传热学教学课件：Recall Fluid Mechanics

HEATTRANSFERRecall:FluidMechanics#1WhatisConvectiveHeatTransfer?Youhavealreadyexperiencedit.Difficultyliesingeneralizingourexperience;filteringitdowntoafewlaws;learninghowtoapplytheselawstosystemsweengineersdesignanduse.HereiswhatIwantyoutodo:Ifapersonmastersthefundamentalsofhissubjectandhaslearnedtothinkandworkindependently,hewillsurelyfindhiswayandbesideswillbetterbeabletoadapthimselftoprogressandchangesthanthepersonwhosetrainingprincipallyconsistsintheacquiringofdetailedknowledge.–AlbertEinsteinSo,pleasereadaheadandcomepreparedwithgoodquestionsfortheclass.#21.Introductionto

DIMENSIONALANALYSISDimensionsEachquantitativeaspectprovidesanumberandaunit.Forexample,ThethreebasicdimensionsareL,T,andM.Alternatively,L,T,andFcouldbeused.WecanwriteThenotationisusedtoindicatedimensionalequality.#32)

DimensionalhomogeneityFundamentalpremise:Alltheoreticallyderivedequationsaredimensionallyhomogeneous----thatis,thedimensionsoftheleftsideoftheequationmustbethesameasthoseontherightside,andalladditiveseparatetermsmusthavethesamedimensions.Forexample,thevelocityequation,Intermsofdimensionstheequationis----dimensionalhomogeneous#43)DimensionalanalysisAproblem.Anincompressible,Newtonianfluid,steadyflow,throughalong,smooth-walled,horizontal,circularpipe.Thenatureoffunctionisunknownandtheexperimentsarenecessary.Wecanrecollectthesevariablesintodimensionlessproducts,Variablesfrom5to2.#5Here,Theresultswillbeindependentofthesystemofunits.Thistypeofanalysisiscalled-----dimensionalanalysis.

#64)BuckinghamPitheoremIfanequationinvolvingkvariablesisdimensionallyhomogeneous,itcanbereducedtoarelationshipamongk-r

independentdimensionlessproducts,whereristheminimumnumberofreferencedimensionsrequiredtodescribethevariables.#7Here,weusethesymboltorepresentadimensionlessproduct.Forequation,Wecanrearrangeto,Usually,thereferencedimensionsrequiredtodescribethevariableswillbethebasicdimensionsM,L,andTorF,L,andT.Insomecases,maybeonlytwoarerequired,orjustone.determinationofPiterms???#82.TheNavier-StokesEquationsCombinethedifferentialequationsofmotion,thestress-deformationrelationshipsandthecontinuityequation.#9Here,fourunknowns(u,v,w,p.)Weknowtheconservationofmassequation,----------fourequations.Nonlinear,secondorder,partialdifferentialequations.#103.generalcharacteristicsofpipeflow

#111)LaminarorturbulentflowOsborneReynolds-------flowrates#12TheReynoldsnumber,Fortheflowinaroundpipe,Laminarflow:Re<2100Transitionalflow:2100<Re<4000Turbulentflow:Re>4000And#132)EntranceregionandfullydevelopedflowTypicalentrancelengthsaregivenbyand#143)Fullydevelopedlaminarflow#154)FullydevelopedturbulentflowTransitionalflow:2100<Re<4000Turbulentflow:Re>4000