Laminar Viscous Flow

ISBN-13: 9781461287063 / Angielski / Miękka / 2011 / 488 str.

V. N. Constantinescu

Opis

Mechanical engineering, an engineering discipline born of the needs of the industrial revolution, is once again asked to do its substantial share in the call for industrial renewal. The general call is urgent as we face profound issues of productivity and competitiveness that require engineering solutions, among others. The Mechanical Engineering Series is a series featuring graduate texts and research monographs intended to address the need for information in contemporary areas of mechanical engineering. The series is conceived as a comprehensive one that covers a broad range of concentrations important to mechanical engineering graduate education and research. We are fortunate to have a distinguished roster of consulting editors, each an expert in one of the areas of concentration. The names of the consulting editors are listed on the following page of this volume. The areas of concentration are applied mechanics, biomechanics, computational mechanics, dynamic systems and control, energetics, mechanics of materials, processing, thermal science, and tribology. Professor Winer, the consulting editor for tribology, and I are pleased to present this volume of the series: Laminar Viscous Flow, by Professor Constantinescu. The selection of this volume underscores again the interest of the Mechanical Engineering Series to provide our readers with topical monographs as well as graduate texts.

Spis treści

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.