Laminar Viscous Flow

1 Properties of Fluids.- 1.1. Physical Properties of Fluids.- 1.1.1. Liquids.- 1.1.2. Gases.- 1.1.3. Thermodynamic Notions.- 1.2. Transfer Properties.- 1.2.1. Viscosity.- 1.2.2. Thermal Conductivity.- 1.2.3. Fluid Mixtures. Mass Transfer.- 1.2.4. Non-Newtonian Media.- 2 Fundamental Equations of Viscous Flow.- 2.1. Kinematics of Fluid Flow.- 2.1.1. Lagrangian and Eulerian Descriptions.- 2.1.2. Strain Rates.- 2.1.3. Circulation. Stokes' Theorem.- 2.2. Equations of Motion.- 2.2.1. Continuity Equation.- 2.2.2. The Equations of Motion in Stresses.- 2.2.3. The Constitutive Relation for a Newtonian Fluid.- 2.2.4. Remarks on the Second Coefficient of Viscosity.- 2.2.5. Navier-Stokes Equations.- 2.2.6. Noninertial Coordinate System.- 2.3. The Energy Equation.- 2.3.1. Energy Balance for a Fluid Particle.- 2.3.2. Energy Equation for Incompressible Fluids.- 2.3.3. Energy Equation for Compressible Fluids.- 2.4 Orthogonal Curvilinear Coordinate Systems.- 2.4.1. Cylindrical Coordinates.- 2.4.2. Spherical Coordinates.- 3 Basic Equations and Flow Pattern.- 3.1. Posing the Problem of Fluid Flow.- 3.1.1. Assumptions Involved and Mathematical Character of the Basic Equations.- 3.1.2. Initial and Boundary Conditions.- 3.2. Dimensionless Parameters in Viscous Fluid Flow.- 3.2.1. Dimensionless Parameters in Navier-Stokes Equations.- 3.2.2. Dimensionless Parameters in the Energy Equation.- 3.3. Viscous Flow Pattern.- 3.3.1. Pure Viscous Flow.- 3.3.2. Visco-inertial Flow.- 3.3.3. The Boundary'Layer Concept.- 3.4. Other Forms of the Basic Equations.- 3.4.1. The Conservative (Eulerian) Form of the Basic Equations.- 3.4.2. The Equation for Vorticity.- 3.4.3. Two-Dimensional Row.- 3.4.4. Integral Relations (Control Volume Formulation).- 4 Steady Parallel Flow of Incompressible Fluids.- 4.1. Plane Parallel Flow.- 4.1.1. Couette Flow.- 4.1.2. Channel (Poiseuille) Flow.- 4.1.3. Open Channel Flow.- 4.1.4. Combined Couette-Poiseuille Flow.- 4.2. General Couette Flow.- 4.2.1 Two Circular Cylinders.- 4.2.2. Translation of a Semiplane in a Channel.- 4.3. Duct Flow.- 4.3.1. Circular Pipe.- 4.3.2. Ducts of Various Cross Sections.- 4.3.3. Hydraulic Radius.- 4.3.4. Analysis of a System of Ducts.- 4.4. Steady Parallel Flow of Viscoplastic Media.- 4.4.1. Plane Parallel Flow.- 4.4.2. Circular Duct.- 4.5. Influence of Porous Surfaces.- 4.5.1. Quasi-Parallel Flow.- 4.5.2. Channel and Duct Flow.- 5 Other Solutions of Navier-Stokes Equations (Steady Incompressible Flow).- 5.1. Flow upon Concentric Circles.- 5.1.1. Coaxial Rotating Cylinders.- 5.1.2. Particular Cases (Vortex).- 5.2. Motions upon Concurrent Lines.- 5.2.1. Motion between Two Nonparallel Walls.- 5.2.2. Approximate Solutions.- 5.3. Self-Similar Solutions.- 5.3.1. Flow Near a Stagnation Point.- 5.3.2. Flow Near a Rotating Disk.- 5.3.3. Fluid Rotation Near a Plane.- 5.4. Other Solutions.- 5.4.1. Solutions for the Stream Function.- 5.4.2. Pseudo-Plane Motions (Noninertial Coordinates).- 6 Unsteady Viscous Incompressible Flow.- 6.1. Parallel Unsteady Flow.- 6.1.1. General Remarks.- 6.1.2. Plane Unsteady Parallel Flow.- 6.1.3. Examples of Unsteady Parallel Flows.- 6.1.4. Parallel Axisymmetric Row in Ducts.- 6.2. Other Unsteady Motions.- 6.2.1. Unsteady Flow upon Concentric Circles.- 6.2.2. Plane Unsteady Flow.