Slow viscous flow:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cham [u.a.]
Springer
2014
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 324 S. graph. Darst. |
| ISBN: | 9783319038346 |
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MARC
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| 245 | 1 | 0 | |a Slow viscous flow |c William E. Langlois ; Michel O. Deville |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Cham [u.a.] |b Springer |c 2014 | |
| 300 | |a XV, 324 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Viscous flow | |
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Record in the Search Index
| _version_ | 1804152197843255296 |
|---|---|
| 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)1032149256 |
| author_facet | Langlois, William E. Deville, Michel 1945- |
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| author_sort | Langlois, William E. |
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| dewey-ones | 532 - Fluid mechanics |
| dewey-raw | 532.5 |
| dewey-search | 532.5 |
| dewey-sort | 3532.5 |
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| discipline | Physik |
| edition | 2. ed. |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-10T01:06:53Z |
| institution | BVB |
| isbn | 9783319038346 |
| language | English |
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| physical | XV, 324 S. graph. Darst. |
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| spelling | Langlois, William E. Verfasser aut Slow viscous flow William E. Langlois ; Michel O. Deville 2. ed. Cham [u.a.] Springer 2014 XV, 324 S. graph. Darst. 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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