Table Of Content(cid:2)
APPLICATIONS OF
MATHEMATICAL HEAT
TRANSFER AND FLUID
FLOW MODELS IN
ENGINEERING AND
MEDICINE
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APPLICATIONS OF
MATHEMATICAL HEAT
TRANSFER AND FLUID
FLOW MODELS IN
ENGINEERING AND
MEDICINE
AbramS.Dorfman
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UniversityofMichigan,USA
ThisWorkisaco-publicationbetweenASMEPressandJohnWiley&Sons,Ltd.
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Thiseditionfirstpublished2017
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LibraryofCongressCataloging-in-PublicationData
Names:Dorfman,A.Sh.(AbramShlemovich),author.
Title:Applicationsofmathematicalheattransferandfluidflowmodelsin
engineeringandmedicine/AbramS.Dorfman.
Description:Chichester,UK;Hoboken,NJ:JohnWiley&Sons,2017.|
Series:Wiley-asmepressseries|Includesbibliographicalreferencesand
index.
Identifiers:LCCN2016033003(print)|LCCN2016049187(ebook)|ISBN
9781119320562(cloth)|ISBN9781119320739(pdf)|ISBN9781119320746
(epub)
Subjects:LCSH:Heat–Transmission–Mathematicalmodels.|Fluid
mechanics–Mathematicalmodels.
Classification:LCCQC320.D592017(print)|LCCQC320(ebook)|DDC
621.402/2–dc23
LCrecordavailableathttps://lccn.loc.gov/2016033003
AcataloguerecordforthisbookisavailablefromtheBritishLibrary.
Setin10/12pt,TimesLTStdbySPiGlobal,Chennai,India.
10987654321
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In memory of my favorite co-author,
who passed away too soon,
Professor of University of Toledo,
Ella Fridman.
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Contents
SeriesPreface xiii
Preface xv
Acknowledgments xxvii
AbouttheAuthor xxix
Nomenclature xxxi
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PartI APPLICATIONSINCONJUGATEHEATTRANSFER
Introduction 1
WhenandwhyConjugateProcedureisEssential 1
ACoreofConjugation 3
1 UniversalFunctionsforNonisothermalandConjugateHeatTransfer 5
1.1 FormulationofConjugateHeatTransferProblem 5
1.2 MethodsofConjugation 9
1.2.1 NumericalMethods 9
1.2.2 UsingUniversalFunctions 10
1.3 IntegralUniversalFunction(Duhamel’sIntegral) 10
1.3.1 Duhamel’sIntegralDerivation 10
1.3.2 InfluenceFunction 12
1.4 DifferentialUniversalFunction(SeriesofDerivatives) 13
1.5 GeneralFormsofUniversalFunction 15
Exercises1.1–1.32 16
1.6 Coefficientsg andExponentsC andC forLaminarFlow 19
k 1 2
1.6.1 FeaturesofCoefficientsg oftheDifferentialUniversalFunction 19
k
1.6.2 EstimationofExponentsC andC forIntegralUniversalFunction 22
1 2
1.7 UniversalFunctionsforTurbulentFlow 24
Exercises1.33–1.47 27
1.8 UniversalFunctionsforCompressibleLow 28
1.9 UniversalFunctionsforPower-LawNon-NewtonianFluids 29
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viii Contents
1.10 UniversalFunctionsforMovingContinuousSheet 32
1.11 UniversalFunctionsforaPlatewithArbitraryUnsteadyTemperature
Distribution 34
1.12 UniversalFunctionsforanAxisymmetricBody 35
1.13 InverseUniversalFunction 36
1.13.1 DifferentialInverseUniversalFunction 36
1.13.2 IntegralInverseUniversalFunction 37
1.14 UniversalFunctionforRecoveryFactor 38
Exercises1.48–1.75 41
2 ApplicationofUniversalFunctions 45
2.1 TheRateofConjugateHeatTransferIntensity 45
2.1.1 EffectofTemperatureHeadDistribution 45
2.1.2 EffectofTurbulence 50
2.1.3 EffectofTime-VariableTemperatureHead 58
2.1.4 EffectsofConditionsandParametersintheInverseProblems 60
2.1.5 EffectofNon-NewtonianPower-LawRheologyFluidBehavior 66
2.1.6 EffectofMechanicalEnergyDissipation 67
2.1.7 EffectofBiotNumberasaMeasureofProblemConjugation 68
Exercises2.1–2.33 70
2.2 TheGeneralConvectiveBoundaryConditions 73
2.2.1 AccuracyofBoundaryConditionoftheThirdKind 73
(cid:2) 2.2.2 ConjugateProblemasanEquivalentConductionProblem 76 (cid:2)
2.3 TheGradientAnalogy 78
2.4 HeatFluxInversion 82
2.5 ZeroHeatTransferSurfaces 84
2.6 OptimizationinHeatTransferProblems 86
2.6.1 ProblemFormulation 87
2.6.2 ProblemFormulation 89
2.6.3 ProblemFormulation 92
Exercises2.34–2.82 95
3 ApplicationofConjugateHeatTransferModelsinExternalandInternal
Flows 102
3.1 ExternalFlows 102
3.1.1 ConjugateHeatTransferinFlowsPastThinPlates 102
Exercises3.1–3.38 123
3.1.2 ConjugateHeatTransferinFlowsPastBodies 126
3.2 InternalFlows-ConjugateHeatTransferinPipesandChannelsFlows 141
4 SpecificApplicationsofConjugateHeatTransferModels 155
4.1 HeatExchangersandFinnedSurfaces 155
4.1.1 HeatExchangeBetweenTwoFluidsSeparatedbyaWall(Overall
HeatTransferCoefficient) 155
4.1.2 ApplicabilityofOne-DimensionalModelsandTwo-Dimensional
Effects 166
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