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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
