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.
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