- 6.2.3. Three-Dimensional Unsteady Row.- 7 Thermal Effects in Incompressible Flow.- 7.1. Thermal Effects in Plane Couette Flow.- 7.1.1. Constant Wall Temperature.- 7.1.2. Adiabatic Wall.- 7.1.3. Variable Viscosity.- 7.1.4. Forced Heat Transfer in Slow Motion.- 7.2. Temperature Field in Flow Near Walls.- 7.2.1. Poiseuille Flow with Constant Viscosity.- 7.2.2. Couette-Poiseuille Flow.- 7.2.3. Free Convection between Parallel Walls.- 7.2.4. Temperature Field in Flow between Nonparallel Walls.- 7.2.5. Temperature Field in Flow between Coaxial Rotating Cylinders.- 7.2.6. Temperature Field Near a Stagnation Point.- 7.3. Temperature Field in Duct Flow.- 7.3.1. Influence of Dissipation.- 7.3.2. Circular Pipes.- 7.3.3. Thermal Entrance.- 7.3.4. Extensions.- 8. Compressible Viscous Fluid Flow.- 8.1. Flow between Parallel Plates.- 8.1.1. Couette Flow.- 8.1.2. Isothermal Flow between Parallel Walls.- 8.1.3. Effect of a Transversal Heat Transfer.- 8.2. Shock Wave Structure.- 8.2.1. Shock Structure without Consideration of the Second Coefficient of Viscosity.- 8.2.2. Influence of the Second Coefficient of Viscosity.- 8.2.3. Weak Shock Wave.- 8.3. Viscosity Effccts in Unsteady Flow.- 8.3.1. Impulsive Motion of a Wall.- 8.3.2. Sound Attenuation.- 9 Slow Viscous Flow in Thin Layers (Hydrodynamic Lubrication).- 9.1. Equations of Motion.- 9.1.1. Simplifications of the Equations of Motion.- 9.1.2. The Pressure Equation.- 9.1.3. Mechanisms of Lubrication.- 9.1.4. Boundary Conditions.- 9.2. Liquid Film Lubrication.- 9.2.1. Self-Acting Films.- 9.2.2. Hydrostatic Films.- 9.2.3. Grease Films.- 9.3. Gas Film Lubrication.- 9.3.1. Self-Acting Gas Films.- 9.3.2. Externally Pressurized Gas Films.- 9.4. Elasto-hydrodynamic Lubrication.- 9.4.1. Hydrodynamic Lubrication of Concentrated Contacts.- 9.4.2. Influence of Surface Deformation.- 10 Slow Viscous Flow.- 10.1. General Remarks.- 10.1.1. The Use of Biharmonic Functions.- 10.1.2. Plane Motions.- 10.1.3. Axisymmetric Flow.- 10.1.4. Hele Shaw Flow.- 10.1.5. Extensions of the Hele Shaw Analogy.- 10.2. Slow Rotation of a Viscous Fluid.- 10.2.1. Coordinate Systems.- 10.2.2. Steady Rotation of a Body.- 10.2.3. Unsteady Rotation of a Body.- 10.3. Flow Around Bodies of Revolution.- 10.3.1. Flow Around a Sphere.- 10.3.2. Extensions.- 10.4. Slow Plane Flow.- 10.4.1. General Considerations.- 10.4.2. Direct Methods.- 10.4.3. The Circle Theorem for Slow Viscous Flow.- 11 Visco-inertial Flow in Thin Layers.- 11.1. Incompressible Flow in Thin Layers.- 11.1.1. Approximate Methods.- 11.1.2. Motions between Surfaces at Rest.- 11.1.3. Two-Dimensional Flow between Moving Surfaces.- 11.1.4. Three-Dimensional Flow in Thin Layers.- 11.2. Compressible Flow in Thin Layers.- 11.2.1. General Equations.- 11.2.2. Motions between Surfaces at Rest.- 11.2.3. High-Speed Sliding Motions.- 12 Visco-inertial Flow Around Bodies.- 12.1. Small Perturbation Slow Flow (Oseen Flow).- 12.1.1. General Equations.- 12.1.2. Flow Around a Sphere.- 12.1.3. Plane Flow Past a Circle.- 12.2. Other Approximations for Visco-inertial Flow.- 12.2.1. Small Perturbations from Irrotational Flow.- 12.2.2. Second Direct Approximation for a Slow Flow Around a Sphere. Whitehead's Paradox.- 12.2.3. The Use of the Singular Perturbation Method.- References.