heat exchangers selection, rating and thermal design

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... steel/titanium heat exchanger Tube-fin heat exchangers Diffusion bonded heat exchangers The printed circuit heat exchanger (PCHE) Welded plate heat exchangers Plate and Frame Heat Exchangers (PHE) and ... Plate and Frame Heat Exchangers (PHE) Brazed Plate Heat Exchangers Welded Plate Heat Exchanger (PHE types) Other specialised PHE types The Plate and Shell Heat Exchanger (PSHE) Spiral Heat Exchangers ... R.K., Kraus, A.D. and Metzger, D., (1990), Compact Heat Exchangers& apos; A Festschritt for A.L. London, Hemisphere, New York. Smith, E.M., (1997), Thermal Design of Heat Exchangers, a Numerical...

... multi-start coil exchangers platen-type heat exchangers RODbaffle shell -and- tube exchangers lamella heat exchangers flattened and helically twisted tubesprinted-circuit heat exchangers HELIXCHANGERsAs ... step-wise rating, and transientsEric M SmithProfessionalJohn Wiley & Sons, LtdAdvances in Thermal Design of Heat Exchangers: A Numerical Approach: Direct-sizing, step-wise rating, and ... equations and building towards understanding of thermal design at every level.Preface'I would like to extend the way in which you may thinkabout the design of heat exchangers...

... WR WKH WKLFNQHVV LW LVSeries in Thermal & Fluid Physics & EngineeringEditor: G.F. HewittPractical Thermal Design of Shell -and- Tube Heat Exchangers R. MukherjeePRUH FRQYHQLHQW...

... 118B.3 Heat Exchangers . . . 121B.3.1 Heat Exchangers with Two Passages of InternalFluid(Fig.2.5) 121B.3.2 Heat Exchangers with Three Passages of InternalFluid(Fig.2.6) 137B.3.3 Heat Exchangers ... W, M and Mare the mass flow rates of the heating fluid and the heated fluid, respectively, inkg/s, t1 and t2are the inlet and outlet temperatures of the heating fluid, t1 and t2arethe ... t2arethe inlet and outlet temperatures of the heated fluid in◦C, cpm and cpmare the meanisobaric specific heat of both the heating and the heated fluid in J/kgK, and ηeis theactual...

... rsinacosRrcosðhÞÀ h0Chapter 4825Dry and Wet Disk Brakes and ClutchesThis chapter on disk brakes and clutches will consider annular contact diskclutches and both caliper and annular contact disk brakes, ... Continued.Dry and Wet Disk Brakes and Clutches 85Evaluation of these integrals is easiest for brake pads with radial and circular boundaries, as in Figure 4, for which equation (1-4) and (1-5) may ... longest life is realized for that pad and caliper combination whichprovides the largest heat sink, shown in Figure 9 and the shortest life for thatwith the smallest heat sink, shown in Figure 10.III....

... processes through overhead cranes,hoists, and industrial brakes and clutches and in farm and garden tractors.Some or all of the following materials, and others, that are now nec-essary to produce ... coefficient is the design parameter to be used. On the other hand, the pertinent design param-eters are the dynamic friction coefficient and its change with temperaturewhen a brake is designed for ... phenolics, furans, and epoxies produces what is known as impervious graphite. Imperviousgraphite, graphite, and carbon resist corrosion by acids, alkalies, and manyinorganic and organic compounds...

... the lining material and the drum, p represents the pressure betweenthe drum and the lining, and w represents the width of the band. Uponsimplifying equations (1-1) and (1-2) and remembering that ... the element ofband length approaches zero, sin(du/2) approaches du/2, cos(du/2)FIGURE2 Quantities and geometry used in the derivation of the band-brake design relations.Band Brakes 19Copyright ... Inc.Sincereinforcementofthebandnearitsleadingenddependsontheforcedecayasafunctionofanglealongtheband,itmaybeofinteresttodisplayhowFdecreaseswithf,measuredfromtheleadingendoftheband.TodothiswesimplyreplaceF2withFandreplaceawithfinequation(1-7)toobtainFF1¼eÀAff¼aÀuð1-12ÞForabrakebandextendingoveranangleffromF1.T¼ðF1ÀFÞr¼F1r1ÀFF1¼F1rð1ÀeÀAfÞð1-13ÞThusthedecayofthebandforcefromitsmaximumattheleadingendofthebandmaybefoundfromFigure3usingthescalesshownontheright-handordinateandassociatingtheabscissawithf.Itisbecauseofthelowcoefficientoffrictionforwetfrictionmaterialthatthebrakebandsinanautomatictransmissionarerelativelythickandcurvedtofitthedrumwithonlyasmallclearance.Thethicknessisrequiredtosupportthelargebandforcenecessarytodeliverarelativelylargetorquewhenoperatingatlowefficiencyandthesmallclearanceisnecessarytominimizetherequiredactivationforcetobendthebandandliningtothedrumradius.II.APPLICATIONInthissectionweconsiderthedesignofabandbraketoexertatorqueof9800.0N-msubjecttotheconditionsthatthedrumwidthbenogreaterthan100mmandthatthedrumdiameterbenogreaterthan750mm.Tocompletethedesignweshouldalsospecifythenecessarylinkstrengthforasafetyfactorof3.5whenusingasteelthathasaworkingstressof410MPa.Othermechanismsrequirethattheangleofwrapnotexceed290j.Liningtemper-atureisnotexpectedtoriseabove300jF(148jC)duringthemostsevereconditions.Selectaliningmaterialthatcansustainamaximumpressureof1.10MPa.ReturntoChapter1tofindthattheliningrepresentedbyFigure4isoneofseveralthatisflexibleenoughforusein...

