On the linear stability of mixed and free convection between inclined parallel plates with fixed heat flux boundary conditions

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1、hr.J.HcurMussTr’runs/?r.Vol.36.No.S.PP.1373-13X7.19930017-9310/93$6.00+0.00PnnkdI"Greathilamt1993PcrgamonPressLtdOnthelinearstabilityofmixedandfreeconvectionbetweeninclinedparallelplateswithfixedheatfluxboundaryconditionsA.S.LAVINEMechanical,AerospaceandNuclearEngineeringDepartment,Univ

2、ersityofCalifornia.LosAngeles.CA900241597.U.S.A.(Recriued26Sepremher1990undin.jitml./brmI9Muy1992)Abstract-Thispaperconcernsthelinearstabilityofmixedornaturalconvectionbetweeninliniteparallelplatesinclinedarbitrarilywithrespecttogravity.Inpreviousanalyses,ithascommonlybeenassumedthatthe

3、temperatureattheboundariesisfixed.Inthepresentwork,theheatfluxattheboundariesislixed.Forthisboundarycondition.itisshownthatifthetemperaturegradientparalleltotheplatesisadverse(temperatureincreasingdownward),theflowisunstableforWI>’valueortheRayleighnumber.Thatis.thecriticalRayleighnumbe

4、riszero.Thisresultholdsindependentofthebasevelocityandtemperaturedistributionsandinclination.INTRODUCTIONdependentonthedetailsofthebaseflowandincli-nation.THISPAPERconcernsthelinearstabilityofmixedTherehasofcoursebeenagreatdealofresearchornaturalconvectionbetweeninfiniteparallelplatesco

5、ncerningnaturalandmixedconvectionbetweeninclinedarbitrarilywithrespecttogravity(seeFig.I).parallelplates.Catton[I]andOstrach[2.31,forexam-Anattempthasbeenmadetoallowtheclassofflowsple,giveextensivereviewsofnaturalconvectioninunderconsiderationtobeasgeneralaspossible,enclosures,including

6、betweenparallelplates.Thealthoughtherearecertainrestrictions(asnotedinthebookbyGershuniandZhukhovitskii[4]givesexten-ProblemStatementsection).Thestudyisfunda-sivecoverageofthestabilitytheoryforvertical,hori-mental,andinconsideringtheapplicabilityofthezontal,andtiltedcases,againmostlyfor

7、naturalcon-resultstorealsystemsitmustberecognizedthattherevection.areidealizationspresent,suchastheinfiniteextentofThepapersreviewedherewillberestrictedtothosethedomain.Nonetheless,itishopedthatthecon-whichareparticularlyrelevanttothepresentworkclusionsofthisstudywillnotonlybeo