An Introduction to Transport Phenomena in Materials Engineering, Second Edition

An

Intr

od

uc

tIon

to

Transport Phenomena

in Materials Engineering

GaskEll

This classic text on fluid flow, heat transport, and mass transport within materials has now been brought up to date and greatly improved with this new second edition. A new chapter on “Boiling and Condensation” expands and rounds out the book’s comprehen-sive coverage on transport phenomena. This new material is particularly important to current research in renewable energy resources involving technologies such as windmills and solar panels.

The book provides materials science and engineering students and professionals with a clear yet thorough introduction to fluid flow, heat transfer, and mass transport. It bal-ances the explanation of the fundamentals governing fluid flow and the transport of heat and mass with common applications of these fundamentals to specific systems existing in materials engineering. Readers will benefit from:

• Theuseoffamiliarexamplessuchasairandwatertointroducetheinfluencesofproperties and geometry on fluid flow.

• Anorganizationwithsectionsdealingseparatelywithfluidflow,heattransfer,and mass transport. This sequential structure allows the development of heat transport concepts to employ analogies of heat flow with fluid flow and the de-velopment of mass transport concepts to employ analogies with heat transport.

• Amplehigh-qualitygraphsandfiguresthroughout.• Keypointspresentedinchaptersummaries.• Endofchapterexercisesandsolutionstoselectedproblems.• Anallnewandimprovedcomprehensiveindex.

About the AuthorDavid R. Gaskell was born in Glasgow, Scotland and received B.Sc. degrees in metallurgy and technical chemistry from the University of Glasgow in 1962. From 1962 to 1964, he was employed as the Metallurgist with Laporte Chemical Ltd., a manufacturer of in-dustrialchemicals,withtwoplantsinEngland.HeobtainedhisPh.D.fromMcMasterUniversity in 1967, and from 1967 to 1982 he was a professor of metallurgy, materials scienceandgeologyattheUniversityofPennsylvania.In1982hecametoPurdue,wherehehaswonfivedepartmentalteachingawards.Hehastaughtavarietyofcoursesdealingwith materials properties, structures and processing, and he is the author of two texts, one on the thermodynamics of materials, which is in its sixth edition, and this book on transportphenomenainmaterialsengineering,whichisnowinitssecondedition.Hisresearch interests include chemical and extraction metallurgy, thermodynamics, kinetics, transport phenomena and materials processing.

www.momentumpress.net

ISBN: 978-1-60650-355-3

9 781606 503553

90000

An IntroductIon to

Transport Phenomena in Materials Engineering

s e c o n d e d I t I o n

DaviD R. GaskEll

An Introduct Ion toTransport Phenomena in Materials Engineeringsecond edIt Ion, By David R. Gaskell

secondedIt Ion

9781606503553_Gaskell_FM.indd xi 07/18/2012 05:42AM

Contents xi

List of Symbols xvii

1 Engineering Units and Pressure in Static Fluids 1

1.1 Origins of Engineering Units 11.2 Concept of Pressure 51.3 Measurement of Pressure 111.4 Pressure in Incompressible Fluids 151.5 Buoyancy 211.6 Summary 26

Problems 27

2 Momentum Transport and Laminar Flow of Newtonian Fluids 30

2.1 Introduction 302.2 Newton’s Lax of Viscosity 322.3 Conservation of Momentum in Steady-State Flow 362.4 Fluid Flow Between Two Flat Parallel Plates 402.5 Fluid Flow down in Inclined Plane 482.6 Fluid Flow in a Vertical Cylindrical Tube 532.7 Capillary Flowmeter 65

xi

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xii Contents

2.8 Fluid Flow in an Annulus 692.9 Mean Residence Time 762.10 Calculation of Viscosity from the Kinetic Theory of Gases 782.11 Viscosities of Liquid Metals 902.12 Summary 96

Problems 98

3 Equations of Continuity and Conservation of Momentum and Fluid Flow Past Submerged Objects 102

3.1 Introduction 1023.2 Equation of Continuity 1023.3 Conservation of Momentum 1043.4 Navier-Stokes Equation for Fluids of Constant Density

and Viscosity 1083.5 Fluid Flow over a Horizontal Flat Plane 1153.6 Approximate Integral Method in Obtaining Boundary

Layer Thickness 1173.7 Creeping Flow past a Sphere 1253.8 Summary 132

Problems 133

4 Turbelent Flow 135

4.1 Introduction 1354.2 Graphical Representation of Fluid Flow 1394.3 Friction Factor and Turbulent Flow in Cylindrical Pipes 1414.4 Flow Over a Flat Plate 1534.5 Flow Past a Submerged Sphere 1604.6 Flow Past a Submerged Cylinder 1634.7 Flow Through Packed Beds 1674.8 Fluidized Beds 1754.9 Summary 180

