Slow viscous flow:
Gespeichert in:
| Hauptverfasser: | , |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cham, [u.a.]
Springer
[2014]
|
| Ausgabe: | Second edition |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xv, 324 Seiten Illustrationen |
| ISBN: | 9783319038346 |
Internformat
MARC
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| 100 | 1 | |a Langlois, William E. |0 (DE-588)1229523049 |4 aut | |
| 245 | 1 | 0 | |a Slow viscous flow |c William E. Langlois ; Michel O. Deville |
| 250 | |a Second edition | ||
| 264 | 1 | |a Cham, [u.a.] |b Springer |c [2014] | |
| 264 | 4 | |c © 2014 | |
| 300 | |a xv, 324 Seiten |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Viscous flow | |
| 650 | 0 | 7 | |a Viskose Strömung |0 (DE-588)4226965-9 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1829213158416318464 |
|---|---|
| adam_text |
Titel: Slow viscous flow
Autor: Langlois, William E
Jahr: 2014
Contents
1 Cartesian Tensors.1
1.1 The Classical Notation.1
1.2 Suffix Notation.6
1.3 The Summation Convention.8
1.4 The Kronccker Delta and the Alternating Tensor.9
1.5 Orthogonal Transformations .11
1.6 Basic Properties of Cartesian Tensors .15
1.7 Isotropic Tensors.17
2 The Equations of Viscous Flow .19
2.1 Kinematics of Flow.19
2.1.1 Description of Deformation in a Fixed
Coordinate System.20
2.1.2 Description of Deformation in a Moving
Coordinate System.29
2.2 Dynamics of Flow .35
2.2.1 Conservation of Momentum.38
2.2.2 Conservation of Angular Momentum.40
2.2.3 The Constitutive Equation for a Newtonian
Viscous Fluid.42
2.2.4 The Constitutive Equation
for a Non-Newtonian Viscous Fluid.48
2.3 Energy Considerations.52
2.3.1 Conservation of Energy in Continuous Media.53
2.3.2 The Energy Equation for a Newtonian
Viscous Fluid.56
2.3.3 Second Principle of Thermodynamics.57
2.4 Incompressible Fluids .59
2.4.1 The Boussinesq Approximation.62
2.5 The Hydrodynamic Equations in Summary.63
2.5.1 Boussinesq Equations.64
xi
Contents
xii
2.6 Boundary Conditions.^
2.6.1 The No-Slip Condition.£4
2.6.2 Force Boundary Conditions.
2.6.3 Thermocapillary Flow .68
2.6.4 Other Boundary Conditions .69
2.7 Similarity Considerations.70
2.7.1 Similarity Rules for Steady, Incompressible
Flow Without Body Forces When No Free
Surface Is Present.71
2.7.2 Similarity Rules for Unsteady,
Incompressible Flow Without Body Forces
When No Free Surface Is Present.73
2.8 Vorticity Transfer.7^
3 Curvilinear Coordinates.81
3.1 General Tensor Analysis.81
3.1.1 Coordinate Transformations.82
3.1.2 The Metric Tensors.85
3.1.3 The Christoffel Symbols: Covariant Differentiation.87
3.1.4 Ricci's Lemma.90
3.2 The Hydrodynamic Equations in General Tensor Form.91
3.3 Orthogonal Curvilinear Coordinates: Physical
Components of Tensors.93
3.3.1 Cylindrical Polar Coordinates.96
3.3.2 Spherical Polar Coordinates.100
4 Exact Solutions to the Equations of Viscous Flow.105
4.1 Rectilinear Flow Between Parallel Plates.106
4.2 Plane Shear Flow of a Non-Newtonian Fluid.108
4.3 The Flow Generated by an Oscillating Plate .109
4.4 Transient Flow in a Semi-infinite Space.Ill
4.5 Channel Flow with a Pulsatile Pressure Gradient.113
4.6 Poiseuille Flow.116
4.7 Starting Transient Poiseuille Flow.119
4.8 Pulsating Flow in a Circular Pipe.122
4.9 Helical Flow in an Annular Region.124
4.9.1 The Newtonian Case.124
4.9.2 The Non-Newtonian Circular Couette Flow.126
4.10 Hamel's Problem: Flow in a Wedge-Shaped Region.127
4.10.1 The Axisymmetric Analog of Hamel's Problem.130
4.11 Bubble Dynamics.131
4.12 The Flow Generated by a Rotating Disc.134
4.13 Free Surface Flow over an Inclined Plane.136
4.14 Natural Convection Between Two Differentially
Heated Vertical Parallel Walls.137
4.15 Flow Behind a Grid. .no
Contents xiii
4.16 Plane Periodic Solutions.141
4.17 Summary.142
5 Pipe Flow.145
5.1 Poisson's Equation for the Velocity.145
5.2 Polynomial Solutions.147
5.2.1 The Elliptical Pipe .147
5.2.2 The Triangular Pipe.148
5.3 Separation of Variables: The Rectangular Pipe.149
5.4 Conformal Mapping Methods.152
5.4.1 Multiply-Connected Regions: Flow Between
Eccentric Cylinders.154
6 Flow Past a Sphere.159
6.1 The Equations of Creeping Viscous Flow.159
6.2 Creeping Flow Past a Sphere.161
6.3 Oseen's Criticism.167
6.4 Matching Techniques.173
6.5 Flow Past Non-spherical Obstacles.180
6.6 Stokcslets .180
6.6.1 Propulsion of Microorganisms.181
7 Plane Flow.183
7.1 Description of Plane Creeping Flow in Terms
of Complex Potentials.184
7.2 The Uniqueness Theorem for Creeping Flows
in Bounded Regions.187
7.3 The Stokes Paradox.190
7.4 Conformal Mapping and Biharmonic Flow .196
7.5 Pressure Flow Through a Channel of Varying Width.201
7.5.1 Wall Slope Everywhere Negligible.202
7.5.2 Wall Curvature Everywhere Negligible.203
7.5.3 Power Series Expansion in the Wall Slope.207
7.5.4 The Flow Through a Smooth Constriction.208
7.6 Hele-Shaw Flow.210
