Preface
1 Introduction
Scope of the Book
Methods of Prediction
Experimental Investigation
Theoretical Calculation
Advantages of a Theoretical Calculation
Disadvantages of a Theoretical Calculation
Choice of Prediction Method
Outline of the Book
2 Mathematical Description of Physical Phenomena
Governing Differential Equations
Meaning of a Differential Equation
Conservation of a Chemical Species
The Energy Equation
A Momentum Equation
The Time-Averaged Equations for Turbulent Flow
The Turbulence-Kinetic-Energy Equation
The General Differential Equation
Nature Coordinates
Independent Variables
Proper Choice of Coordinates
One-Way and Two-Way Coordinates
Problems
3 Discretization Methods
The Nature of Numerical Methods
The Task
The Discretization Concept
The Structure of the Discretization Equation
Methods of Deriving the Discretization Equations
Taylor-Series Formulation
Variational Formulation
Method of Weighted Residuals
Control-Volume Formulation
An Illustrative Example
The Four Basic Rules
Closure
Problems
4 Heat Conduction
Objectives of the Chapter
Steady One-dimensional Conduction
The Basic Equations
The Grid Spacing
The Interface Conductivity
Nonlinearity
Source-Term Linearization
Boundary Conditions
Solution of the Linear Algebraic Equations
Unsteady One-dimensional Conduction
The General Discretization Equation
Explicit, Crank-Nicolson, and Fully Implicit Schemes
The Fully Implicit Discretization Equation
Two- and Three-dimensional Situations
Discretization Equation for Two Dimensions
Discretization Equation for Three Dimensions
Solution of the Algebraic Equations
Overrelaxatioin and Underrelaxation
Some Geometric Considerations
Location of the Control-Volume Faces
Other Coordinate Systems
Closure
Problems
5 Convection and Diffusion
The Task
Steady One-dimensional Convection and Diffusion
A Preliminary Derivation
The Upwind Scheme
The Exact Solution
The Exponential Scheme
The Hybrid Scheme
The Power-Law Scheme
A Generalized Formulation
Consequences of the Various Schemes
Discretization Equation for Two Dimensions
Details of the Derivation
The Final Discretization Equation
Discretization Equation for Three Dimensions
A One-Way Space Coordinate
What Makes a Space Coordinate One-Way
The Outflow Boundary Condition
False Diffusion
The Common View of the False Diffusion
The Proper View of False Diffusion
Closure
Problems
6 Calculation of the Flow Field
Need for a Special Procedure
The Main Difficulty
Vorticity-based Methods
Some Related Difficulties
Representation of the Pressure-Gradient Term
Representation of the Continuity Equation
A Remedy: The Staggered Grid
The Momentum Equations
The Pressure and Velocity Corrections
The Pressure-Correction Equation
The SIMPLE Algorithm
Sequence of Operations
Discussion of the Pressure-Correction Equation
Boundary Conditions for the Pressure-Correction Equation
The Relative Nature of Pressure
A Revised Algorithm: SIMPLER
Motivation
The Pressure Equation
The SIMPLER Algorithm
Discussion
Closure
Problems
7 Finishing Touches
The Iterative Nature of the Procedure
Source-Term Linearization
Discussion
Source Linearization for Always-Positive Variables
Irregular Geometries
Orthogonal Curvilinear Coordinates
Regular Grid with Blocked-off Regions
Conjugate Heat Transfer
Suggestions for Computer-Program Preparation and Testing
8 Special Topics
Two-dimensional Parabolic Flow
Three-dimensional Parabolic Flow
Partially Parabolic Flow
The Finite-Element Method
Motivation
Difficulties
A Control-Volume-based Finite-Element Method
9 Illustrative Applications
Developing Flow in a Curved Pipe
Combined Convection in a Horizontal Tube
Melting around a Vertical Pipe
Turbulent Flow and Heat Transfer in Internally Finned Tubes
A Deflected Turbulent Jet
A Hypermixing Jet within a Thrust-Augmenting Ejector
A Periodic Fully Developed Duct Flow
Thermal Hydraulic Analysis of a Steam Generator
Closing Remarks
Nomenclature
References
Index
Biography
Suhas Patankar
