Brenn Analytical Solutions for Transport Processes

Fluid Mechanics, Heat and Mass Transfer
1. Auflage 2017
ISBN: 978-3-662-51423-8
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 306 Seiten

Reihe: Mathematical Engineering

This book provides analytical solutions to a number of classical problems in transport processes, i.e. in fluid mechanics, heat and mass transfer. Expanding computing power and more efficient numerical methods have increased the importance of computational tools. However, the interpretation of these results is often difficult and the computational results need to be tested against the analytical results, making analytical solutions a valuable commodity. Furthermore, analytical solutions for transport processes provide a much deeper understanding of the physical phenomena involved in a given process than do corresponding numerical solutions. Though this book primarily addresses the needs of researchers and practitioners, it may also be beneficial for graduate students just entering the field. 

Autoren/Hrsg.

Brenn, Günter

Inhaltsverzeichnis

1;Preface;7
2;Acknowledgements;9
3;Contents;10
4;Acronyms;14
5;Part I Fluid Mechanics;15
6;1 The Equations of Change in Fluid Mechanics and Their Analytical Solutions;16
6.1;1.1 The Equations of Change in Fluid Mechanics;16
6.2;1.2 Exact Solutions of the Equations of Change;18
6.2.1;1.2.1 Hydraulically Developed Flow;19
6.2.2;1.2.2 Further Exact Solutions;20
6.3;1.3 Approaches by Solving Simplified Equations of Change;20
6.3.1;1.3.1 Slender Flow Fields with Negligible Inertial Influence---The Lubrication Approximation;21
6.3.2;1.3.2 Slender Flow Fields at High Reynolds Number---The Boundary-Layer Approximation;24
6.3.3;1.3.3 Quasi One-Dimensional Flow;26
6.3.4;1.3.4 Quasi One-Dimensional Flow in a Slender Liquid Jet;31
6.3.5;1.3.5 Quasi One-Dimensional Flow in a Boundary Layer;33
6.4;References;36
7;2 The Equation for the Stokesian Stream Function and Its Solutions;37
7.1;2.1 The Equation for the Stream Function in Cartesian Coordinates;37
7.1.1;2.1.1 Linear, Unsteady Flow;39
7.1.2;2.1.2 Linear, Steady Flow;43
7.1.3;2.1.3 Nonlinear, Steady Flow with Constant Pressure;44
7.2;2.2 The Equation for the Stream Function in Cylindrical Coordinates;46
7.2.1;2.2.1 Polar, Linear, Unsteady Flow;47
7.2.2;2.2.2 Polar, Linear, Steady Flow;48
7.2.3;2.2.3 Polar, Nonlinear, Steady Flow;49
7.2.4;2.2.4 Axisymmetric, Linear, Unsteady Flow;50
7.2.5;2.2.5 Axisymmetric, Linear, Steady Flow;54
7.2.6;2.2.6 Axisymmetric, Nonlinear, Steady Flow with Constant Pressure;55
7.3;2.3 The Equation for the Stream Function in Spherical Coordinates;57
7.3.1;2.3.1 Linear, Unsteady Flow;58
7.3.2;2.3.2 Linear, Steady Flow;59
7.3.3;2.3.3 Nonlinear, Steady Flow with Constant Pressure;60
7.4;References;61
8;3 Laminar Two-Dimensional Flow;62
8.1;3.1 Steady Flow;62
8.1.1;3.1.1 Channel and Pipe Flows;62
8.1.2;3.1.2 Flow Between Coaxial Spinning Cylinders;67
8.1.3;3.1.3 Flow Outside a Spinning Sphere;68
8.1.4;3.1.4 Duct Flow with Injection and Suction Through the Walls;70
8.2;3.2 Unsteady Flow;73
8.2.1;3.2.1 The Two Stokesian Problems;73
8.2.2;3.2.2 Flow Outside a Cylinder in Oscillatory Spinning Motion;78
8.2.3;3.2.3 Starting and Fading Plane Couette Flow;80
8.2.4;3.2.4 Starting and Fading Channel and Pipe Flows;83
8.2.5;3.2.5 Pulsating Pipe Flow;89
8.2.6;3.2.6 Onset of Flow Between Two Concentric Spherical Shells;91
8.3;References;95
9;4 Lubrication Flow;96
9.1;4.1 Lubrication Approximation;96
9.2;4.2 Plane Slide Bearing;99