8 Rotary Flow.213
8.1 The Equations Governing Creeping Rotary Flow.214
8.2 Flow Between Parallel Discs.215
8.3 Flow Between Coaxial Cones.217
8.4 Flow Between Concentric Spheres.220
8.4.1 Secondary Flow.222
8.5 Rotlets.227
9 Lubrication Theory .229
9.1 Physical Origins of Fluid-Film Lubrication.230
9.2 The Mathematical Foundations of Lubrication Theory.232
XIV
Contents
9.3 Slider Bearings.~
9.4 Externally Pressurized Bearings .—
9.5 Squeeze Films.~
9.6 Journal Bearings."
9.6.1 The Wannicr Flow.-l
10 Introduction to the Finite Element Method .251
10.1 Weak Formulation.
10.2 The Finite Elements.254
10.3 One-Dimensional Q i Lagrange Element.
10.4 One-Dimensional Q2 Lagrange Element.257
10.5 Implementation of the Galcrkin Method.258
10.6 Natural Boundary Conditions.261
10.7 Multidimensional Finite Elements.262
10.7.1 Two-Dimensional Q\ Element.263
10.7.2 Implementation of the 2D Galcrkin Method.264
10.7.3 Three-Dimensional Q1 Element .265
10.8 Two-Dimensional Qj Element.266
10.9 Triangular Elements .267
10.9.1 P1 Finite Element.267
10.9.2 P2 Finite Element.268
10.10 Spectral and Mortar Element Method.269
11 Variational Principle, Weak Formulation and Finite Elements.271
U.l Variational Principle.271
11.2 Weak Form of the Stokes Problem.273
11.3 Finite Element Discretization of the Stokes Equation.275
11.4 Stable Finite Elements for Viscous Incompressible Fluids.277
11.5 Unsteady Stokes Equation.279
11.6 Advcction-Diffusion Equation.282
11.6.1 One Dimensional Burgers Equation.282
11.6.2 Multidimensional Burgers Equation .286
11.7 Navicr-Stokes Equation.287
11.8 Spectral Elements for the Navicr-Stokes Equation.288
12 Stokes Flow and Corner Eddies.293
12.1 Two-Dimensional Corners.293
12.2 The Paint-Scraper Problem.295
12.3 Two-Dimensional Corner Eddies .296
12.3.1 Real Solutions for A (a 73.15°).298
12.3.2 Complex Solutions for A (a 73.15°) .298
12.4 Stokes Eigenmodcs and Corner Eddies.300
12.4.1 Periodic Stokes Eigcnmodes.301
12.4.2 Channel Flow Stokes Eigenmodcs. . 301
Contents xv
12.4.3 Stokes Eigenmodcs in the Square Domain.303
12.4.4 Corner Modes in the Cubic Domain.304
12.5 Three-Dimensional Stokes Solution.304
Appendix Comments on Some Bibliographical Entries.307
References.311
Index. 317 |
| any_adam_object | 1 |
| author | Langlois, William E. Deville, Michel 1945- |
| author_GND | (DE-588)1229523049 (DE-588)1032149256 |
| author_facet | Langlois, William E. Deville, Michel 1945- |
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| author_sort | Langlois, William E. |
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| classification_rvk | UF 4000 |
| ctrlnum | (OCoLC)889970155 (DE-599)BVBBV041851276 |
| dewey-full | 532.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 532 - Fluid mechanics |
| dewey-raw | 532.5 |
| dewey-search | 532.5 |
| dewey-sort | 3532.5 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| edition | Second edition |
| format | Book |
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| id | DE-604.BV041851276 |
| illustrated | Illustrated |
| indexdate | 2025-04-12T16:00:08Z |
| institution | BVB |
| isbn | 9783319038346 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027295729 |
| oclc_num | 889970155 |
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| physical | xv, 324 Seiten Illustrationen |
| publishDate | 2014 |
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| publisher | Springer |
| record_format | marc |
| spelling | Langlois, William E. (DE-588)1229523049 aut Slow viscous flow William E. Langlois ; Michel O. Deville Second edition Cham, [u.a.] Springer [2014] © 2014 xv, 324 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Viscous flow Viskose Strömung (DE-588)4226965-9 gnd rswk-swf Viskose Strömung (DE-588)4226965-9 s DE-604 Deville, Michel 1945- Verfasser (DE-588)1032149256 aut Erscheint auch als Online-Ausgabe 978-3-319-03835-3 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027295729&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Langlois, William E. Deville, Michel 1945- Slow viscous flow Viscous flow Viskose Strömung (DE-588)4226965-9 gnd |
| subject_GND | (DE-588)4226965-9 |
| title | Slow viscous flow |
| title_auth | Slow viscous flow |
| title_exact_search | Slow viscous flow |
| title_full | Slow viscous flow William E. Langlois ; Michel O. Deville |
| title_fullStr | Slow viscous flow William E. Langlois ; Michel O. Deville |
| title_full_unstemmed | Slow viscous flow William E. Langlois ; Michel O. Deville |
| title_short | Slow viscous flow |
| title_sort | slow viscous flow |
| topic | Viscous flow Viskose Strömung (DE-588)4226965-9 gnd |
| topic_facet | Viscous flow Viskose Strömung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027295729&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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