Heat and Mass Transfer

705 Pages·2006·11.808 MB·English

by  Dr.-Ing. E. h. Dr.-Ing. Hans Dieter Baehr, Dr.-Ing. E. h. mult. Dr.-Ing. Karl Stephan (auth.)

HansDieterBaehr·KarlStephan
HeatandMassTransfer
Hans Dieter Baehr · Karl Stephan
Heat and
Mass Transfer
Second,revisedEdition
With327Figures
123
Dr.-Ing.E.h.Dr.-Ing.HansDieterBaehr
Professorem.ofThermodynamics,UniversityofHannover,Germany
Dr.-Ing.E.h.mult.Dr.-Ing.KarlStephan
Professor(em.)InstituteofThermodynamicsandThermalProcessEngineering
UniversityofStuttgart
70550Stuttgart
Germany
e-mail:[email protected]
LibraryofCongressControlNumber:2006922796
ISBN-10 3-540-29526-7 SecondEdition SpringerBerlinHeidelbergNewYork
ISBN-13 978-3-540-29526-6 SecondEdition SpringerBerlinHeidelbergNewYork
ISBN3-540-63695-1 FirstEdition Springer-VerlagBerlinHeidelbergNewYork
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Preface to the second edition
In this revised edition of our book we retained its concept: The main empha-
sis is placed on the fundamental principles of heat and mass transfer and their
application to practical problems of process modelling and the apparatus design.
Like the first edition, the second edition contains five chapters and several
appendices, particularly a compilation of thermophysical property data needed
for the solution of problems. Changes are made in those chapters presenting
heat and mass transfer correlations based on theoretical results or experimental
findings. They were adapted to the most recent state of our knowledge. Some of
theworkedexamples, whichshouldhelptodeepenthecomprehensionofthetext,
were revised or updated as well. The compilation of the thermophysical property
data was revised and adapted to the present knowledge.
Solving problems is essential for a sound understanding and for relating prin-
ciples to real engineering situations. Numerical answers and hints to the solution
of problems are given in the final appendix.
The new edition also enabled us to correct printing errors and mistakes.
In preparing the new edition we were assisted by Jens K¨orber, who helped
us to submit a printable version of the manuscript to the publisher. We owe him
sincere thanks.
We also appreciate the efforts of friends and colleagues who provided their
good advice with constructive suggestions.
Bochum and Stuttgart, H.D. Baehr
March 2006 K. Stephan
Preface to the first edition
ThisbookistheEnglishtranslationofourGermanpublication,whichappearedin
1994 with the title “W¨arme und Stoffu¨bertragung” (2nd edition Berlin: Springer
Verlag 1996). The German version originated from lecture courses in heat and
mass transfer which we have held for many years at the Universities of Hannover
and Stuttgart, respectively. Our book is intended for students of mechanical
and chemical engineering at universities and engineering schools, but will also be
of use to students of other subjects such as electrical engineering, physics and
chemistry. Firstly our book should be used as a textbook alongside the lecture
course. Its intention is to make the student familiar with the fundamentals of
heatandmasstransfer, andenablehimto solvepractical problems. Ontheother
hand we placed special emphasis on a systematic development of the theory of
heat and mass transfer and gave extensive discussions of the essential solution
methods for heat and mass transfer problems. Therefore the book will also serve
in the advanced training of practising engineers and scientists and as a reference
work for thesolution of their tasks. Thematerial is explained with theassistance
of a large number of calculated examples, and at the end of each chapter a series
of exercises is given. This should also make self study easier.
Many heat and mass transfer problems can be solved using the balance equa-
tions and the heat and mass transfer coefficients, without requiring too deep a
knowledge of the theory of heat and mass transfer. Suchproblems are dealt with
in the first chapter, which contains the basic concepts and fundamental laws of
heat and mass transfer. The student obtains an overview of the different modes
of heat and mass transfer, and learns at an early stage how to solve practical
problems andtodesign heatandmass transfer apparatus. This increases themo-
tivation to study the theory more closely, which is the object of the subsequent
chapters.