Problems 181

5 Mechanical Energy Balance and Its Application to Fluid Flow 185

5.1 Introduction 1855.2 Bernoulli’s Equation 185

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Contents xiii

5.3 Friction Loss, Ef 1885.4 Influence of Bends, Fittings, and Changes in the

Pipe Radius 1905.5 Concept of Head 2035.6 Fluid Flow in an Open Channel 2055.7 Drainage from a Vessel 2075.8 Emptying a Vessel by Discharge Through an Orifice 2095.9 Drainage of a Vessel Using a Drainage Tube 2135.10 Emptying a Vessel by Drainage Through a Drainage Tube 2155.11 Bernoulli Equation for Flow of Compressible Fluids 2195.12 Pilot Tube 2215.13 Orifice Plate 2255.14 Summary 228

Problems 229

6 Transport of Heat by Conduction 235

6.1 Introduction 2356.2 Fourier’s Law and Newton’s Law 2366.3 Conduction 2386.4 Conduction in Heat Sources 2566.5 Thermal Conductivity and the Kinetic Theory of Gases 2676.6 General Heat Conduction Equation 2746.7 Conduction of Heat at Steady State in Two Dimensions 2786.8 Summary 289

Problems 290

7 Transport of Heat by Convection 295

7.1 Introduction 2957.2 Heat Transfer by Forced Convection from a Horizontal Flat Plate

at a Uniform Constant Temperature 2957.3 Heat Transfer from a Horizontal Flat Plate with Uniform Heat Flux

Along the Plate 3157.4 Heat Transfer During Fluid Flow in Cylindrical Pipes 3177.5 Energy Balance in Heat Transfer by Convection Between

a Cylindrical Pipe and a Flowing Fluid 3227.6 Heat Transfer by Forced Convection from

Horizontal Cylinders 3317.7 Heat Transfer by Forced Convection from a Sphere 3347.8 General Energy Equation 3357.9 Heat Transfer from a Vertical Plate by Natural Convection 346

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xiv Contents

7.10 Heat Transfer from Cylinders by Natural Convection 3587.11 Summary 360

Problems 361

8 Transient Heat Flow 365

8.1 Introduction 3658.2 Lumped Capacitance Method; Newtonian Cooling 3658.3 Non-Newtonian Cooling in Semi-infinite Systems 3738.4 Non-Newtonian Cooling in a One-Dimensional

Finite Systems 3828.5 Non-Newtonian Cooling in a Two-Dimensional

Finite Systems 3948.6 Solidification of Metal Castings 4018.7 Summary 416

Problems 416

9 Heat Transport by Thermal Radiation 421

9.1 Introduction 4219.2 Intensity and Emissive Power 4239.3 Blackbody Radiation 4279.4 Emissivity 4319.5 Absorptivity, Reflectivity, and Transmissivity 4369.6 Kirchhoff’s Law and the Hohlraum 4379.7 Radiation Exchange Between Surfaces 4399.8 Radiation Exchange Between Blackbodies 4509.9 Radiation Exchange Between Diffuse-Gray Surfaces 4539.10 Electric Analogy 4589.11 Radiation Shields 4609.12 Reradiating Surface 4639.13 Heat Transfer from a Surface by Convection and Radiation 4669.14 Summary 471

Problems 472

10 Mass Transport by Diffusion in the Solid State 476

10.1 Introduction 47610.2 Atomic Diffusion as a Random-Walk Process 47610.3 Fick ’s First Law of Diffusion 480

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Contents xv

10.4 One-Dimensional Non-Steady-State Diffusion in a Solid; Fick ’s Second Law of Diffusion 483

10.5 Infinite Diffusion Couple 48910.6 One-Dimensional Diffusion in a Semi-infinite System Involving a

Change of Phase 49110.7 Steady-State Diffusion Through a Composite Wall 49810.8 Diffusion in Substitutional Solid Solutions 50210.9 Darken’s Analysis 50210.10 Self-Diffusion Coefficient 50610.11 Measurement of the Interdifussion Coefficient: Boltzmann–

Matano Analysis 51010.12 Influence of Temperature on the Diffusion Coefficient 51410.13 Summary 518

Problems 520

11 Mass Transport in Fluids 522

11.1 Introduction 52211.2 Mass and Molar Fluxes in a Fluid 52211.3 Equations of Diffusion with Convection in a Binary

Mixture A–B 52411.4 One-Dimensional Transport in a Binary Mixture of

Ideal Gases 52711.5 Equimolar Counterdiffusion 52811.6 One-Dimensional Steady-State Diffusion of Gas A Through

