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List of contents
Preface
Nomenclature
Part I: Basic Equations and Numerical Analysis
1. Review of Basic Laws and Equations
1.1 Basic Equations
1.2 Fluid Flows
1.2.1 Fluid Properties
1.2.2 Basic Equations in Integral Forms
1.2.3 Differential Analysis of Fluid Motion
1.2.4 Boundary Conditions for Flow Field
1.3 Heat Transfer
1.3.1 Basic Modes and Transport Rate Equation
1.3.2 The First Law of Thermodynamics and Heat Equations
1.3.3 Thermal Initial and Boundary Conditions
1.4 Mass Transfer
1.4.1 Basic Modes and Transport Rate Equation
1.4.2 Conservation of Mass Species and Mass Concentration Equation
1.4.3 Initial and Boundary Conditions for Mass Transfer
1.5 Mathematical Classification of Governing Equation
Problems
2. Approximations and Errors
2.1 Truncation Error
2.2 Round off Error
2.2.1 Significant Figures or Digits
2.2.2 Computers Number System
2.2.3 Machine Epsilon
2.3 Error Definitions
2.4 Approximate Error
2.5 Convergence Criteria
Problems
3. Numerical Solution of Systems of Equations
3.1 Mathematical Background
3.1.1 Representation of the System of Equations
3.1.2 The Cramer's Rule and the Elimination of Unknowns
3.2 Direct Methods
3.2.1 Gauss Elimination
3.2.2 Gauss-Jordon Elimination Method
3.2.3 Decomposition of Factorization Methods
3.2.4 Banded Systems
3.2.5 Error Equations and Iterative Refinement
3.3 Iterative Methods
3.3.1 Jacobi Method
3.3.2 Gauss-Seidel Method
3.3.3 Convergence Criterion for Iterative Methods
3.3.4 Successive Over-Relaxation (SOR) method
3.3.5 Conjugate Gradient Method
3.3.6 Pre-conditioned Conjugate Gradient Method
Problems
4. Numerical Integration
4.1 Newton - Cotes Integration Formulas
4.1.1 The Trapezoidal Rule
4.1.2 Simpson's Integration Formula
4.1.3 Summary of Newton-Cotes Integration Formulas
4.2 Romberg Integration
4.3
About the author
Majumdar, Pradip; Majumdar, Pradip
Summary
This book introduces the fundamentals of the finite difference-control volume and finite element methods, two important computational techniques for solving heat and mass transfer and fluid flow problems.