In the second chapter we consider steady-state and transient heat conduction
andmassdiffusioninquiescentmedia. Thefundamentaldifferentialequations for
the calculation of temperature fields are derived here. We show how analytical
and numerical methods are used in the solution of practical cases. Alongside the
Laplace transformation and the classical method of separating the variables, we
havealso presentedan extensive discussion of finite difference methods which are
very important in practice. Many of the results foundfor heat conduction can be
transferredtotheanalogous processofmassdiffusion. Themathematical solution
formulations are the same for both fields.
viii Preface
The third chapter covers convective heat and mass transfer. The derivation
of the mass, momentum and energy balance equations for pure fluids and multi-
componentmixtures aretreated first,beforethematerial lawsareintroducedand
the partial differential equations for the velocity, temperature and concentration
fields are derived. As typical applications we consider heat and mass transfer in
flow over bodies and through channels, in packed and fluidised beds as well as
free convection and the superposition of free and forced convection. Finally an
introduction to heat transfer in compressible fluids is presented.
In the fourth chapter the heat and mass transfer in condensation and boil-
ing with free and forced flows is dealt with. The presentation follows the book,
“Heat Transfer in Condensation and Boiling” (Berlin: Springer-Verlag 1992) by
K.Stephan. Here,weconsidernotonlypuresubstances;condensationandboiling
in mixtures of substances are also explained to an adequate extent.
Thermal radiation is the subject of the fifth chapter. It differs from many
other presentations in so far as the physical quantities needed for the quantita-
tive description of the directional and wavelength dependency of radiation are
extensively presented first. Only after a strict formulation of Kirchhoff’s law, the
idealradiator, theblackbody, isintroduced. Afterthisfollows adiscussion ofthe
material laws of real radiators. Solar radiation and heat transfer by radiation are
considered as the main applications. Anintroduction to gas radiation, important
technicallyforcombustionchambersandfurnaces,isthefinalpartofthischapter.
As heat and mass transfer is a subject taught at a level where students have
alreadyhadcoursesincalculus,wehavepresumedaknowledgeofthisfield. Those
readers who only wish to understand the basic concepts and become familiar
with simple technical applications of heat and mass transfer need only study the
first chapter. More extensive knowledge of the subject is expected of graduate
mechanical and chemical engineers. The mechanical engineer should be familiar
with the fundamentals of heat conduction, convective heat transfer and radiative
transfer, aswellashavingabasicknowledgeofmasstransfer. Chemicalengineers
alsorequire,inadditiontoasoundknowledgeoftheseareas,agoodunderstanding
of heat and mass transfer in multiphase flows. The time set aside for lectures is
generallyinsufficientforthetreatmentofallthematerialinthisbook. However,it
isimportantthatthestudentacquiresabroadunderstandingofthefundamentals
andmethods. Thenitissufficienttodeepenthisknowledgewithselectedexamples
and thereby improve problem solving skills.
In the preparation of the manuscript we were assisted by a number of our
colleagues, aboveall byNicola JanePark,MEng., University ofLondon,Imperial
College of Science, Technology and Medicine. We owe her sincere thanks for
the translation of our German publication into English, and for the excellent
cooperation.
