ /F1 11.955 Tf 8.52 0 Td[(T(4(i)]TJ /F1 11.955 Tf 9.69 0 Td[(1)+4)));% 104

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Q e(j,i)=real(((Ah lv j(i)D ab j(i)P)/(Rt vsT m vs j(i)))... log((P)]TJ /F1 11.955 Tf 10.22 0 Td[((10000010(a+b/T(4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+5)... +((c(T(4(i)]TJ /F1 11.955 Tf 9.69 0 Td[(1)+5)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g))/T(4(i)]TJ /F1 11.955 Tf 9.69 0 Td[(1)+5))(10(d(T(4(i)]TJ /F1 11.955 Tf 9.69 0 Td[(1)+5)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g)2))]TJ /F1 11.955 Tf 9.62 0 Td[(1)... +e10(f(617.27)]TJ /F1 11.955 Tf 10.03 0 Td[(T(4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+5))1.25))))... /(P)]TJ /F1 11.955 Tf 10.21 0 Td[((10000010(a+b/T(4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+4)... +((c(T(4(i)]TJ /F1 11.955 Tf 9.69 0 Td[(1)+4)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g))/T(4(i)]TJ /F1 11.955 Tf 9.69 0 Td[(1)+4))(10(d(T(4(i)]TJ /F1 11.955 Tf 9.69 0 Td[(1)+4)2)]TJ /F1 11.955 Tf 9.88 0 Td[(g)2))]TJ /F1 11.955 Tf 9.62 0 Td[(1)... +e10(f(617.27)]TJ /F1 11.955 Tf 10.03 0 Td[(T(4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+4))1.25)+hS j(i)+kS j(i)2)))));% Q r(j,i)=real((1/((1/eps w)+(1/eps cf))]TJ /F1 11.955 Tf 9.62 0 Td[(1))... Asigma(T(4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+4)4)]TJ /F1 11.955 Tf 9.55 0 Td[(T(4(i)]TJ /F1 11.955 Tf 9.69 0 Td[(1)+5)4));% Q s(j,i)=real((Ak ha j(i)/t vs)(T(4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+4))]TJ /F1 11.955 Tf 8.52 0 Td[(T(4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+5)));%%orfromMcBain Q cf(j,i)=real((k l j(i)A/t cf j(i)))(T(4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+5))]TJ /F1 11.955 Tf 8.53 0 Td[(T(4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+6));% ifi==n Q c pna(j,i)=real((A(5.7+3.8u a)(T(4(i)]TJ /F1 11.955 Tf 9.69 0 Td[(1)+7))]TJ /F1 11.955 Tf 10.53 0 Td[(T inf)));% Q r pna(j,i)=real(sigmaeps pA(T(4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+7)4)]TJ /F1 11.955 Tf 11.17 0 Td[(T surr4));% Q d(j,i)=real((k pA/t p)(T(4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+6))]TJ /F1 11.955 Tf 15.69 0 Td[(T(4(i)]TJ /F1 11.955 Tf 9.69 0 Td[(1)+7)));% %forrecuperatoronbackplate %ifj==1 %Q lhr(j,i)=.1(Nu hrk br j(n)A)/(D)(T(4(i)]TJ /F1 11.955 Tf 9.7 0 Td[(1)+7))]TJ /F1 11.955 Tf -428.27 -23.9 Td[(T lhr j); %else Q lhr(j,i)=(Nu hrk br j(n)A)/(D)(T(4(i)]TJ /F1 11.955 Tf 9.69 0 Td[(1)+7))]TJ /F1 11.955 Tf 10.89 0 Td[(T lhr j);% 105

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%end end end end %calculatetotalmdot evaptocalculatemdot supplybasedonFR ifm==1 mdot evap sum temp(l,:)=(mdot evap);% %needvector,ifresolutionisone,thenthesumisnotneeded else mdot evap sum temp(l,:)=sum(mdot evap);%%turnsmatrixintovector end end %calculatefinalmassflowratesatbottomofsystemforheatrecuperation mdot w(j+1,:)=mdot w(j,:))]TJ /F1 11.955 Tf 16.54 0 Td[(mdot evap(j,:);% mdot cf(j+1,:)=mdot cf(j,:)+mdot evap(j,:);% mdot supply final=mdot supply(l,:);% S(j+1,:)=S(j,:).mdot w(j,:)./(mdot w(j,:))]TJ /F1 11.955 Tf 9.37 0 Td[(mdot evap(j,:));% T lhr temp(:,q)=T lhr;% end end %Totalsystemenergybalance %Totalsystemenergyin Q net in=alpha g(Q supply)m+(Q supplytau galpha p)m 106

