Analytical Solutions for Transport Processes (eBook)

Preface 7
Acknowledgements 9
Contents 10
Acronyms 14
Part I Fluid Mechanics 15
1 The Equations of Change in Fluid Mechanics and Their Analytical Solutions 16
1.1 The Equations of Change in Fluid Mechanics 16
1.2 Exact Solutions of the Equations of Change 18
1.2.1 Hydraulically Developed Flow 19
1.2.2 Further Exact Solutions 20
1.3 Approaches by Solving Simplified Equations of Change 20
1.3.1 Slender Flow Fields with Negligible Inertial Influence---The Lubrication Approximation 21
1.3.2 Slender Flow Fields at High Reynolds Number---The Boundary-Layer Approximation 24
1.3.3 Quasi One-Dimensional Flow 26
1.3.4 Quasi One-Dimensional Flow in a Slender Liquid Jet 31
1.3.5 Quasi One-Dimensional Flow in a Boundary Layer 33
References 36
2 The Equation for the Stokesian Stream Function and Its Solutions 37
2.1 The Equation for the Stream Function in Cartesian Coordinates 37
2.1.1 Linear, Unsteady Flow 39
2.1.2 Linear, Steady Flow 43
2.1.3 Nonlinear, Steady Flow with Constant Pressure 44
2.2 The Equation for the Stream Function in Cylindrical Coordinates 46
2.2.1 Polar, Linear, Unsteady Flow 47
2.2.2 Polar, Linear, Steady Flow 48
2.2.3 Polar, Nonlinear, Steady Flow 49
2.2.4 Axisymmetric, Linear, Unsteady Flow 50
2.2.5 Axisymmetric, Linear, Steady Flow 54
2.2.6 Axisymmetric, Nonlinear, Steady Flow with Constant Pressure 55
2.3 The Equation for the Stream Function in Spherical Coordinates 57
2.3.1 Linear, Unsteady Flow 58
2.3.2 Linear, Steady Flow 59
2.3.3 Nonlinear, Steady Flow with Constant Pressure 60
References 61
3 Laminar Two-Dimensional Flow 62
3.1 Steady Flow 62
3.1.1 Channel and Pipe Flows 62
3.1.2 Flow Between Coaxial Spinning Cylinders 67
3.1.3 Flow Outside a Spinning Sphere 68
3.1.4 Duct Flow with Injection and Suction Through the Walls 70
3.2 Unsteady Flow 73
3.2.1 The Two Stokesian Problems 73
3.2.2 Flow Outside a Cylinder in Oscillatory Spinning Motion 78
3.2.3 Starting and Fading Plane Couette Flow 80
3.2.4 Starting and Fading Channel and Pipe Flows 83
3.2.5 Pulsating Pipe Flow 89
3.2.6 Onset of Flow Between Two Concentric Spherical Shells 91
References 95
4 Lubrication Flow 96
4.1 Lubrication Approximation 96
4.2 Plane Slide Bearing 99
4.3 Pressure-Driven Flow Through a Plane Gap 101
4.4 Cylindrical Bearing 102
4.5 Pressure-Driven Flow Through a Cylindrical Gap 105
4.6 Pressure-Driven Flow Through a Spherical Gap 107
4.7 Wire Coating---Extended Lubrication Theory 109
References 111
5 Boundary-Layer Flow 112
5.1 Laminar Flow Along a Flat Plate 112
5.2 Flow Along a Slender Body of Revolution 116
5.3 Plane Submerged Free Jet 119
5.4 Axisymmetric Submerged Free Jet 123
5.5 Plane Free Shear Layer 129
5.6 Wake Behind a Flat Plate 131
References 133
6 Flows with Interfaces 134
6.1 Linear Temporal Instability of a Plane Liquid Sheet 134
6.2 Linear Temporal Capillary Instability of a Liquid Jet 141
6.3 Linear Spatial Capillary Instability of a Liquid Jet 151
6.4 Linear Oscillations of Drops and Bubbles 153
6.4.1 Linear Shape Oscillations of a Viscoelastic Drop 155
6.4.2 Linear Shape Oscillations of a Bubble in a Viscoelastic Liquid 165
6.5 Liquid Films from Drop Impact on Solid Substrates 176
6.6 Steady Creeping Flow Around a Spherical Particle 177
6.6.1 Hadamard--Rybczynski Flow Around a Fluid Spherical Particle 178
6.6.2 Stokes Flow Around a Solid Spherical Particle 181
References 183
Part II Heat and Mass Transfer 185
7 The Equations of Change for Heat and Mass Transfer and Their Analytical Solutions 186
7.1 The Thermal Energy Equation 186
7.2 Concepts for Simplifying the Thermal Energy Equation 187
7.3 The Equations of Change for Mass Transport 189
7.3.1 The Description of Fluid Mixtures 189
7.3.2 The Continuity Equation for a Mixture Component 191
7.4 Concepts for Simplifying the Continuity Equations 196
References 197
8 Heat Transfer 198
8.1 Heat Conduction 198
8.1.1 Steady Heat Conduction 199
8.1.2 Unsteady Heat Conduction---Early After Start or in Infinite Systems 206
8.1.3 Unsteady Heat Conduction---Long After Start in Finite Systems 209
8.2 Heat Transfer with Lumped Capacitances of Simple Geometries 230
8.3 Convective Heat Transport---Forced Convection 231
8.3.1 Heat Transfer Across a Flat-Plate Surface in Parallel Flow 232
8.3.2 Laminar Pipe Flow with Heat Transfer 236
8.4 Convective Heat Transport---Natural Convection 238
8.4.1 Natural Convection Along a Vertical Flat Plate 240
8.4.2 Natural Convection Between Two Vertical Flat Plates 244
References 246
9 Mass Transfer 247
9.1 Steady Diffusive Mass Transport---Equimolar and Stefan Flow 247
9.2 Diffusive Transfer Across Spherical, Spheroidal and Hyperboloidal Interfaces 249
9.2.1 Introduction 249
9.2.2 The Sherwood Number of Equimolar Diffusion for a Sphere 249
9.2.3 The Sherwood Number of Equimolar Diffusion on Spheroidal and Hyperboloidal Surfaces 251
9.3 Convective Mass Transfer from Flat Plate Surfaces 260
9.4 Liquid Phase Analysis in the Convective Drying of Drops 264
9.4.1 Introduction 264
9.4.2 Mathematical Description 265
9.4.3 Definition of the Problem 265
9.4.4 Analytical Solution of the Problem 269
9.4.5 Evaluation of the Equations and Example Calculations 273
References 277
Part IIIAppendices 279
Appendix AThe Equations of Change in TransportProcesses 280
Appendix BBasic Vector Analytical Operations 289
Appendix CSpecial Functions of Mathematical Physics 293
Index 305