Hannover and Stuttgart, H.D. Baehr
Spring 1998 K. Stephan
Contents
Nomenclature xvi
1 Introduction. Technical Applications 1
1.1 The differenttypesofheattransfer. . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Heatconduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.2 Steady,one-dimensionalconductionofheat . . . . . . . . . . . . . 5
1.1.3 Convectiveheattransfer. Heattransfercoefficient . . . . . . . . . 10
1.1.4 Determiningheattransfercoefficients. Dimensionlessnumbers . . 15
1.1.5 Thermalradiation . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
1.1.6 Radiativeexchange . . . . . . . . . . . . . . . . . . . . . . . . . . 27
1.2 Overallheattransfer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
1.2.1 The overallheattransfercoefficient . . . . . . . . . . . . . . . . . 30
1.2.2 Multi-layerwalls . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
1.2.3 Overallheattransferthroughwalls with extendedsurfaces . . . . 33
1.2.4 Heatingandcoolingofthin walled vessels . . . . . . . . . . . . . . 37
1.3 Heatexchangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
1.3.1 Types ofheatexchangerand flowconfigurations . . . . . . . . . . 40
1.3.2 Generaldesignequations. Dimensionlessgroups . . . . . . . . . . 44
1.3.3 Countercurrentandcocurrentheatexchangers . . . . . . . . . . . 49
1.3.4 Crossflowheatexchangers. . . . . . . . . . . . . . . . . . . . . . . 56
1.3.5 Operatingcharacteristicsoffurtherflowconfigurations. Diagrams 63
1.4 The differenttypesofmasstransfer . . . . . . . . . . . . . . . . . . . . . 64
1.4.1 Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
1.4.1.1 Compositionofmixtures . . . . . . . . . . . . . . . . . . . 66
1.4.1.2 Diffusivefluxes . . . . . . . . . . . . . . . . . . . . . . . . 67
1.4.1.3 Fick’s law . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
1.4.2 Diffusionthrougha semipermeableplane. Equimolardiffusion . . 72
1.4.3 Convectivemass transfer . . . . . . . . . . . . . . . . . . . . . . . 76
1.5 Masstransfertheories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
1.5.1 Film theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
1.5.2 Boundarylayertheory . . . . . . . . . . . . . . . . . . . . . . . . . 84
1.5.3 Penetrationandsurfacerenewaltheories . . . . . . . . . . . . . . 86
1.5.4 Applicationoffilm theoryto evaporativecooling . . . . . . . . . . 87
x Contents
1.6 Overallmasstransfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
1.7 Masstransferapparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
1.7.1 Materialbalances . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
1.7.2 Concentrationprofilesandheightsofmass transfercolumns. . . . 97
1.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
2 Heat conduction and mass diffusion 105
2.1 The heatconductionequation . . . . . . . . . . . . . . . . . . . . . . . . 105
2.1.1 Derivationofthe differentialequationforthe temperaturefield . . 106
2.1.2 The heatconductionequationforbodieswith constant
materialproperties. . . . . . . . . . . . . . . . . . . . . . . . . . . 109
2.1.3 Boundaryconditions . . . . . . . . . . . . . . . . . . . . . . . . . . 111
2.1.4 Temperaturedependentmaterialproperties . . . . . . . . . . . . . 114
2.1.5 Similartemperaturefields . . . . . . . . . . . . . . . . . . . . . . . 115
2.2 Steady-stateheatconduction . . . . . . . . . . . . . . . . . . . . . . . . . 119
2.2.1 Geometricone-dimensionalheatconductionwith heatsources . . 119
2.2.2 Longitudinalheatconductionina rod . . . . . . . . . . . . . . . . 122
2.2.3 The temperaturedistributionin fins andpins . . . . . . . . . . . . 127
2.2.4 Finefficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
2.2.5 Geometricmulti-dimensionalheatflow. . . . . . . . . . . . . . . . 134
2.2.5.1 Superpositionofheatsourcesandheatsinks. . . . . . . . 135
2.2.5.2 Shape factors . . . . . . . . . . . . . . . . . . . . . . . . . 139
