An Evaporating Ethanol Meniscus—Part II Analytical Studies

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1、F.J.Renk1AnEvaporatingEthanolMeniscusP.C.Wayner,Jr.DepartmentofChemicalandEnvironmentalEngineering,PartII:AnalyticalStudiesRensselaerPolytechnicInstitute,Troy,N.Y.12181AmodelofcapillaryflowheattransferisusedtoanalyzethedataobtainedinPartI.Theresultsindicatethatfluidflowresulting

2、fromachangeinthemeniscusprofilereplenishestheliquidevaporatedinastationaryevaporatingmeniscus.Localevaporativeheatfluxescanbeveryhighneartheinterlineregionofafinitecontactanglemeniscus.Therefore,asmallstationaryevaporatingmeniscuscanbeusedasaveryeffectivelocalheatsink.Introducti

3、onBasicEquationsThecoordinatesystemfortheanalysisoffluidflowinthevicinityThechangeinshapeofahorizontal,two-dimensionalevaporatingoftheinterlineofanevaporatingmeniscusisdepictedinFig.1.Theethanolmeniscushasbeenexperimentallydeterminedasafunctionmeniscusprofileisdenotedbyh(x),whic

4、hgivesthelocationoftheofheatflux[1,2].Thiswasobtainedbymeasuringthechangeintheliquid-vaporinterface.TheNavier-Stokesequationsforsteady,locationofnaturallyoccurringinterferencefringeswithheatinputtwo-dimensionalflowwithconstantpropertiescanbesolvedbyusingasdiscussedinPartI[2].The

5、evaporativeheatdissipationinthevi•thelubricationapproximations(slightliquidfilmtaper,bodyandcinityofthemeniscusinterlinewasalsoobtainedfromthemeasuredinertialforcesnegligible).Theliquid-vaporinterfaceisconsideredtemperaturedistributioninthesubstrate.Theincomingvolumetrictobeshea

6、rfree.Inaddition,noslipoccursattheliquid-solidboundaryflowratenecessarytomaintainastationary,steady-stateevaporatingwhichisdefinedtobethezerostreamline.Thesolutionforthestreammeniscuswascalculatedfromthisvalue.Herein,amathematicalfunctionundertheseconditionsismodelisusedtorelate

7、theshapeoftheevaporatingmeniscustothepressuregradientnecessarytosupplytherequiredvolumetricflow—1HP*=-*(3y2h(x)-y3)(1)rate.Themodelrepresentsthefluidflowdistributioninafinite6/jdxcontactanglemeniscusinwhichthepressuregradientisassumedtoThelocalvolumetricflowcanbeobtainedasbesole

8、lyduetocapillarity,thatis,acurvaturegradientalo