ch 11_micro and nanoscale fluid flow and heat transfer

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1、11MicroandNanoscaleFluidFlowandHeatTransferRecently,therehasbeenmuchinterestinunderstandingmicro/nanoscalefluidflowandheattransferphenomena.Thisinterestislargelydrivenbyrapidadvancesinmicrodevicesformicroelectronic,microeletromechanicalandbiomedicalapplications.Tworecentmonogra

2、phshavebeendevotedtothetopicoffluidflowinmicroandnanochannelsandstructures,andthatofmicroscaleheattransferinrapidthermallaserprocessingofthinfilms,respectively[1,2].Studiesshowthatasthetimeandlengthscalesarereduced,someoftheassumptionsusedorimpliedinthemacroscopicdescriptionoft

3、hefluidflowandheattransferphenomenabasedonthecontinuumtheoremmaybecomeinvalidandmodificationsareneededtoimprovethemathematicaldescription.Forthecasesofgasflowinmicrochannels,forexample,thenear-wallanalysissuggeststhattheno-clipcondition,whichhasbeentakenforgrantedinmacroscopicf

4、luidmechanics,isnolongervalid.Thecollisionofthemoleculeswiththewallsresultsinaslipofthemoleculesalongthesolidwall.TherealsohavebeenattemptstodirectlyapplytheBoltzmanntransportequationtodescribethefluidflowphenomenaatmicroscales.Oneofthewidelyobservedphenomenaassociatedwiththemi

5、croscalethermaltransportisthephase-lagbehavior,whichoccursinthinfilmsunderirradiationbyapulsinglaser.Whenthepulsedurationandthelengthscalearereducedtoalevelcomparablewiththemeanfreepathofthephonons,thetemperaturegradientandtheheatfluxnolongertravelatthesamespeed,makinginvalidth

6、eequal-speedassumptionimpliedintheclassicalFourierlawforheatconduction.Anappropriatedescriptionofthethermalphenomenaatmicroscalesthusrequiresthemodificationoftheexistingheattransferequations.Researchindicatesthatamathematicaldescriptionofmicroscaleheattransferphenomenamaybevery

7、similartothatformacrophenomenawithrelevantmodificationsforcertainspecificapplicationsandthatthedescriptioncanbevastlydifferentforotherconditions.Inthischapter,wefocusontwoclassesofmathematicaldescriptionoffluidflowandheattransferproblemsatmicroandnanoscalesforwhichthediscontinu

8、ousfiniteelementmethodsareparticularlysuited.Thefirstc