Laminar Flow and Convective Transport Processes

Transcription

1 Laminar Flow and Convective Transport Processes Scaling Principles and Asymptotic Analysis L. Gary Leal Department of Chemical and Nuclear Engineering University of California Santa Barbara Butterworth-Heinemann Boston London Oxford Singapore Sydney Toronto Wellington

2 Contents Preface xiii Acknowledgments xvii CHAPTER 1 Introduction 1 A Brief Historical Perspective 1 Asymptotic Methods in Transport Processes 2 Organization of the Book 4 CHAPTER 2 Basic Principles 11 The Continuum Approximation 11 Conservation of Mass; The Continuity Equation 16 Conservation of Linear and Angular Momentum 23 Conservation of Energy 30 Constitutive Equations 35 Fluid Statics-Constitutive Equations for a Stationary Fluid 37 Constitutive Equations for a Flowing Fluid General Considerations 45 Constitutive Equations for a Flowing Fluid The Newtonian Fluid 49 Constitutive Equations for a Flowing Field Non-Newtonian Fluids 51 The Equations of Motion for a Newtonian Fluid: The Navier-Stokes Equations 61 Boundary Conditions 63 ix

3 x LAMINAR FLOW AND CONVECTIVE TRANSPORT PROCESSES CHAPTER 3 Unidirectional Flows 71 Simplification of the Navier-Stokes Equations for Unidirectional Flows 72 Steady Unidirectional Flows Nondimensionalization and Characteristic Scales 74 Start-up Flow in a Circular Tube Solution by Separation of Variables 83 The Rayleigh Problem Solution by Similarity Transformation 91 Start-up of Simple Shear Flow 100 Pulsatile Flow in a Circular Tube 105 CHAPTER 4 Creeping Flows 119 Nondimensionalization and the Creeping Flow Equations 121 Some General Consequences of Linearity and the Creeping Flow Equations 125 Representation of Two-Dimensional and Axisymmetric Flows in Terms of the Streamfunction 144 Solutions via Eigenfunction Expansions for Two-Dimensional Creeping Flows 149 Eigenfunction Expansion for Axisymmetric Creeping Flows in Spherical Coordinates 160 Solutions via Superposition of Vector Harmonie Functions General Three-Dimensional Problems 177 CHAPTER 5 Further Results in the Creeping Flow Limit 197 The Motions of Bubbles and Drops 197 Fundamental Solutions of the Creeping Flow Equations 229 Further Topics in Creeping Flow Theory 251 CHAPTER 6 Asymptotic Approximations for Unidirectional, One-Dimensional, and Nearly Unidirectional Flows 275 Pulsatile Flow in a Circular Tube Revisited Asymptotic Solutions for High and Low Frequencies 276 Asymptotic Expansions General Considerations 289 The Motion of a Fluid Through a Slightly Curved Tube 292 Bubble Growth in a Quiescent Fluid 302

4 Contents xi CHAPTER 7 Thin Films, Lubrication, and Related Problems 345 The Eccentric Cylinder Problem 346 General Equations for Lubrication Problems 387 Applications of the General Equations of Lubrication Theory 396 Thin Films with Inertia 406 CHAPTER 8 Weak Convection Effects 449 Forced Convection Heat Transfer General Considerations 450 Heat Transfer by Conduction (Pe -* 0) 454 Heat Transfer from a Solid Sphere in a Uniform Streaming Flow at Small, but Nonzero, Peclet Numbers 456 Heat Transfer from a Body of Arbitrary Shape in a Uniform Streaming Flow at Small, but Nonzero, Peclet Numbers 470 Heat Transfer from a Sphere in Simple Shear Flow at Low Peclet Numbers 477 Uniform Flow Past a Solid Sphere at Small, but Nonzero, Reynolds Numbers 488 CHAPTER 9 Strona Convection Effects in Heat and Mass Transfer at Low Reynolds Number 511 Heat Transfer from a Solid Sphere in Streaming Flow for Small Reynolds Number and Large Peclet Number 513 Generalization of the Correlation Between Nu and Pe to Solid Bodies of Nonspherical Shape in Uniform Streaming Flow 526 Boundary-Layer Analysis of Heat Transfer from a Solid Sphere in Generalized Shear Flows at Low Reynolds Number 532 Mass Transfer from a Bubble or Drop that Translates Through a Quiescent Fluid at Low Re and Large Pe 536 Heat Transfer at High Peclet Number across Regions of Closed-Streamline Flow 540 CHAPTER 1 0 Laminar Boundary-Layer Theory 557 Potential Flow Theory 558 The Boundary-Layer Equations 565

5 xii LAMINAR FLOW AND CONVECTIVE TRANSPORT PROCESSES Streaming Flow Past a Horizontal Fiat Plate The Blasius Solution 575 Streaming Flow Past a Semi-Infinite Wedge The Falkner-Skan Solution 582 Streaming Flow Past Cylindrical Bodies Boundary-Layer Separation 589 An Approximate Method to Estimate Shear Stress in Boundary-Layer Flows 598 Streaming Flow Past Axisymmetric Bodies A Generalization of die Blasius Series 603 The Boundary-Layer on a Spherical Bubble 609 CHAPTER 1 Thermal Boundary-Layer Theory at Large Reynolds Number 637 Governing Equations (Re» 1, Pe» 1, with Pr Arbitrary) 638 Exact Solutions for Pr ~ 0(1) 641 The Asymptotic Limit, Pr 5S> The Asymptotic Limit, Pr<SC Discussion of the Asymptotic Results for Pr <3C 1 and Pr» Approximate Results for Surface Temperature with Specified Heat Flux or Mixed Boundary Conditions 660 CHAPTER 1 2 Natural and Mixed Convection Flows 669 The Boussinesq Equations 670 Natural Convection Boundary-Layers at High Grasshof Numbers 673 The Laminar Plume Above a Line or Point Source of Heat 691 Combined Forced and Free Convection 700 Natural Convection in a Horizontal Fluid Layer Heated From Below The Rayleigh-Benard Problem 718 Index 733