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%Q refl=Q supplym)]TJ /F1 11.955 Tf 17.27 0 Td[(Q net in; %Withoutrecuperation Q net out=(sum(mdot w(m+1,:).Cp br(m,:).(T w(m,:))]TJ /F1 11.955 Tf 10.53 0 Td[(T inf))... +sum(mdot cf(m+1,:).Cp l(m,:).(T cf(m,:))]TJ /F1 11.955 Tf 10.53 0 Td[(T inf)))+sum(Q d(:,n))... +sum(Q c ga)+sum(Q r ga) %Withlatentheatrecuperationonfinalcondenser Q net out lhr=(sum(mdot w(m+1,:).Cp br(m,:).(T w(m,:))]TJ /F1 11.955 Tf -385.65 -23.91 Td[(T lhr out))... +sum(mdot cf(m+1,:).Cp l(m,:).(T cf(m,:))]TJ /F1 11.955 Tf 10.46 0 Td[(T lhr out)))+sum(Q d(:,n))... +sum(Q c ga)+sum(Q r ga) %Withsensibleheatrecuperationfrommassflowswithtotalmixing %f Q net out SHR1=(1)]TJ /F1 11.955 Tf 11.67 0 Td[(eff).(sum(mdot w(m+1,:).Cp br(m,:).(T w(m,:))]TJ /F1 11.955 Tf 10.46 0 Td[(T lhr out))... +sum(mdot cf(m+1,:).Cp l(m,:).(T cf(m,:))]TJ /F1 11.955 Tf 10.46 0 Td[(T lhr out)))+sum(Q d(:,n))... +sum(Q c ga)+sum(Q r ga) %g %Withsensibleheatrecuperationfrommassflowswithindividualmixing %f Q net out SHR2=sum((1)]TJ /F1 11.955 Tf 12.15 0 Td[(eff).(mdot w(m+1,:).Cp br(m,:).(T w(m,:))]TJ /F1 11.955 Tf 10.46 0 Td[(T lhr out).. 107

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+mdot cf(m+1,:).Cp l(m,:).(T cf(m,:))]TJ /F1 11.955 Tf 10.47 0 Td[(T lhr out)))+sum(Q d(:,n))... +sum(Q c ga)+sum(Q r ga) %g %WithlatentandSHR1 Q net out LHR SHR1=(1)]TJ /F1 11.955 Tf 11.67 0 Td[(eff).(sum(mdot w(m+1,:).Cp br(m,:).(T w(m,:)... )]TJ /F1 11.955 Tf 10.47 0 Td[(T lhr out))+sum(mdot cf(m+1,:).Cp l(m,:).(T cf(m,:))]TJ /F1 11.955 Tf 10.47 0 Td[(T lhr out)))... +sum(Q d(:,n))+sum(Q c ga)+sum(Q r ga) %WithlatentandSHR2 Q net out LHR SHR2=sum((1)]TJ /F1 11.955 Tf 12.16 0 Td[(eff).(mdot w(m+1,:).Cp br(m,:).(T w(m,:)... )]TJ /F1 11.955 Tf 10.47 0 Td[(T lhr out)+mdot cf(m+1,:).Cp l(m,:).(T cf(m,:))]TJ /F1 11.955 Tf 10.46 0 Td[(T lhr out)))... +sum(Q d(:,n))+sum(Q c ga)+sum(Q r ga) %Netperformanceratio %ifm==1 %PR net=(sum(h lv j.(mdot evap)))/(mQ supply) %else %PR net=(sum(h lv j.sum(mdot evap)))/(mQ supply) %end B.4ControlPanelThisrstscriptisv3_ctrl_panel.manditisresponsibleforvaryingparametersofthestillsuchasthenumberofeffects,orthemethodofheatrecouperation.Itisalsowherethedimensionsofthestillandheatuxintothestillareinput. 108