2.3 Transientheatconduction. . . . . . . . . . . . . . . . . . . . . . . . . . . 140
2.3.1 Solutionmethods . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
2.3.2 The Laplacetransformation. . . . . . . . . . . . . . . . . . . . . . 142
2.3.3 The semi-infinitesolid . . . . . . . . . . . . . . . . . . . . . . . . . 149
2.3.3.1 Heatingandcoolingwith differentboundaryconditions . 149
2.3.3.2 Two semi-infinitebodiesin contactwith eachother . . . . 154
2.3.3.3 Periodictemperaturevariations . . . . . . . . . . . . . . . 156
2.3.4 Cooling orheatingofsimplebodiesin one-dimensionalheatflow . 159
2.3.4.1 Formulationofthe problem . . . . . . . . . . . . . . . . . 159
2.3.4.2 Separatingthe variables . . . . . . . . . . . . . . . . . . . 161
2.3.4.3 Resultsfor theplate . . . . . . . . . . . . . . . . . . . . . 163
2.3.4.4 Resultsfor thecylinderandthe sphere . . . . . . . . . . . 167
2.3.4.5 Approximationfor largetimes: Restrictionto the first
term inthe series . . . . . . . . . . . . . . . . . . . . . . . 169
2.3.4.6 A solutionfor smalltimes . . . . . . . . . . . . . . . . . . 171
2.3.5 Cooling andheatinginmulti-dimensionalheatflow . . . . . . . . 172
2.3.5.1 Productsolutions . . . . . . . . . . . . . . . . . . . . . . . 172
2.3.5.2 Approximationfor smallBiotnumbers . . . . . . . . . . . 175
2.3.6 Solidificationofgeometricallysimplebodies . . . . . . . . . . . . . 177
2.3.6.1 The solidificationofflatlayers(Stefanproblem). . . . . . 178
2.3.6.2 The quasi-steadyapproximation . . . . . . . . . . . . . . 181
2.3.6.3 Improvedapproximations . . . . . . . . . . . . . . . . . . 184
2.3.7 Heatsources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
Contents xi
2.3.7.1 Homogeneousheatsources . . . . . . . . . . . . . . . . . . 186
2.3.7.2 Point andlinearheatsources . . . . . . . . . . . . . . . . 187
2.4 Numericalsolutionsto heatconductionproblems . . . . . . . . . . . . . . 192
2.4.1 Thesimple,explicitdifferencemethodfortransientheatconduction
problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
2.4.1.1 The finite differenceequation . . . . . . . . . . . . . . . . 193
2.4.1.2 The stability condition . . . . . . . . . . . . . . . . . . . . 195
2.4.1.3 Heatsources. . . . . . . . . . . . . . . . . . . . . . . . . . 196
2.4.2 Discretisationoftheboundaryconditions . . . . . . . . . . . . . . 197
2.4.3 The implicitdifferencemethodfrom J.CrankandP. Nicolson . . 203
2.4.4 Noncartesiancoordinates. Temperaturedependentmaterial
properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
2.4.4.1 The discretisationofthe self-adjointdifferentialoperator . 207
2.4.4.2 Constantmaterialproperties. Cylindricalcoordinates . . 208
2.4.4.3 Temperaturedependentmaterialproperties . . . . . . . . 209
2.4.5 Transienttwo-andthree-dimensionaltemperaturefields . . . . . . 211
2.4.6 Steady-statetemperaturefields . . . . . . . . . . . . . . . . . . . . 214
2.4.6.1 A simple finite difference method for plane, steady-state
temperaturefields . . . . . . . . . . . . . . . . . . . . . . 214
2.4.6.2 Considerationofthe boundaryconditions . . . . . . . . . 217
2.5 Massdiffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
2.5.1 Remarksonquiescentsystems . . . . . . . . . . . . . . . . . . . . 222
2.5.2 Derivationofthe differentialequationforthe concentrationfield . 225
2.5.3 Simplifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
2.5.4 Boundaryconditions . . . . . . . . . . . . . . . . . . . . . . . . . . 231
2.5.5 Steady-statemassdiffusionwith catalyticsurfacereaction. . . . . 234
2.5.6 Steady-statemassdiffusionwith homogeneouschemicalreaction . 238
2.5.7 Transientmassdiffusion . . . . . . . . . . . . . . . . . . . . . . . . 242
2.5.7.1 Transientmassdiffusionina semi-infinitesolid . . . . . . 243
2.5.7.2 Transientmassdiffusioninbodiesofsimplegeometry
with one-dimensionalmassflow . . . . . . . . . . . . . . . 244
2.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
3 Convective heat and mass transfer. Single phase flow 253
