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Transport Phenomena by George Hirasaki - HTML preview
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Transport Phenomena
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Transport Phenomena
Table of Contents
Chapter
1
.
Introduction
1.1
.
Introduction
Prerequisites and text books
Scalar, vector and tensor fields
Curves, surfaces, and volumes
Coordinate systems
Units
Continuum approximation
Densities, potential gradients, and fluxes
Reading assignment
Chapter
2
.
Cartesian Vectors and Tensors: Their Algebra
2.1
.
Definition of a vector
Examples of vectors
Scalar multiplication
Addition of vectors – Coplanar vectors
Unit vectors
Scalar product – Orthogonality
Directional Cosines for Coordinate Transformation
Vector Product
Velocity due to rigid body rotations
Triple scalar product
Triple vector product
Second order tensors
Examples of second order tensors
Scalar multiplication and addition
Contraction and multiplication
The vector of an antisymmetric tensor
Canonical form of a symmetric tensor
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
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)
Exercise
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
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
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
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
Summary of Equations
Summary of Diagrams
New References
Chapter
8
.
Laminar Flows with Dependence on One Dimension
8.1
.
Couette Flow
Plane-Poiseuille and Hele-Shaw flow
Poiseuille Flow
Steady film flow down inclined plane
Unsteady viscous flow
Chapter
9
.
Multidimensional Laminar Flow
9.1
.
Lubrication and Film Flow
Laminar Boundary Layer
Blasius solution for boundary layer flow past a flat plate
Chapter
10
.
Flow with Free Surface
10.1
.
Boundary Conditions at a Fluid-Fluid Interface
Film Drainage and Deposition with Laplace Pressure
Chapter
11
.
Numerical Simulation
11.1
.
The Stream Function - Vorticity Method
Finite Difference Approximation
Solution of Linear Equations
FORTRAN on Owlnet
Transients and Finite Reynolds Number
Calculation of Pressure
Cylindrical-Polar Coordinates
Index
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