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%ParametricControlPanel %Description:Outermostloopforparametricallyvaryingparametersand %solvingforPR %Parametricallyvarysecondparameter forr=1:1 %eps w=0.9)]TJ /F1 11.955 Tf 10.07 0 Td[((r)]TJ /F1 11.955 Tf 9.7 0 Td[(1).25;%FR=1.2+(r)]TJ /F1 11.955 Tf 9.7 0 Td[(1)0.4; %eps cf=0.9)]TJ /F1 11.955 Tf 10.07 0 Td[((r)]TJ /F1 11.955 Tf 9.7 0 Td[(1).25;%FR r(r)=FR; %t vs=0.000+r0.002;%GapSpacing %t vs r(r)=t vs; %Q in=300+r100;%k s=0.06+(r)]TJ /F1 11.955 Tf 9.69 0 Td[(1)4; %Q in r(r)=Q in;%k s r(r)=k s; %T inf=273.16+20+(r)]TJ /F1 11.955 Tf 9.7 0 Td[(1)5;%S supply=20+(r)]TJ /F1 11.955 Tf 9.69 0 Td[(1)5; %T inf r(r)=T inf;%S supply r(r)=S supply; %u a=1+(r)]TJ /F1 11.955 Tf 9.7 0 Td[(1)1;%Coolingvelocity %u a r(r)=u a; %eps p=.1+(r)]TJ /F1 11.955 Tf 9.69 0 Td[(1).8; %eps p1=.1+(r)]TJ /F1 11.955 Tf 9.7 0 Td[(1).8; %Solvesystemacrossdomaint fort=1 %m=0+t; %m t(t)=m; %u a=2.1)]TJ /F1 11.955 Tf 10.22 0 Td[(.2t;%Coolingvelocity %u a t(t)=u a; %eps w=1.1)]TJ /F1 11.955 Tf 11.65 0 Td[(t.1;%wickemissivity %eps w t(t)=eps w; %eps cf=1.1)]TJ /F1 11.955 Tf 11.64 0 Td[(t.1;%condenseremissivity 109

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%eps cf t(t)=eps cf; N=0+t;%numberofeffects N t(t)=N; %FR=1.5+t.1; %FR t(t)=FR; %SystemDimensions#####################################3 W=0.0762;%1;%systemwidth(meters) L=0.3048;%1;%systemheight(meters) area=WL;%systemfrontalarea %Parameters######################################## q flux=800;%3875;%heatfluxofradiationsource(W/m2) Q in=q fluxarea;%heatRate(flux)ofradiationsource(W/m2) %N=5;%Numberofeffects m=30;%5%Resolution(ifm=1,thenmustchangemdot evap sum temp %equationtowithoutthesumterm) S supply=35;%InletSalinity(g/kg) %mdot supply=[.0004088.0003386.0002825.0002389.0002059.0001813 %.0001629.0001486.0001359];%flowrateofsupplytoeacheffect FR=2; %ComponentDimensions####################################### t vs=0.0042;%0.0349;%0.0124;%0.0127;%gapspacing(m) t p=0.009525;%panelthickness(m) t w=0.001;%0.001%wickthickness(m) t ag=0.01;%airgapbetweenglazingandabsorber t hr=0.003175;%.02;%thicknessofheatrecuperator(1/8thinch) 110

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%ComponentProperties############################################# k p=115;%thermalconducitivityofpanel(W/mK) k g=1;%thermalconducitivityofglasswhenapplicable(W/mK) k s=0.06;%thermalconducitivityofwickmaterial(W/mK) Nu w1=1;%Nusseltnumberofwickflow phi=0.6;%(V/V)porosityasvolumeoftotalairspacedividedby %volumeofmatrix %k a=0.06;%thermalconductivityofairinairgap(W/mK) %Radiationconstants############################################# eps g=0.9;%emissivityofglass eps p1=0.2;%emissivityofabsorberplate eps p=0.9;%emissivityoflastpanelsurfaceforheatrejection eps w=0.9;%emissivityofwicksurface eps cf=0.9;%emissivityofcondensersurfaces tau g=0.99;%0.9%transmissivityofglazing(constantorchangeswith %incidentangle) alpha g=0.01;%0.1%aborptivityofglazing alpha p=0.99;%0.9%absorptivityofabsorberplate %HeatRejection u a=1;%velocityofambiantaironlastpanel(m/s) %SensibleHeatRecuperation eff=.8;%heatexchangereffectiveness 111

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%SHR=1;%%chooseoneortheother)]TJ /F1 11.955 Tf 10.14 0 Td[(turnsonSHRwiththermalmixingall %%effectstooneequilibriumtemperature SHR=2;%turnsonSHRwithmixingateacheffecttoanequilibrium %temperatureforeacheffect %LatentHeatRecuperator Nu hr=11;%4.86;%numberpredictedbyboliangscode4.86;%constantTandinsulated(ShahandLondon) %Nu hr=1; D=4(t hrW)/(2t hr+2W);%characteristicdiameterofheatrecuperator %(area/perimeter) %EnvironmentTemperatures T inf=25+273.16;%(K)last25Temperatureofambientair%originally30+273.16; T surr=25+273.16;%(K)Temperatureofskyforreradiation T source=22.3+273.16;%25%22.3(K)Temperatureofsupplybrine %T source=T inf %SystemPressure P=101325;%(PaorN/m2) %RunProgram v3 sngl soln outline; %CalculateResultsfor1stsetofparameterst################### 112