3.1 Preliminaryremarks: Longitudinal,frictionlessflowovera flatplate . . . 253
3.2 The balanceequations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258
3.2.1 Reynolds’transporttheorem . . . . . . . . . . . . . . . . . . . . . 258
3.2.2 The massbalance . . . . . . . . . . . . . . . . . . . . . . . . . . . 260
3.2.2.1 Pure substances. . . . . . . . . . . . . . . . . . . . . . . . 260
3.2.2.2 Multicomponentmixtures . . . . . . . . . . . . . . . . . . 261
3.2.3 The momentumbalance . . . . . . . . . . . . . . . . . . . . . . . . 264
3.2.3.1 The stresstensor . . . . . . . . . . . . . . . . . . . . . . . 266
3.2.3.2 Cauchy’sequationofmotion. . . . . . . . . . . . . . . . . 269
3.2.3.3 The straintensor . . . . . . . . . . . . . . . . . . . . . . . 270
xii Contents
3.2.3.4 Constitutive equationsforthe solution ofthe
momentumequation . . . . . . . . . . . . . . . . . . . . . 272
3.2.3.5 The Navier-Stokesequations. . . . . . . . . . . . . . . . . 273
3.2.4 The energybalance . . . . . . . . . . . . . . . . . . . . . . . . . . 274
3.2.4.1 Dissipatedenergyandentropy . . . . . . . . . . . . . . . 279
3.2.4.2 Constitutive equationsforthe solution ofthe energy
equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281
3.2.4.3 Someother formulationsofthe energyequation . . . . . . 282
3.2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
3.3 Influenceofthe Reynoldsnumberon the flow . . . . . . . . . . . . . . . . 287
3.4 Simplificationsto the Navier-Stokesequations . . . . . . . . . . . . . . . 290
3.4.1 Creepingflows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290
3.4.2 Frictionlessflows . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291
3.4.3 Boundarylayerflows . . . . . . . . . . . . . . . . . . . . . . . . . 291
3.5 The boundarylayerequations . . . . . . . . . . . . . . . . . . . . . . . . 293
3.5.1 The velocityboundarylayer . . . . . . . . . . . . . . . . . . . . . 293
3.5.2 The thermalboundarylayer . . . . . . . . . . . . . . . . . . . . . 296
3.5.3 The concentrationboundarylayer . . . . . . . . . . . . . . . . . . 300
3.5.4 Generalcommentsonthe solutionofboundarylayerequations . . 300
3.6 Influenceofturbulenceonheatandmasstransfer . . . . . . . . . . . . . 304
3.6.1 Turbulentflows nearsolidwalls. . . . . . . . . . . . . . . . . . . . 308
3.7 Externalforcedflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312
3.7.1 Parallelflowalonga flatplate . . . . . . . . . . . . . . . . . . . . 313
3.7.1.1 Laminarboundarylayer . . . . . . . . . . . . . . . . . . . 313
3.7.1.2 Turbulentflow . . . . . . . . . . . . . . . . . . . . . . . . 325
3.7.2 The cylinderin crossflow . . . . . . . . . . . . . . . . . . . . . . . 330
3.7.3 Tube bundlesin crossflow . . . . . . . . . . . . . . . . . . . . . . . 334
3.7.4 Someempiricalequationsforheatandmass transferin
externalforcedflow . . . . . . . . . . . . . . . . . . . . . . . . . . 338
3.8 Internalforcedflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341
3.8.1 Laminarflowincirculartubes . . . . . . . . . . . . . . . . . . . . 341
3.8.1.1 Hydrodynamic,fullydeveloped,laminarflow . . . . . . . 342
3.8.1.2 Thermal,fully developed,laminarflow . . . . . . . . . . . 344
3.8.1.3 Heattransfercoefficientsinthermallyfully developed,
laminarflow . . . . . . . . . . . . . . . . . . . . . . . . . . 346
3.8.1.4 The thermalentryflow withfully developedvelocity
profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349
3.8.1.5 Thermallyandhydrodynamicallydevelopingflow . . . . . 354
3.8.2 Turbulentflowincirculartubes . . . . . . . . . . . . . . . . . . . 355
3.8.3 Packedbeds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357
3.8.4 Fluidisedbeds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361
3.8.5 Someempiricalequationsforheatandmass transferinflow
throughchannels,packedandfluidisedbeds. . . . . . . . . . . . . 370
3.9 Freeflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373