Natural Convective Heat Transfer from Short Inclined Cylinders

133 Pages·2014·4.095 MB·English

by  Patrick H. Oosthuizen, Abdulrahim Y. Kalendar (auth.)

SpringerBriefs in Applied Sciences and Technology
Thermal Engineering andApplied Science
SeriesEditor
FrancisA.Kulacki,UniversityofMinnesota,USA
Forfurthervolumes:
http://www.springer.com/series/10305
Patrick H. Oosthuizen • AbdulrahimY. Kalendar
Natural Convective Heat
Transfer from Short Inclined
Cylinders
2123
PatrickH.Oosthuizen AbdulrahimY.Kalendar
DepartmentofMechanical PublicAuthorityforAppliedEducation
andMaterialsEngineering andTraining
Queen’sUniversity CollegeofTechnologicalStudies(CTS)
Kingston,ON KuwaitCity
Canada Kuwait
ISSN2191-530X ISSN2191-5318(electronic)
ISBN978-3-319-02458-5 ISBN978-3-319-02459-2(eBook)
DOI10.1007/978-3-319-02459-2
SpringerChamHeidelbergNewYorkDordrechtLondon
LibraryofCongressControlNumber:2013949031
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Preface
This book is concerned with natural convective heat transfer from relatively short
cylindersthathaveanexposedtopsurfaceandaremountedonaplaneadiabaticbase.
Attentionisgiventocylindershavingcircular,square,andrectangularcross-sections
andtocylinderspointingverticallyupwardorverticallydownwardandtocylinders
setatanarbitraryangletothevertical.Theinterestinthesituationshereconsidered
arisesfromthefactthatanumberofelectricalmeasurementsystemsandelectronic
systems that are cooled by natural convection can be approximately modeled as
involving short cylinders with a flat exposed top surface. These components are
also sometimes mounted at an angle to the vertical. Knowledge of the effect of
cross-sectional shape, of the height to cross-sectional size, and of the inclination
angleofthecylindertotheverticalonthenaturalconvectiveheattransferratefrom
suchcylindersisthereforerequiredinthethermaldesignofelectricalandelectronic
components that can be modeled as short cylinders with exposed top surfaces. A
discussionofrepresentativegeneralpaststudiesofheattransferfromcylindersisfirst
givenandthenmoredetailedresultsforcircular,square,andrectangularcylindersare
discussed.Attentionhasmainlybeengiventotheresultsofnumericalsolutionsbut
someexperimentalresultsarealsopresented.Adiscussionofcorrelationequations
basedonthenumericalandexperimentalresultsforsomeofthesituationsconsidered
isalsopresented.
June,2013 PatrickH.OosthuizenandAbdulrahimY.Kalendar
v
Contents
1 Introduction................................................... 1
2 NaturalConvectiveHeatTransferfromShortCylindricalCylinders
HavingExposedUpperSurfacesandMountedonFlatAdiabaticBases 15
3 NaturalConvectiveHeatTransferFromShortSquareCylinders
HavingExposedUpperSurfacesandMountedonFlatAdiabaticBases 51
4 NaturalConvectiveHeatTransferfromShortRectangularCylinders
HavingExposedUpperSurfacesandMountedonFlatAdiabaticBases 93
vii
Chapter 1
Introduction
Keywords Natural convection · Cylinders · Short · Numerical · Experimental ·
Cylindrical·Square·Rectangular·Inclined
1.1 Introduction
This book is concerned with natural convective heat transfer from relatively short
cylindersmountedonaplaneadiabaticbase,thecylindershavinganexposed“top”
surface. Attention is given to cylinders having circular, square, and rectangular
cross-sectionalshapes.Therefore,thesituationsconsideredareasshowninFig.1.1.
Attentionwillbegiventocylinderspointingverticallyupwardandverticallydown-
ward and to cylinders set at an arbitrary angle to the vertical. These situations are
illustratedinFig.1.2.
Theinterestinthesituationsconsideredherearisesfromthefactthatanumber
of electrical and electronic systems that are cooled by natural convection can be
approximatelymodeledasinvolvingshortcylinderswithaflatexposed“top”surface.
Thesecomponentsarealsosometimesmountedatanangletothevertical.Knowledge
of the effect of cross-sectional shape, size, and inclination angle on the natural
convectiveheattransferratefromsuchcylindersisthereforerequiredinthethermal
design of such electrical and electronic components that can be modeled as short
cylinderswithexposeduppersurfaces.Thepurposeofthisbookistogiveareviewof
somerecentstudiesofnaturalconvectiveheattransferfromrelativelyshortcircular,
square,andrectangularcylinders.Beforeproceedingtothisdiscussion,areviewof
representative earlier studies of natural convective heat transfer from cylinders in
generalwillbepresentedinthischapter.
1.2 VerticalandHorizontalCircularCylinders
Naturalconvectiveheattransferfromrelativelylongverticalandhorizontalcylinders
withadiabaticendsurfaces(seeFig.1.3)hasbeenstudiedformanyyears,reviews
of these studies being presented in many heat transfer books such as McAdams
(1954),Jaluria(1980),HolmanandWhite(1992),Burmeister(1993),Bejan(1995),
Oosthuizen and Naylor (1999), Lindon (2000), Incropera et al. (2005), William