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T w t(:,:,t)=T w; %T cf t(:,:,t)=T cf; %mdot evap t(:,:,t)=mdot evap(:,:); ifm==1 mdot evap sum t(:,t)=mdot evap; mdot evap sum sum t(t)=sum(mdot evap); PR net(:,t)=(sum(h lv j.(mdot evap)))/(mQ supply); else mdot evap sum t(:,t)=sum(mdot evap(:,:)); mdot evap sum sum t(t)=sum(sum(mdot evap)); PR net(:,t)=(sum(h lv j.sum(mdot evap)))/(mQ supply); end %ifr==1 %save('temp','PR net','eps p1','T source','t','r') %clearall %load('temp','PR net','eps p1','T source','t','r') %else %save('temp','PR net','PR net r','eps p1','T source','t','r') %clearall %load('temp','PR net','PR net r','eps p1','T source','t','r') %end end %Saveresultsfor2ndsetofparametersr PR net r(r,:)=PR net; end return 113

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%f %Display %HeatRateRatios %Q e HRR=Q e./(Q d);%ratioofevaporativeheatratetototalheatrate %throughthepartitionofthateffect %Q r HRR=Q r./(Q d);%ratioofradiationheatratetototalheatrate %throughthepartitionofthateffect %Q s HRR=Q s./(Q d);%ratioofconductiveheatratetototalheatrate %throughthepartitionofthateffect %Q w f HRR=Q w f./(Q d);%ratioofconductiveheatratetototalheat %ratethroughthepartitionofthateffect %%OverallPercentages %Q refl HRR tot=Q refl/(Q supplym); %Q r ga HRR tot=sum(Q r ga)/(Q supplym); %Q c ga HRR tot=sum(Q c ga)/(Q supplym); %Q r pna HRR tot=sum(Q r pna)/(Q supplym); %Q c pna HRR tot=sum(Q c pna)/(Q supplym); %fori=1:n%percentageswithineacheffect %Q e HRR tot(i)=sum(Q e(:,i))/(Q supplym); 114

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%Q r HRR tot(i)=sum(Q r(:,i))/(Q supplym); %Q s HRR tot(i)=sum(Q s(:,i))/(Q supplym); %Q w f HRR tot(i)=sum(Q w f(:,i))/(Q supplym); %Q cf f HRR tot(i)=sum(Q cf f(:,i))/(Q supplym); %g B.5FlowChartsThefollowingowchartsareintendedtoillustratewhatthecodeisdoinggraphically.Coupledwiththesourcecode,itshouldprovidethereaderwithenoughunderstandingtouseormodifythesimulationaccordingtotheirneeds.SomeofthecommentsoriginallyfromtheworkbyMitten[ 1 ]havebeenomittedforthesakeofbrevity. 115

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FigureB-1. SingleSolverFlowchart. 116

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FigureB-2. SingleMasterFlowchart. 117

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FigureB-3. SingleSolutionOutlineFlowchartPart1 118

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FigureB-4. SingleSolutionOutlineFlowchartPart2 119

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FigureB-5. SingleSolutionOutlineFlowchartPart1 120

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FigureB-6. SingleSolutionOutlineFlowchartPart2 121

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REFERENCES [1] NathanMitten.Analysisandoptimizationofdiffusion-driven,multiple-effectsolarstill.PhDthesis,UniversityofFlorida,2009. [2] U.S.CensusBureau.Internationaldatabase(IDB).(http://www.census.gov/ipc/www/idb/worldpopgraph.php),December2009. [3] wbcsd.Worldbusinesscouncilforsustainabledevelopment,factsandtrends:water.(www.wbcsd.org),2009. [4] T.OkiandS.Kanae.GlobalHydrologicalCyclesandWorldWaterResources.Science,313:1068,2006. [5] F.Rijsberman.Waterscarcity:Factorction?AgriculturalWaterManagement,80:5,2006. [6] WorldWaterAssesmentProgramme.Theunitednationsworldwaterdevelopementreport3:waterinachangingworld.online,March2009. [7] U.S.DOE.Energydemandsonwaterresources,Reporttocongressontheinterdependancyofenergyandwater.online,December2006. [8] J.Tarjuelo,JDeJuan,M.Moreno,andJ.Ortega.Review.Waterresourcesdecitandwaterengineering.SpanishJournalofAgriculturalResearch,8:s102s121,2010. [9] S.Kalogirou.Seawaterdesalinationusingrenewableenergysources.ProgressinEnergyandCombustionScience,31:242,2005. [10] T.Pankratz.Advancesindesalinationtechnology.InternationalJournalofNuclearDesalination,1:450,2005. [11] A.D.Khawaji,I.K.Kutubkhana,andJ.Wie.Advancesinseawaterdesalinationtechnologies.Desalination,221:47,2008. [12] R.Semiat.EnergyIssuesinDesalinationProcesses.EnvironmentalScienceandTechnology,42:8193,2008. [13] I.ElSaliby,Y.Okour,H.Shon,J.Kandasamy,andS.Kim.DesalinationplantsinAustralia,reviewandfacts.Desalination,247:1,2009. [14] AndrewPorteous,editor.DesalinationTechnology:developementsandpractice.ElsevierSciencePub.Co.,1983. [15] AnilKumarRajvanshi.Analyticalandexperimentalinvestigationoftheeffectofdyesonsolardistillation.PhDthesis,UniversityofFlorida,1979. 122

