Transport Phenomena by George Hirasaki - HTML preview
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Transport Phenomena
Table of Contents
- Chapter 1. Introduction
- Chapter 2. Cartesian Vectors and Tensors: Their Algebra
- 2.1.
- Definition of a vector
- Examples of vectors
- Addition of vectors – Coplanar vectors
- Directional Cosines for Coordinate Transformation
- Vector Product
- Velocity due to rigid body rotations
- Triple scalar product
- Triple vector product
- Second order tensors
- Scalar multiplication and addition
- Contraction and multiplication
- The vector of an antisymmetric tensor
- Canonical form of a symmetric tensor
- 2.1.
- Chapter 3. Cartesian Vectors and Tensors: Their Calculus
- 3.1.
- Tensor functions of time-like variable
- Curves in space
- Line integrals
- Surface integrals
- Volume integrals
- Change of variables with multiple integrals
- Vector fields
- The vector operator ∇-gradient of a scalar
- The divergence of a vector field
- The curl of a vector field
- Green's theorem and some of its variants
- Stokes' theorem
- The classification and representation of vector fields
- Irrotational vector fields
- Solenoidal vector fields
- Helmholtz' representation
- Vector and scalar potential
- Tensor functions of time-like variable
- 3.1.
- Chapter 4. The Kinematics of Fluid Motion
- 4.1.
- Particle paths and material derivatives
- Streamlines
- Streaklines
- Dilatation
- Use of a stream function to satisfy the mass-conservation equation (Batchelor, 1967)
- Reynolds' transport theorem
- Conservation of mass and the equation of continuity
- Deformation and rate of strain
- Physical interpretation of the (rate of) deformation tensor
- Principal axis of deformation
- Vorticity, vortex lines, and tubes
- 4.1.
- Chapter 5. Stress in Fluids
- 5.1.
- Cauchy's stress principle and the conservation of momentum
- The stress tensor
- The symmetry of the stress tensor
- Hydrostatic pressure
- Buoyancy (Deen, 1998)
- Principal axes of stress and the notion of isotropy
- The Stokesian fluid
- Constitutive equations of the Stokesian fluid
- The Newtonian fluid
- Interpretation of the constants λ and μ
- 5.1.
- Chapter 6. Equations of Motion and Energy in Cartesian Coordinates
- 6.1.
- Equations of motion of a Newtonian fluid
- The Reynolds number
- Dissipation of Energy by Viscous Forces
- The energy equation
- The Effect of Compressibility (Batcehlor, 1967)
- Resume of the development of the equations
- Special cases of the equations
- Boundary conditions
- Scaling, Dimensional Analysis, and Similarity
- Bernoulli Theorems
- 6.1.
- Chapter 7. Solution of the Partial Differential Equations
- 7.1.
- Classes of partial differential equations
- Systems described by the Poisson and Laplace equation
- Systems described by the diffusion equation
- Green's function, convolution, and superposition
- Method of Images
- Existence and Uniqueness of the Solution to the Poisson Equation
- Green's function for the diffusion equation
- Convective-Diffusion Equation
- Similarity transformation
- Complex potential for irrotational flow
- Solution of hyperbolic systems
- Mass Balance Across Shock
- New References
- 7.1.
- Chapter 8. Laminar Flows with Dependence on One Dimension
- Chapter 9. Multidimensional Laminar Flow
- Chapter 10. Flow with Free Surface
- Chapter 11. Numerical Simulation
- Index