ANALYTICAL AND NUMERICAL STUDIES ON SOME NATURAL CONVECTION IN CAVITY

Abstract

The physicalphenomenaofnaturalconvectioninacavityfilledwithfluid/nanofluidor fluid/nanofluid saturatedporousmediumisoffundamentalimportanceintheoreticalas well aspracticalapplications.Itisknownthatsteady,incompressible,andNewtonian flowmayexistinacavityboundedbyimpermeableandisothermalwallskeptatdifferent temperatures. Theflowmaybeduetotheactionofbuoyancyforcewhichinturncauses natural convection.Thesetypesofflowmaybeconfigured,withdifferentfeatures,either for ananofluidinthecorrugatedcavity[20]orforafluid/nanofluid-saturatedporouscavity [112, 164]andthephysicalphenomenaofthistypeofflowhasdirectedintenseresearch effortstowarditsunderstanding.However,thepresentstateoftheartinthisdirectionin- dicates theexistenceofdifferentgapsandraisesdifferentquestions.Consequently,astep has beentakeninthisthesistoanswersomeofthesequestionsraisedintheliteraturere- viewbystudyingsomenaturalconvectioninacavityfilledwithnanofluidoracavityfilled with fluid/nanofluidsaturatedhighpermeableporousmedium.Inthiscontext,fourphys- ical problemsrelatedto(i)naturalconvectioninasquarecavityfilledwithananisotropic porous mediumduetosinusoidalheatfluxonhorizontalwalls,aperspectiveviewoflo- cal thermalnon-equilibrium(LTNE)stateonnaturalconvection(ii)inafluid-saturated anisotropic porousenclosure,(iii)inananofluidsaturatedporouscavity,and(iv)magneto- hydrodynamic(MHD)naturalconvectioninacorrugatedcavityfilledwithnanofluid,have been considered.Throughoutthethesistosolvethegoverningequationsnumerically,the finite differencemethodandfinitevolumemethodshavebeenadopted.Thefirstandlast problems arecompletelybasedonthenumericalinvestigation,whereas,thesecondand third arestudiednumericallyaswellasanalytically(forsomespecialcases).Theclosed- form analyticalsolutionisbasedonthefourhypothesis:(i)theflowisatasteady-state,(ii) the aspectratioofthecavityismuchgreaterthanunity,(iii)theflowvelocityisparalleland in theverticaldirectiononly,also(iv)thetemperaturecanbedecomposedintoalinearly varyinglongitudinalpartandanunknowntransversefunction.