Laminar Flow and Convective Transport Processes (eBook)

Front Cover 1
Laminar Flow and Convective Transport Processes: Scaling Principles and 
4 
Copayright Page 7
Table of Contents 10
Dedication 8
Preface 14
Acknowledgments 18
CHAPTER 1. Introduction 22
A Brief Historical Perspective 22
Asymptotic Methods in Transport Processes 23
Organization of the Book 25
CHAPTER 2. Basic Principles 32
The Continuum Approximation 32
Conservation of Mass The Continuity Equation
Conservation of Linear and Angular Momentum 44
Conservation of Energy 51
Constitutive Equations 56
Fluid Statics-Constitutive Equations for a Stationary Fluid 58
Constitutive Equations for a Flowing Fluid—General Considerations 66
Constitutive Equations for a Flowing Fluid—The Newtonian Fluid 70
Constitutive Equations for a Flowing Field—Non-Newtonian Fluids 72
The Equations of Motion for a Newtonian Fluid: The Navier-Stokes Equations 82
Boundary Conditions 84
CHAPTER 3. Unidirectional Flows 92
Simplification of the Navier-Stokes Equations for Unidirectional Flows 93
Steady Unidirectional Flows—Nondimensionalization and Characteristic Scales 95
Start-up Flow in a Circular Tube—Solution by Separation of Variables 104
The Rayleigh Problem—Solution by Similarity Transformation 112
Start-up of Simple Shear Flow 121
Pulsatile Flow in a Circular Tube 126
CHAPTER 4. Creeping Flows 140
Nondimensionalization and the Creeping Flow Equations 142
Some General Consequences of Linearity and the Creeping Flow Equations 146
Representation of Two-Dimensional and Axisymmetric Flows in Terms of the Streamfunction 165
Solutions via Eigenfunction Expansions for Two-Dimensional Creeping Flows 170
Eigenfunction Expansion for Axisymmetric Creeping Flows in Spherical Coordinates 181
Solutions via Superposition of Vector Harmonic Functions—General Three-Dimensional Problems 198
CHAPTER 5. Further Results in the Creeping Flow Limit 218
The Motions of Bubbles and Drops 218
Fundamental Solutions of the Creeping Flow Equations 250
Further Topics in Creeping Flow Theory 272
CHAPTER 6. Asymptotic Approximations for Unidirectional, One-Dimensional, and Nearly Unidirectional Flows 296
Pulsatile Flow in a Circular Tube Revisited—Asymptotic Solutions for High and Low Frequencies 297
Asymptotic Expansions—General Considerations 310
The Motion of a Fluid Through a Slightly Curved Tube 313
Bubble Growth in a Quiescent Fluid 323
CHAPTER 7. Thin Films, Lubrication, and Related Problems 366
The Eccentric Cylinder Problem 367
General Equations for Lubrication Problems 408
Applications of the General Equations of Lubrication Theory 417
Thin Films with Inertia 427
CHAPTER 8. Weak Convection Effects 470
Forced Convection Heat Transfer—General Considerations 471
Heat Transfer by Conduction (Pe . 0) 475
Heat Transfer from a Solid Sphere in a Uniform Streaming Flow at Small, but Nonzero, Peclet Numbers 477
Heat Transfer from a Body of Arbitrary Shape in a Uniform Streaming Flow at Small, but Nonzero, Peclet Numbers 491
Heat Transfer from a Sphere in Simple Shear Flow at Low Peclet Numbers 498
Uniform Flow Past a Solid Sphere at Small, but Nonzero, Reynolds Numbers 509
CHAPTER 9. Strona Convection Effects in Heat and Mass Transfer at Low Reynolds Number 532
Heat Transfer from a Solid Sphere in Streaming Flow for Small Reynolds Number and Large Peclet Number 534
Generalization of the Correlation Between Nu and Pe to Solid Bodies of Nonspherical Shape in Uniform Streaming Flow 547
Boundary-Layer Analysis of Heat Transfer from a Solid Sphere in Generalized Shear Flows at Low Reynolds Number 553
Mass Transfer from a Bubble or Drop that Translates Through a Quiescent Fluid at Low Re and Large Pe 557
Heat Transfer at High Peclet Number across Regions of Closed-Streamline Flow 561
CHAPTER 10. Laminar Boundary-Layer Theory 578
Potential Flow Theory 579
The Boundary-Layer Equations 586
Streaming Flow Past a Horizontal Flat Plate—The Blasius Solution 596
Streaming Flow Past a Semi-Infinite Wedge—The Falkner-Skan Solution 603
Streaming Flow Past Cylindrical Bodies—Boundary-Layer Separation 610
An Approximate Method to Estimate Shear Stress in Boundary-Layer Flows 619
Streaming Flow Past Axisymmetric Bodies—A Generalization of the Blasius Series 624
The Boundary-Layer on a Spherical Bubble 630
CHAPTER 11. Thermal Boundary-Layer Theory at Large Reynolds Number 658
Governing Equations (Re » 1, Pe » 1, with Pr Arbitrary) 659
Exact Solutions for Pr ~ 0(1) 662
The Asymptotic Limit, Pr » 1 665
The Asymptotic Limit, Pr « 1 672
Discussion of the Asymptotic Results for Pr « 1 and Pr » 1 679
Approximate Results for Surface Temperature with Specified Heat Flux or Mixed Boundary Conditions 681
CHAPTER 12. Natural and Mixed Convection Flows 690
The Boussinesq Equations 691
Natural Convection Boundary-Layers at High Grasshof Numbers 694
The Laminar Plume Above a Line or Point Source of Heat 712
Combined Forced and Free Convection 721
Natural Convection in a Horizontal Fluid Layer Heated From Below—The Rayleigh-Benard Problem 739
Index 754