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 Eguations 4.2-2 The Grid Spacing 4.2-3 The Interface Conductivity 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 5.2-5 The Hybrid Scheme 5.2-6 The Power-Law Scheme 5.2-7 A Generalized Formulation 5.2-8 Consequences of the Various Schemes 5.3 Discretization Equation for Two Dimensions 5.3-1 Details of the Derivation 5.3-2 The Final Discretization Equation 5.4 Discretization Equation for Three Dimensions 5.5 A One-Way Space Coordinate 5.5-1 What Makes a Space Coordinate One-Way 5.5-2 The Outflow Boundary Condition 5.6 False Diffusion 5.6-1 The Common View of False Diffusion 5.6-2 The Proper View of False Diffusion 5.7 Closure Problems 6 CALCULATION OF THE FLOW FIELD 6.1 Need for a Special Procedure 6.1-1 The Main Difficulty 6.1-2 Vorticity-based Methods 6.2 Some Related Difficulties 6.2-1 Representation of the Pressure-Gradient Term 6.2-2 Representation of the Continuity Equation 6.3 A Remedy:The Staggered Grid 6.4 The Momentum Equations 6.5 The Pressure and Velocity Corrections 6.6 The Pressure-Correction Equation 6.7 The SIMPLE Algorithm 6.7-1 Sequence of Operations 6.7-2 Discussion of the Pressure-Correction Equation 6.7-3 Boundary Conditions for the Pressure-Correction Equation
6.7-4 The Relative Nature of Pressure 6.8 A Revised Algorithm:SIMPLER 6.8-1 Motivation 6.8-2 The Pressure Equation 6.8-3 The SIMPLER Algorithm 6.8-4 Discussion 6.9 Closure Problems 7 FINISHING TOUCHES 7.1 The Iterative Nature of the Procedure 7.2 Source-Term Linearization 7.2-1 Discussion 7.2-2 Source Linearization for Always-Positive Variables 7.3 Irregular Geometries 7.3-1 Orthogonal Curvilinear Coordinates 7.3-2 Regular Grid with Blocked-off Regions 7.3-3 Conjugate Heat Transfer 7.4 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 Flows 8.4 The Finite-Element Method 8.4-1 Motivation 8.4-2 Difficulties 8.4-3 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 Nomenclature References Index
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