... Inc.Thislinkforceandtheactivatingmomentbothactonthesecondaryshoe,sothattheforceandmomentequationsofequilibriumforthesecond-aryshoebecomeFr2¼ÀrwZf2f1pcosfdfþArwZf1f2psinfdfþFlsinf2þh2ð5-7ÞFu2¼ÀrwZf2f1psinfdfþArwZf2f1pcosfdfþFlcosf2þh2ð5-8Þwhere2histheanglesubtendedbytheadjustinglink.Next,Ma2¼Mp2þMf2À2RFlsinf22sinf22þh2ð5-9ÞwhereMp2andMf2areagaingivenbyequations(5.1 )and( 5.2)intermsofthepressuredistributiononthesecondaryshoe.TorqueforeithershoemaybecalculatedfromT¼ArwZf2f1pdfð5-10ÞEventhoughtheseequationsdonotuniquelydeterminethepressuredistributionoverthebrakelining,theyarestillofusebecausetheyallowthedesignengineertocomparetheeffectsofdifferentrealisticpressuredistribu-tionandtodesigndrumsandshoeswhoserigiditywillinduceparticularpressuredistributionsovertheprimaryandsecondaryshoes.Thefirstofthetwopressuredistributionsconsideredisasynthesisof(1)thesinusoidaldistributionassociatedwithanondeformingdrumandshoe,generallyassociatedwithalightlyloadedbrake ,and( 2)theforcepeaksthatoccurattheendsofload-bearingmembersincontact.Thesecondofthetwoisasysthesisof(1)theconstantdistributionsaidtobeassociatedwithmoreheavilyloadedbrakes ,and( 2)thepreviouslynotedforcepeaks.Thusthepressuredistributionswillberepresentedeitherbypp0¼eÀc1c=f0ðÞcoscf0kc2þc3c¼fÀf1ð5-11Þorbypp0¼eÀc1c=f0ðÞcoscf0kc2þc3sincþf1ðÞð5-12Þfortheprimaryshoes,wherethepeakpressureoneachshoeoccursattheheelbecauseitspivotcannotsustainaradialforceintheoutwarddirection.TheserelationsproducethepressuredistributionsshowninFigures1 4and1 5forthe ... brake life, heat dissipation, fading, and braking torque capability.III. DESIGN OF DUAL-ANCHOR TWIN-SHOE DRUMBRAKESFor both external and internal shoes and for either direction of rotation ... Inc.rotatesawayfromthepivot,self-lockingcanbeavoidedifMf/MpisalwaysgreaterthanÀ1.Similarcriteriaholdforinternalbrakesexceptthatthedirectionsofrotationarereversedforthesamealgebraicsigns.Sincemostbrakesaredesignedforrotationinbothdirections,itisgenerallyconvenienttocombinethesecriteriaintoasinglecriterion,whichisthatself-lockingofbothinternalandexternaldrumbrakesmaybeavoidedifÀ1VMfMpVþ1ð3-3ÞSelectionofshoeanddrumanglesanddimensionsinaccordancewiththiscriterionmaybeaidedbyconstructionofdesigncurvessuchasillustratedinFigures 7and8 ,inwhichtheratioMf/AMpisplottedagainstanglef2forselectedvaluesofthecoefficientoffriction.ExternalshoesarecharacterizedbyR/rratiosgreaterthanunityandinternalshoesbyr/Rratioslessthanunity.TheratioMf/AMphasbeenplottedinsteadofMf/MpinFigures 7and8 because...

