Computational Methods for Heat and Mass Transfer (Paperback, 1)

PrefaceNomenclaturePart I: Basic Equations and Numerical Analysis1. Review of Basic Laws and Equations1.1 Basic Equations1.2 Fluid Flows1.2.1 Fluid Properties1.2.2 Basic Equations in Integral Forms1.2.3 Differential Analysis of Fluid Motion 1.2.4 Boundary Conditions for Flow Field1.3 Heat Transfer1.3.1 Basic Modes and Transport Rate Equation1.3.2 The First Law of Thermodynamics and Heat Equations1.3.3 Thermal Initial and Boundary Conditions 1.4 Mass Transfer1.4.1 Basic Modes and Transport Rate Equation1.4.2 Conservation of Mass Species and Mass Concentration Equation1.4.3 Initial and Boundary Conditions for Mass Transfer1.5 Mathematical Classification of Governing EquationProblems2. Approximations and Errors2.1 Truncation Error2.2 Round off Error2.2.1 Significant Figures or Digits2.2.2 Computers Number System2.2.3 Machine Epsilon2.3 Error Definitions2.4 Approximate Error2.5 Convergence CriteriaProblems3. Numerical Solution of Systems of Equations 3.1 Mathematical Background3.1.1 Representation of the System of Equations3.1.2 The Cramer's Rule and the Elimination of Unknowns3.2 Direct Methods3.2.1 Gauss Elimination3.2.2 Gauss-Jordon Elimination Method3.2.3 Decomposition of Factorization Methods3.2.4 Banded Systems3.2.5 Error Equations and Iterative Refinement3.3 Iterative Methods3.3.1 Jacobi Method3.3.2 Gauss-Seidel Method3.3.3 Convergence Criterion for Iterative Methods3.3.4 Successive Over-Relaxation (SOR) method3.3.5 Conjugate Gradient Method3.3.6 Pre-conditioned Conjugate Gradient MethodProblems4. Numerical Integration 4.1 Newton - Cotes Integration Formulas4.1.1 The Trapezoidal Rule 4.1.2 Simpson's Integration Formula4.1.3 Summary of Newton-Cotes Integration Formulas4.2 Romberg Integration4.3