In 1972，l taught an informal course on numerical solution of heat transfer and fluid flow to a small group of research workers at Imperial CoUege，London. Later，the material was expanded and formalized for presentation in graduate courses at the University of Waterloo in Canada（in 1974），at the Norwegian Institute of Technology，Trondheim(in 1977），and at the Uni-versity of Minnesota(in 1975，1977，and 1979）. During the last two years，I have also presented the same material in a short-course format at ASMEnational meetings. The enthusiastic response accorded to these courses has encouraged me to write this book，which can be used as a text for a graduate course as well as a reference book for computational work in heat transfer and fluid flow.
　　Although there is an extensive literature on computational thermofluid analysis，the newcomer to the field has insufficient help available. The graduate student，the researcher，and the practicing engineer must stru e through journal articles or be content with elementary presentation in bookson numerical analysis. Often，it is the subtle details that determine the successor failure of a computational activity; yet，the practices that are learned through experience by successful computing groups rarely appear in print. A consequence is that many workers either give up the computational approach after many months of frustrating pursuit or struggle through to the end with inefficient computer programs.
　　Being aware of this situation，I have tried to present in this book a self-contained，simple，and practical treatment of the subject. The book is introductory in style and is intended for the potential practitioner of numerical heat transfer and fluid flow; it is not designed for the experts in the subject area. In developing the numerical techniques，I emphasize physical significance rather than mathematical manipulation. Indeed，most of the mathematics used here is limited to simple algebra. The result is that，whereas the book enables the reader to travel all the way to the present-day frontier of the subject，the journey takes place through delightfully simple and illuminating physical concepts and considerations. In teaching the materialwith such an approach，I have often been pleasantly surprised by the fact thatthe students not only learn about numerical methods but also develop a better appreciation of the relevant physical processes.
　　As a user of numerical techniques，l have come to prefer a certain fanuly of methods and a certain set of practices. This repertoire has been collected partly from the literature and subsequently has been enriched，adapted，and modified. Thus，since a considerable amount of sorting and sifting of available methods has already taken place(albeit with my own bias），I have limited the scope of this book to the set of methods that I wish to recommend. I do not attempt to present a comparative study of all available methods; other methods are only occasionally mentioned when they serve to illuminate a specific feature under consideration. In this sense，this book represents my personal view of the subject. Although I am，of course，enthusiastic about this viewpoint，I recognize that my choices have been influenced by my back-ground，personal preferences，and technical objectives. Others operating in different environments may well come to prefer alternative approaches.
　　To illustrate the application of the material，problems are given at the end of some chapters. Most of the problems can be solved by using a pocket calculator，although some of them should be programmed for a digital computer. The problems are not meant for testing the student reader，but are included primarily for extending and enriching the learning process. They suggest alternative techniques and present additional material. At times，in my attempt to give a hint for the problem solution，I almost disclose the full answer. In such cases，arriving at the correct answer is not the main objective;the reader should focus on the message that the problem is designed to convey.
　　This book carries the description of the numerical method to a point where the reader could begin to write a computer program. Indeed，the reader should be able to construct computer programs that generate the kind of results presented in the final chapter of the book. A range of computer programs of varying generality can be designed depending upon the nature of the problems to be solved. Many readers might have found it helpful if a representative computer program were included in tlus book. I did consider the possibility. However，the task of providing a reasonably general computer program，its detailed description，and several examples of its use seemed so formidable that it would have considerably delayed the publication of this book. For the time being，I have included a section on the preparation and testing of a computer program(Section 7.4），where many useful procedures and practices gathered through experience are described.

Preface
1 INTRODUCTION
1．1 Scope of the Book
1．2 Methods of Prediction
1．2-1 Experimental Investigation
1．2-2 Theoretical Calculation
1．2-3 Advantages of a Theoretical Calculation
1．2-4 Disadvantages of a Theoretical Calculation
1．2-5 Choice of Prediction Method
1．3 Outline of the Book

2 MATHEMATICAL DESCRIPTION OF PHYSICAL PHENOMENA
2．1 Governing Differential Equations
2．1-1 Meaning of a Differential Equation
2．1-2 Conservation of a Chemical Species
2．1-3 The Energy Equation
2．1-4 A Momentum Equation
2．1 5 The Time-Averaged Equations for Turbulent Flow
2．1-6 The Turbulence-Kinetic-Energy Equation
2．1-7 The General Differential Equation
2．2 Nature of Coordinates
2．2-1 Independent Variables
2．2-2 Proper Choice of Coordinates
2．2-3 One-Way and Two-Way Coordinates
Problems

3 DISCRETIZATION METHODS
3．1 The Nature of Numerical Methods
3，1-1 The Task
3，1 2 The Discretization Concept
3．1-3 The Structure of the Discretization Equation
3．2 Methods of Deriving the Discretization Equations
3．2-1 Taylor-Series Formulation
3．2-2 Variational Formulation
3．2-3 Method of Weighted Residuals
3．2-4 Control-Volume Formulation
3．3 An Illustrative Example
3．4 The Four Basic Rules
3．5 Closure
Problems

4 HEAT CONDUCTION
4．1 Objectives of the Chapter
4．2 Steady One-dimensional Conduction
4．2-1 The Basic Equations
4．2-2 The Grid Spacing
4．2-3 The Interface Conductmty
4．2-4 Nonlinearity
4．2-5 Source-Term Linearization
4．2-6 Boundary Conditions
4．2-7 Solution of the Linear Algebraic Equations
4．3 Unsteady One-dimensional Conduction
4．3-1 The General Discretization Equation
4．3-2 Explicit， Crank-Nicolson， and Fully Implicit Schemes
4．3-3 The Fully Implicit Discretization Equation
4．4 Two- and Three-dimensional Situations
4．4-1 Discretization Equation for Two Dimensions
4．4-2 Discretization Equation for Three Dimensions
4．4-3 Solution of the Algebraic Equations
4．5 Overrelaxation and Underrelaxation
4．6 Some Geometric Considerations
4．6-1 Location of the Control-Volume Faces
4．6-2 Other Coordinate Systems
4．7 Closure
Problems

5 CONVECTION AND DIFFUSION
5．1 The Task
5．2 Steady One-dimensional Convection and Diffusion
5．2-1 A Preliminary Derivation
5．2-2 The Upwind Scheme
5．2-3 The Exact Solution
5．2-4 The Exponential Scheme
……
6 CALCULATION OF THE FLOW FIELD
7 FINISHING TOUCHES
8 SPECIAL TOPICS
9 ILLUSTRATIVE APPLICATIONS
Nomenclature
References
Index