Stationary Gas B 52911.7 Sublimation of a Sphere into a Stationary Gas 53611.8 Film Model 53811.9 Catalytic Surface Reactions 53911.10 Diffusion and Chemical Reaction in Stagnant Film 54211.11 Mass Transfer at Large Fluxes and Large Concentrations 54711.12 Influence of Mass Transport on Heat Transfer in

Stagnant Film 55011.13 Diffusion into a Falling Film of Liquid 55311.14 Diffusion and the Kinetic Theory of Gases 56011.15 Mass Transfer Coefficient and Concentration Boundary Layer on a

Flat Plate 56911.16 Approximate Integral Method 57311.17 Mass Transfer by Free Convection 58311.18 Simultaneous Heat and Mass Transfer: Evaporate Cooling 58611.19 Chemical Reaction and Mass Transfer: Mixed Control 58911.20 Dissolution of Pure Metal A in Liquid B: Mixed Control 59311.21 Summary 596

Problems 598

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xvi Contents

12 Condensation and Boiling 601

12.1 Introduction 60112.2 Dimensionless Parameters in Boiling and Condensation 60212.3 Modes of Boiling 60312.4 Pool Boiling Correlations 60612.5 Summary 612

Problems 612

Appendix A Elementary and Derived SI Units and Symbols 615

Appendix B Prefixes and Symbols for Multiples and Submultiples of SI Units 617

Appendix C Conversion from British and U.S. Units to SI Units 618

Appendix D Properties of Solid Metals 620

Appendix E Properties of Nonmetallic Solids 623

Appendix F Properties of Gases at 1 Atm Pressure 627

Appendix G Properties of Saturated Liquids 635

Appendix H Properties of Liquid Metals 639

Recommended Readings 642

Answers to Problems 643

Index 651

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xvii

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xviii List of Symbols

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List of Symbols xix

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xx List of Symbols

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An

Intr

od

uc

tIon

to

Transport Phenomena

in Materials Engineering

GaskEll

This classic text on fluid flow, heat transfer, and mass transport has been brought up to date in this second edition. The author has added a chapter on “Boiling and Conden-sation” that expands and rounds out the book’s comprehensive coverage on transport phenomena. These new topics are particularly important to current research in renewable energy resources involving technologies such as windmills and solar panels.

The book provides you and other materials science and engineering students and pro-fessionals with a clear yet thorough introduction to these important concepts. It balances the explanation of the fundamentals governing fluid flow and the transport of heat and mass with common applications of these fundamentals to specific systems existing in materials engineering. You will benefit from:

• Theuseoffamiliarexamplessuchasairandwatertointroducetheinfluencesofproperties and geometry on fluid flow.

• Anorganizationwithsectionsdealingseparatelywithfluidflow,heattransfer,and mass transport. This sequential structure allows the development of heat transport concepts to employ analogies of heat flow with fluid flow and the de-velopment of mass transport concepts to employ analogies with heat transport.

• Amplehigh-qualitygraphsandfiguresthroughout.

• Keypointspresentedinchaptersummaries.

• Endofchapterexercisesandsolutionstoselectedproblems.

• Anallnewandimprovedcomprehensiveindex.

About the AuthorDavid r. Gaskell was born in Glasgow, Scotland and received B.Sc. degrees in metal-lurgy and technical chemistry from the University of Glasgow in 1962. From 1962 to 1964, he was employed as the Metallurgist with Laporte Chemical Ltd., a manufacturer ofindustrialchemicals,withtwoplantsinEngland.HeobtainedhisPh.D.fromMcMas-ter University in 1967, and from 1967 to 1982 he was a professor of metallurgy, materials scienceandgeologyattheUniversityofPennsylvania.In1982hecametoPurdue,wherehehaswonfivedepartmentalteachingawards.Hehastaughtavarietyofcoursesdealingwith materials properties, structures and processing, and he is the author of two texts, one on the thermodynamics of materials, which is in its sixth edition, and this book on transportphenomenainmaterialsengineering,whichisnowinitssecondedition.Hisresearch interests include chemical and extraction metallurgy, thermodynamics, kinetics, transport phenomena and materials processing.

www.momentumpress.net

ISBN: 978-1-60650-355-3

9 781606 503553

90000

An IntroductIon to

Transport Phenomena in Materials Engineering

s e c o n d e d I t I o n

DaviD R. GaskEll

An Introduct Ion toTransport Phenomena in Materials Engineeringsecond edIt Ion, By David R. Gaskell

secondedIt Ion

An Introduction to Transport Phenomena in Materials Engineering, Second Edition

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Transcript of An Introduction to Transport Phenomena in Materials Engineering, Second Edition