Viscous Fluid Flow – Tasos C. Papanastasiou, Georgios C. Georgiou – 1st Edition

1. Vector and Tensor Calculus
1.1 Systems of coordinates
1.2 Vectors
1.2.1 Vectors in fluid mechanics
1.2.2 Unit tangent and normal vectors
1.3 Tensors
1.3.1 Principal directions and invariants
1.3.2 Index notation and summation convention
1.3.3 Tensors in fluid mechanics
1.4 Differential operators
1.4.1 The substantial derivative
1.5 Integral theorems
1.6 Problems
1.7 References
2. Introduction to the Continuum Fluid
2.1 Properties of the continuum fluid
2.2 Macroscopic and microscopic balances
2.3 Local fluid kinematics
2.4 Elementary fluid motions
2.5 Problems
2.6 References
3. Conservation Laws
3.1 Control volume and surroundings
3.2 The general equations of conservation
3.3 The differential forms of the conservation equations
3.4 Problems
3.5 References
4. Static Equilibrium of Fluids and Interfaces
4.1 Mechanics of static equilibrium
4.2 Mechanics of fluid interfaces
4.2.1 Interfaces in static equilibrium
4.3 Problems
4.4 References
5. The Navier-Stokes Equations
5.1 The Newtonian liquid
5.2 Alternative forms of the Navier-Stokes equations
5.3 Boundary conditions
5.4 Problems
5.5 References
6. Unidirectional Flows
6.1 Steady, one-dimensional rectilinear flows
6.2 Steady, axisymmetric rectilinear flows
6.3 Steady, axisymmetric torsional flows
6.4 Steady, axisymmetric radial flows
6.5 Steady, spherically symmetric radial flows
6.6 Transient one-dimensional unidirectional flows
6.7 Steady two-dimensional rectilinear flows
6.8 Problems
6.9 References
7. Approximate Methods
7.1 Dimensional analysis
7.1.1 Non-dimensionalization of the governing equations
7.2 Perturbation methods
7.2.2 Singular perturbations
7.3 Perturbation methods in fluid mechanics
7.4 Problems
7.5 References
8. Laminar Boundary Layer Flows
8.1 Boundary layer flow
8.2 Boundary layer equations
8.3 Approximate momentum integral theory
8.4 Boundary layers within accelerating potential flow
8.5 Flow over non-slender planar bodies
8.6 Rotational boundary layers
8.7 Problems
8.8 References
9. Almost Unidirectional Flows
9.1 Lubrication flows
9.1.1 Lubrication vs. rectilinear flow
9.1.2 Derivation of lubrication equations
9.1.3 Reynolds equation for lubrication
9.1.4 Lubrication flows in two directions
9.2 Stretching flows
9.2.1 Fiber spinning
9.2.2 Compression molding
9.3 Problems
9.4 References
10. Creeping Bidirectional Flows
10.1 Plane flow in polar coordinates
10.2 Axisymmetric flow in cylindrical coordinates
10.3 Axisymmetric flow in spherical coordinates
10.4 Problems
10.5 References
List of Symbols