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[16] H.Fath.Solardistillation:apromisingalternativeforwaterprovisionwithfreeenergy,simpletechnology,andacleanenvironment.Desalination,116:45,1998. [17] H.Tanaka,T.Nosoko,andT.Nagata.Ahighlyproductivebasin-type-multiple-effectcoupledsolarstill.Desalination,130:279,2000. [18] M.Al-ShammiriandM.Safar.Multi-effectdistillationplants:stateoftheart.Desalination,126:45,1999. [19] M.F.A.Goosens,S.S.Sablani,W.H.Shayya,C.Paton,andH.Al-Hinai.Thermodynamicandeconomicconsiderationsinsolardesalination.Desalina-tion,129:63,2000. [20] B.Bouchekima,B.Gros,R.Ouahes,andM.Diboun.Performancestudyofthecapillarylmsolardistiller.Desalination,116:63,1998. [21] VanCarey.Liquid-VaporPhase-ChangePhenonmena.TayorandFrancis,2edition,2008. [22] H.M.QiblaweyandF.Banat.Solarthermaldesalinationtechnologies.Desalina-tion,220:633,2008. [23] L.Garcia-Rodriguez.Seawaterdesalinationdrivenbyrenewableenergies:areview.ProgressinEnergyandCombustionScience,143:103,2002. [24] H.TanakaandY.Nakatake.Asimpleandhightlyproductivesolarstill:averticalmultiple-effectdiffusion-typesolarstillcoupledwithaat-platemirror.Desalination,173:287,2005. [25] S.N.RaiandG.N.Tiwari.Singlebasinsolarstillcoupledwithatplatecollector.EnergyConversionManagement,23:145,1983. [26] S.KumarandS.Sinha.Transientmodelandcomparativestudyofconcentratorcoupledregernerativesolarstillinforcedcirculationmode.EnergyConversionManagement,37:629,1996. [27] WaterDesalination.DepartmentoftheArmy,USA,1986. [28] H.TanakaandY.Nakatake.Factorsinuencingtheproductivityofamultipleeffectdiffusion-typesolarstillcoupledwithaatplatecollectorreector.Desalination,186:299,2005. [29] A.A.El-Sebaii.Effectofwindspeedonactiveandpassivesolarstills.EnergyConversionandManagement,45:1187,2004. [30] H.Tanaka,T.Nosoko,andT.Nagata.Experimentalstudyofbasin-type,multiple-effect,diffusion-coupledsolarstill.Desalination,150:131,2002. 123

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[31] FrankIncropera.FundamentalsofHeatandMassTransfer.JohnWileyandSons,6edition,2007. [32] H.S.VarolandA.Yazar.Ahybridhighefciencysingl-basinsolarstill.InternationalJournalofEnergyResearch,20:541,1996. [33] P.I.Cooper.Themaximumefciencyofsingle-effectsolarstills.SolarEnergy,15:205,1972. [34] H.Tanaka,T.Nosoko,andT.Nagata.Experimentalstudyofverticalmultiple-effectdiffusionsolarstillcoupledwithaatplatereector.Desalination,249:34,2009. 124

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BIOGRAPHICALSKETCH GabrielEspinoswasborninMiami,Florida.HeearnedhishighschooldiplomaatMiramarHighSchool,wherehegraduatedfromtheInternationalBaccalaureateprogram.AfterearninghisBSmechanicalengineeringfromtheUniversityofFloridain2008,GabrielreturnedtoearnhisDoctorofPhilosophyinMechanicalEngineering.Aftergraduating,GabrielwillattendtheUnitedStatesAirForceOfcerTrainingSchool,and,upongraduation,becommissionedasaSecondLieutenant.GabrielhopestoonedayownaBiofuelcompanythatwillmakehydrocarbonfuelsfromavarietyoffeedstocks. 125