9.3;4.3 Pressure-Driven Flow Through a Plane Gap;101
9.4;4.4 Cylindrical Bearing;102
9.5;4.5 Pressure-Driven Flow Through a Cylindrical Gap;105
9.6;4.6 Pressure-Driven Flow Through a Spherical Gap;107
9.7;4.7 Wire Coating---Extended Lubrication Theory;109
9.8;References;111
10;5 Boundary-Layer Flow;112
10.1;5.1 Laminar Flow Along a Flat Plate;112
10.2;5.2 Flow Along a Slender Body of Revolution;116
10.3;5.3 Plane Submerged Free Jet;119
10.4;5.4 Axisymmetric Submerged Free Jet;123
10.5;5.5 Plane Free Shear Layer;129
10.6;5.6 Wake Behind a Flat Plate;131
10.7;References;133
11;6 Flows with Interfaces;134
11.1;6.1 Linear Temporal Instability of a Plane Liquid Sheet;134
11.2;6.2 Linear Temporal Capillary Instability of a Liquid Jet;141
11.3;6.3 Linear Spatial Capillary Instability of a Liquid Jet;151
11.4;6.4 Linear Oscillations of Drops and Bubbles;153
11.4.1;6.4.1 Linear Shape Oscillations of a Viscoelastic Drop;155
11.4.2;6.4.2 Linear Shape Oscillations of a Bubble in a Viscoelastic Liquid;165
11.5;6.5 Liquid Films from Drop Impact on Solid Substrates;176
11.6;6.6 Steady Creeping Flow Around a Spherical Particle;177
11.6.1;6.6.1 Hadamard--Rybczynski Flow Around a Fluid Spherical Particle;178
11.6.2;6.6.2 Stokes Flow Around a Solid Spherical Particle;181
11.7;References;183
12;Part II Heat and Mass Transfer;185
13;7 The Equations of Change for Heat and Mass Transfer and Their Analytical Solutions;186
13.1;7.1 The Thermal Energy Equation;186
13.2;7.2 Concepts for Simplifying the Thermal Energy Equation;187
13.3;7.3 The Equations of Change for Mass Transport;189
13.3.1;7.3.1 The Description of Fluid Mixtures;189
13.3.2;7.3.2 The Continuity Equation for a Mixture Component;191
13.4;7.4 Concepts for Simplifying the Continuity Equations;196
13.5;References;197
14;8 Heat Transfer;198
14.1;8.1 Heat Conduction;198
14.1.1;8.1.1 Steady Heat Conduction;199
14.1.2;8.1.2 Unsteady Heat Conduction---Early After Start or in Infinite Systems;206
14.1.3;8.1.3 Unsteady Heat Conduction---Long After Start in Finite Systems;209
14.2;8.2 Heat Transfer with Lumped Capacitances of Simple Geometries;230
14.3;8.3 Convective Heat Transport---Forced Convection;231
14.3.1;8.3.1 Heat Transfer Across a Flat-Plate Surface in Parallel Flow;232
14.3.2;8.3.2 Laminar Pipe Flow with Heat Transfer;236
14.4;8.4 Convective Heat Transport---Natural Convection;238
14.4.1;8.4.1 Natural Convection Along a Vertical Flat Plate;240
14.4.2;8.4.2 Natural Convection Between Two Vertical Flat Plates;244
14.5;References;246
15;9 Mass Transfer;247
15.1;9.1 Steady Diffusive Mass Transport---Equimolar and Stefan Flow;247
15.2;9.2 Diffusive Transfer Across Spherical, Spheroidal and Hyperboloidal Interfaces;249
15.2.1;9.2.1 Introduction;249
15.2.2;9.2.2 The Sherwood Number of Equimolar Diffusion for a Sphere;249
15.2.3;9.2.3 The Sherwood Number of Equimolar Diffusion on Spheroidal and Hyperboloidal Surfaces;251
15.3;9.3 Convective Mass Transfer from Flat Plate Surfaces;260
15.4;9.4 Liquid Phase Analysis in the Convective Drying of Drops;264
15.4.1;9.4.1 Introduction;264
15.4.2;9.4.2 Mathematical Description;265
15.4.3;9.4.3 Definition of the Problem;265
15.4.4;9.4.4 Analytical Solution of the Problem;269
15.4.5;9.4.5 Evaluation of the Equations and Example Calculations;273
15.5;References;277
16;Part IIIAppendices;279
17;Appendix AThe Equations of Change in TransportProcesses;280
18;Appendix BBasic Vector Analytical Operations;289
19;Appendix CSpecial Functions of Mathematical Physics;293
20;Index;305