Table of Contents:

Preface

1 Introduction
1.1 Scope of the Book
1.2 Methods of Prediction
1.3 Experimental Investigation
1.4 Theoretical Calculation
1.5 Advantages of a Theoretical Calculation
1.6 Disadvantages of a Theoretical Calculation
1.7 Choice of Prediction Method
1.8 Outline of the Book

2 Mathematical Description of Physical Phenomena
2.1 Governing Differential Equations
2.2 Meaning of a Differential Equation
2.3 Conservation of a Chemical Species
2.4 The Energy Equation
2.5 A Momentum Equation
2.6 The Time-Averaged Equations for Turbulent Flow
2.7 The Turbulence-Kinetic-Energy Equation
2.8 The General Differential Equation
2.9 Nature Coordinates
2.10 Independent Variables
2.11 Proper Choice of Coordinates
2.12 One-Way and Two-Way Coordinates
2.13 Problems

3 Discretization Methods
3.1 The Nature of Numerical Methods
3.2 The Task
3.3 The Discretization Concept
3.4 The Structure of the Discretization Equation
3.5 Methods of Deriving the Discretization Equations
3.6 Taylor-Series Formulation
3.7 Variational Formulation
3.8 Method of Weighted Residuals
3.9 Control-Volume Formulation
3.10 An Illustrative Example
3.11 The Four Basic Rules
3.12 Closure
3.13 Problems

4 Heat Conduction
4.1 Objectives of the Chapter
4.2 Steady One-dimensional Conduction
4.3 The Basic Equations
4.4 The Grid Spacing
4.5 The Interface Conductivity
4.6 Nonlinearity
4.7 Source-Term Linearization
4.8 Boundary Conditions
4.9 Solution of the Linear Algebraic Equations
4.10 Unsteady One-dimensional ConductionThe General Discretization Equation
4.11 Explicit, Crank-Nicolson, and Fully Implicit Schemes
4.12 The Fully Implicit Discretization Equation
4.13 Two- and Three-dimensional Situations
4.14 Discretization Equation for Two Dimensions
4.15 Discretization Equation for Three Dimensions
4.16 Solution of the Algebraic Equations
4.17 Overrelaxatioin and Underrelaxation
4.18 Some Geometric Considerations
4.19 Location of the Control-Volume Faces
4.20 Other Coordinate Systems
4.21 Closure
4.22 Problems

5 Convection and Diffusion
5.1 The Task
5.2 Steady One-dimensional Convection and Diffusion
5.3 A Preliminary Derivation
5.4 The Upwind Scheme
5.5 The Exact Solution
5.6 The Exponential Scheme
5.7 The Hybrid Scheme
5.8 The Power-Law Scheme
5.9 A Generalized Formulation
5.10 Consequences of the Various Schemes
5.11 Discretization Equation for Two Dimensions
5.12 Details of the Derivation
5.13 The Final Discretization Equation
5.14 Discretization Equation for Three Dimensions
5.15 A One-Way Space Coordinate
5.16 What Makes a Space Coordinate One-Way
5.17 The Outflow Boundary Condition
5.18 False Diffusion
5.19 The Common View of the False Diffusion
5.20 The Proper View of False Diffusion
5.21 Closure
5.22 Problems

6 Calculation of the Flow Field
6.1 Need for a Special Procedure
6.2 The Main Difficulty
6.3 Vorticity-based Methods
6.4 Some Related Difficulties
6.5 Representation of the Pressure-Gradient Term
6.6 Representation of the Continuity Equation
6.7 A Remedy: The Staggered Grid
6.8 The Momentum Equations
6.9 The Pressure and Velocity Corrections
6.10 The Pressure-Correction Equation
6.11 The SIMPLE Algorithm
6.12 Sequence of Operations
6.13 Discussion of the Pressure-Correction Equation
6.14 Boundary Conditions for the Pressure-Correction Equation
6.15 The Relative Nature of Pressure
6.16 A Revised Algorithm: SIMPLER
6.17 Motivation
6.18 The Pressure Equation
6.19 The SIMPLER Algorithm
6.20 Discussion
6.21 Closure
6.22 Problems

7 Finishing Touches
7.1 The Iterative Nature of the Procedure
7.2 Source-Term Linearization
7.3 Discussion
7.4 Source Linearization for Always-Positive Variables
7.5 Irregular Geometries
7.6 Orthogonal Curvilinear Coordinates
7.7 Regular Grid with Blocked-off Regions
7.8 Conjugate Heat Transfer
7.9 Suggestions for Computer-Program Preparation and Testing

8 Special Topics
8.1 Two-dimensional Parabolic Flow
8.2 Three-dimensional Parabolic Flow
8.3 Partially Parabolic Flow
8.4 The Finite-Element Method
8.5 Motivation
8.6 Difficulties
8.7 A Control-Volume-based Finite-Element Method

9 Illustrative Applications
9.1 Developing Flow in a Curved Pipe
9.2 Combined Convection in a Horizontal Tube
9.3 Melting around a Vertical Pipe
9.4 Turbulent Flow and Heat Transfer in Internally Finned Tubes
9.5 A Deflected Turbulent Jet
9.6 A Hypermixing Jet within a Thrust-Augmenting Ejector
9.7 A Periodic Fully Developed Duct Flow
9.8 Thermal Hydraulic Analysis of a Steam Generator
9.9 Closing Remarks
9.10 Nomenclature
9.11 References
9.12 Index

This book focuses on heat and mass transfer, fluid flow, chemical reaction, and other related processes that occur in engineering equipment, the natural environment, and living organisms. Using simple algebra and elementary calculus, the author develops numerical methods for predicting these processes mainly based on physical considerations. Through this approach, readers will develop a deeper understanding of the underlying physical aspects of heat transfer and fluid flow as well as improve their ability to analyze and interpret computed results.