etal.(2005),KakaçandYener(1995),OlegandPavel(2005),MickleandMarient
P.H.Oosthuizen,A.Y.Kalendar,NaturalConvectiveHeatTransferfromShortInclined 1
Cylinders,SpringerBriefsinAppliedSciencesandTechnology13,
DOI10.1007/978-3-319-02459-2_1,©TheAuthor(s)2014
2 1 Introduction
Fig.1.1 Cylindergeometries
considered
(2009), andEckert(1959). However, mostofthesestudiesarebasedontheuseof
theboundarylayerassumptionsandontheassumptionthatthelength-to-diameter
ratioofthecylinderisrelativelylarge.
Some limited studies for relatively short cylinders are available, e.g., see Oost-
huizenandChow(1986).Integralmethodresultsfornaturalconvectiveheattransfer
fortheisothermalwallconditionwereobtainedbyLeFevreandEde(1956).They
providedacorrelationequationforaverageheattransferthatincludedthecurvature
effectsofthecylinder.SparrowandGregg(1956)providedanapproximatesolution
forlaminarfreeconvectiveflowofairoveraverticalcylinderwithuniformsurface
temperature by applying the similarity method. Minkowycz and Sparrow (1974)
usedthelocalnonsimilaritysolutionmethodtoreexaminethecaseofanisothermal
verticalcylinderandwereabletoobtainnumericalresultsforaPrandtlnumberof
0.733forawiderrangeofcurvatureparameters.Cebeci(1974)numericallystudied
freeconvectiveheattransferfromslendercylinderswithauniformsurfaceheatflux
fordifferentPrandtlnumbersfrom0.01to100usingafinitedifferencetechnique,
whileHeckeletal. (1989)studiedtheeffectofavariablesurfaceheatflux. Corre-
lationequationsfortheheattransferratefromcylindersarediscussedbyChurchill
andChu(1975),Yang(1987),andMunoz-Coboetal.(2003).
Mostexistingexperimentalstudiesofnaturalconvectiveheattransferratesfrom
cylindershaveessentiallyallbeenconcernedwithlongcylindersorcylinderswhere
1.2 VerticalandHorizontalCircularCylinders 3
Fig. 1.2 Inclined cylinders. (Adapted from: Kalendar and Oosthuizen (2009a) ASME Paper
IMECE2009-12777.Bypermission)
theendsareinsulated(seeFig.1.3).TypicalofthesestudiesarethoseofFukusawa
andIguchi(1962)andFujiietal.(1986).TheeffectofPrandtlnumberwasfurther
studiedbyCrane(1976).Typicalrecentstudiesthathavefurtherextendedtheearlier
workonnaturalconvectiveflowinducedaroundheatedverticalcylindersincludethe
experimentalstudybyKimura(2004)andJarallandCampo(2005).Kimura(2004)
observed the influence of cylinder diameter on the transition to turbulent flow and
on the local heat transfer characteristics using water as a test fluid. The diameters
ofthecylindersusedvariedfrom10to165mmandtheywere1,200mminlength.
Fromhisexperimentalresultsandfromthevisualizationoftheflow,heshowedthat
theonsetofturbulenttransitionshiftsdownstreamwithdecreasingcylinderdiameter
andthelocalheattransfercoefficientsincreasesinbothlaminarandturbulentflow
4 1 Introduction
Fig.1.3 Longcylinderswith
adiabaticendpieces
regionswithdecreasingdiameter.Gorietal.(2006)studiedthelocalnonsimilarity
solution with the first level of truncation for natural convection around “a needle”
immersedinliquidswithauniformheatfluxatthesurface.Thegoverningequations
are similar to those studied by Minkowycz and Sparrow (1974). Their analytical
solutionresultswerefoundtobeingoodagreementwiththeexperimentalresults.
Free convective heat transfer rates to air from relatively short vertical cylinders
attached to an insulated surface on one side and with the other end exposed and
atthesametemperatureasthecylindricalsurfacehasbeenexperimentallystudied
byOosthuizen(1979).Elevenmodelshavingvariouslength-to-diameterratiosand
oriented in both the upright and inverted positions were used. The results showed
thattheheattransferratefromshortcylinderswithexposedendsinbothorientations
islowerthanthatfromcylinderswithinsulatedends.Freeconvectiveheattransfer
ratestoairfromhorizontalcylindersattachedtoaninsulatedsurfaceononesideand
with the other end exposed and at the same temperature as the cylindrical surface
has been experimentally studied by Oosthuizen and Paul (1981a). Models having
variouslength-to-diameterratioswereused.Theirresultsshowedthatduetothree-
dimensionaleffects,theNusseltnumberbasedondiameterincreasesasthelength-
to-diameterratiodecreases.
Natural convective heat transfer from a short vertical cylinder with an exposed
horizontaltopsurfaceandwithaconstantsurfacetemperaturewasnumericallystud-
iedbyOosthuizen(2008),andOosthuizenandPaul(2008)whilenaturalconvective
heattransferfromashortverticalcylinderwithanexposedhorizontaltopsurfaceand
with a constant surface heat flux was numerically studied by Oosthuizen (2007b).
ThesestudiesindicatedthatthemeanNusseltnumberfortheheatedtopsurfaceis
muchlowerthanthatoftheheatedverticalsidesurfaceandthis, togetherwiththe
fact that the area of the top surface at the lower values of cylinder dimensionless
radiusconsideredismuchlessthanthatoftheverticalsidesurface,meansthatthe