... 4LinearlyActingExternalandInternalDrumBrakesLinearlyactingdrumbrakesarethosefittedwithshoeswhich,whenacti-vated,approachthedrumbymovingparalleltoaradiusthroughthecen-teroftheshoe.TypicallinearlyactingdrumbrakesareillustratedinFigures1–3.Analysisoflinearlyactingbrakesincludesthoseinwhichthecentrallypivotedshoesareattachedtopivotedlevers,asinFigure1.Includingbrakesofthisdesignwithinthecategoryoflinearlyactingbrakesisjustifiediftheyaredesignedsothattheappliedforcesontheshoesandliningsactalongtheradiioftheshaftsthattheygripwhenthebrakesareapplied.Brakesofthistypemayacteitheruponbrakedrumsordirectlyuponrotatingshaftsandaresuitableforuseinheavy-dutyapplications,suchasfoundinminingandconstructionequipmentandinmaterials-handlingmachinery.Internallinearlyactingdrumbrakes,suchasusedontrucksinEurope,maybedesignedasinFigure2.Eitherpneumaticorhydrauliccylindersorcams ... Inc.Letusdefinetheefficiencyofabrakeastheratioofthetorqueprovidedbythebraketothetorquethatcouldbehadbyapplyingtheforcedirectlytothedrum,orshaft.Accordingtothisdefinition,theefficiencybecomesTFsr¼Apmaxr2wðsinu2Àsinu1Þð1=2Þpmaxr2wðf0þsinf0Þ¼2Asinu2Àsinu1f0þsinf0ð1-10ÞUponsubstitutingforu1andu2inequation(1-8)andrecallingequations(1-6) and( 1-7)wefindthatTFsr¼4Asinðf0=2Þf0þsinf0¼ARrð1-11Þwheretheright-handsidehasalreadybeenplottedinFigure5.Fromthatfigurewefindthatalthoughmaximumefficiencymaybeachievedonlyifeachshoeandliningextendoverhalfofthedrum,orshaft,relativelylittleefficiencyislostiftheliningextendsoveronly160jinsteadof180j.This,togetherwiththenearimpossibilityofmaintaininggoodcontactbetweentheliningandthedrumneartheendsofashoesubtending180jatthecenterofthedrum,accountsfortheangulardimensionsofthebrakeliningsshowninFigure1.Finally,itfollowsfromequation(1-11)thatiftheshoeissymmetricallypivotedandifequation(1-7)holds,theappliedtorqueisgivenbyT¼ARFsð1-12ÞII.BRAKINGTORQUEANDMOMENTSFORSYMMETRICALLYSUPPORTEDINTERNALSHOESPressurepandbrakingtorqueareagaingivenbyequations(1-2 )and( 1-4),respectively,foraninternalshoemovedagainstarotatingdrumalongalineparalleltoitsaxisofsymmetry,lineOB,inFigure6.Inthefollowinganalysisit ... Inc.Letusdefinetheefficiencyofabrakeastheratioofthetorqueprovidedbythebraketothetorquethatcouldbehadbyapplyingtheforcedirectlytothedrum,orshaft.Accordingtothisdefinition,theefficiencybecomesTFsr¼Apmaxr2wðsinu2Àsinu1Þð1=2Þpmaxr2wðf0þsinf0Þ¼2Asinu2Àsinu1f0þsinf0ð1-10ÞUponsubstitutingforu1andu2inequation(1-8)andrecallingequations(1-6) and( 1-7)wefindthatTFsr¼4Asinðf0=2Þf0þsinf0¼ARrð1-11Þwheretheright-handsidehasalreadybeenplottedinFigure5.Fromthatfigurewefindthatalthoughmaximumefficiencymaybeachievedonlyifeachshoeandliningextendoverhalfofthedrum,orshaft,relativelylittleefficiencyislostiftheliningextendsoveronly160jinsteadof180j.This,togetherwiththenearimpossibilityofmaintaininggoodcontactbetweentheliningandthedrumneartheendsofashoesubtending180jatthecenterofthedrum,accountsfortheangulardimensionsofthebrakeliningsshowninFigure1.Finally,itfollowsfromequation(1-11)thatiftheshoeissymmetricallypivotedandifequation(1-7)holds,theappliedtorqueisgivenbyT¼ARFsð1-12ÞII.BRAKINGTORQUEANDMOMENTSFORSYMMETRICALLYSUPPORTEDINTERNALSHOESPressurepandbrakingtorqueareagaingivenbyequations(1-2 )and( 1-4),respectively,foraninternalshoemovedagainstarotatingdrumalongalineparalleltoitsaxisofsymmetry,lineOB,inFigure6.Inthefollowinganalysisit...