Computational Fluid Dynamics and Heat Transfer
- Available for pre-order. Item will ship after August 20, 2021
This book provides a thorough understanding of fluid dynamics and heat and mass transfer. It contains new chapters on mesh generation and computational modeling of turbulent flow. Combining theory and practice in classic problems and computer code, the text includes examples in ANSYS, STAR CCM+, and COMSOL.
With detailed explanations on how to implement computational methodology into a computer code, students will be able to solve complex problems on their own, including problems in heat transfer, mass transfer, and fluid flows. These problems are solved and illustrated in step-by-step derivations and figures.
The text will be valuable to Engineering instructors and students taking courses in computational heat transfer and computational fluid dynamics.
Table of Contents
Contents 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 Kinematics of Fluid and Kinematic Properties Type of Forces in a Fluid 1.2.2 Basic Equations in Integral Forms Basic Equations for a System Basic Equations for a Control Volume 1.2.3 Differential Analysis of Fluid Motion Conservation of Mass Conservation of Momentum 1.2.4 General form of Incompressible Momentum Equations 1.2.5 Turbulent Flow Equations 1.2.6 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 Initial and Boundary Conditions for Heat Transfer 1.4 Mass Transfer 1.4.1 Basic Modes and Transport Rate Equations Diffusion Mass Transfer Convection Mass Transfer Relation between Heat and Mass Transfer 1.4.2 Conservation of Mass Species and Mass Concentration Equation 1.4.3 Initial and Boundary Conditions for Mass Transfer 1.5 General Form of Transport Equations for Computational Solution 1.6 Mathematical Classification of Governing Equations Problems 2. Approximations and Errors 2.1 Truncation Error 2.2 Round off Error 2.2.1 Significant Figures 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 or Factorization Methods The Basic LU Decomposition Cholesky Factorization Method QR Factorization by Householder Method 3.2.4 Banded Systems 3.2.5 Error Equations and Iterative Refinements 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 3.3.7 Generalized Minimal Residual (GMRES) 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 Gauss Quadrature 4.3.1 Two-Point Gauss-Legendre Formula 4.3.2 Higher-Points Gauss-Legendre Formulas 4.4 Multi-Dimensional Numerical Integration Problems Part II: Finite Difference - Control Volume Method 5. Basics of Finite Difference - Control Volume Method 5.1 Introduction and Basic steps in Finite Difference Method 5.2 Discretization of the Domain 5.3 Discretization of the Mathematical Model 5.3.1 The Taylor Series Method 5.3.2 Control Volume Method 5.4 One-dimensional Steady State Diffusion 5.5 Variable Source Term 5.6 Boundary Conditions 5.7 Grid Size Distribution 5.8 Non-uniform Transport Property 5.9 Nonlinearity 5.10 Linearization of a Variable Source Term Problems 6. Finite Difference- Control Volume Method: Multi-Dimensional Problems 6.1 Two-dimensional Steady State Problems 6.2 Boundary Conditions 6.2.1 Corner Boundary Nodes 6.3 Irregular Geometries 6.4 Three-Dimensional Steady State Problems 6.5 Solution Techniques and Computer Implementation Problems 7. Finite Difference- Control Volume Method: Unsteady State Diffusion Equation 7.1 Time Discretization Procedure 7.2 Explicit Scheme 7.2.1 Discretization Equation by Control Volume Approach 7.2.2 Finite Difference Equation by Taylor Series Expansions 7.2.3 Stability Consideration 7.2.4 Other Explicit Schemes Richardson Scheme Dufort-Frankel Scheme 7.2.5 Boundary Conditions 7.3 Implicit Scheme 7.3.1 Discretization Equation by Control Volume Approach 7.3.2 Finite Difference Equation by Taylor Series Expansion 7.3.3 A General Formulation of Fully Implicit Scheme for One-dimensional Problems 7.3.4 A General Formulation of Fully Implicit Scheme for Two-dimensional Problems 7.3.5 Solution Methods for Two-dimensional Implicit Scheme 7.3.6 Boundary Conditions for Implicit Scheme 7.4 Crank-Nicolson Scheme 7.4.1 Solution Method for Crank-Nicolson Method 7.5 Splitting Method 7.5.1 ADI Method 7.5.2 ADE Method Problems 8. Finite Difference-Control Volume Method: Convection Problems 8.1 Spatial Discretization using Control Volume Metho 8.1.1 Central Difference Scheme 8.1.2 Upwind Scheme 8.1.3 Exponential Scheme 8.1.4 Hybrid Scheme 8.1.5 Power Law Scheme 8.1.6 Generalized Convection-Diffusion Scheme 8.1.7 Higher-order Discretization schemes for Convective Terms 8.2 Discretization of a General Transport Equation 8.2.1 One-dimensional Unsteady State Problems 8.2.2 Two-dimensional Unsteady State Problems 8.2.3 Three-dimensional Unsteady State Problems 8.3 Solution of Flow Field 8.3.1 Stream Function/Vorticity-Based Method 8.3.2 Direct Solution with the Primitive Variables Problems 9. Additional Features in Computational Model and Mesh Generations 9.1 Boundary Conditions 9.1.1 Inlet conditions 9.1.2 Outlet conditions 9.1.3 Wall Boundary Conditions 9.1.4 Pressure conditions at the Inlets and Outlets 9.1.5 Symmetric and Periodic Boundary Conditions 9.1.6 Periodic Boundary Planes and Conditions 9.2 Mesh Types and Mesh Generation 9.2.1 Mesh Types 9.2.2 Mesh Size Distributions 9.2.3 Mesh Generation Procedure 9.2.4 Multiblock Mesh System 9.2.5 Prism Layers 9.3 Multi-grid (MG) methods 9.3.1 Algebraic Multigrid Method (AMG) 10. Turbulent Flow Modeling 10.1 Physical Description of Turbulence 10.2 Governing Equation for Turbulent Fluid Flow Analysis 10.3 Computational Model for Turbulent Flow 10.3.1 Direct Numerical Simulation (DNS) 10.3.2 Averaged or Filtered Simulation 10.4 Reynolds Averaged Navier-Stokes (RANS) Model 10.4.1 Turbulent Kinetic Energy Transport Equation 10.4.2 Boussinesq Eddy Viscosity Concept and Prandtl Mixing Length Model 10.5 Different Classes of Turbulence Closure Models 10.6 Classification of Turbulence Models 10.6.1 Algebraic Turbulence Model or Zero-Equation Model 10.6.2 One Equation Models 10.6.3 Two Equation Models 10.7 Reynolds Stress Models (RSM) 10.8 Near-Wall Region Modeling 10.9 Estimation of y-plus 10.10 Boundary Conditions for Turbulence Quantities 10.10.1 Inlet Turbulence 10.10.2 Wall Boundary Conditions Part III: Finite Element Method 11. Introduction and Basic Steps in Finite Element Method 11.1 Comparison Between Finite Difference/Control Volume Method and Finite Element Method 11.2 Basic Steps in Finite Element Method 11.3 Integral Formulation 11.3.1 Variational Formulation 11.3.2 Method of Weighted Residuals 11.4 Variational Methods 11.4.1 The Rayleigh-Ritz Variational Method 11.4.2 Weighted Residual Variational Methods Problems 12. Element Shape Functions 12.1 One-dimensional Element 12.1.1 One-dimensional Linear Element 12.1.1 One-dimensional Quadratic Line Element 12.1.2 One-dimensional Cubic Element 12.2 Two-dimensional Element 12.2.1 Linear Triangular Element 12.2.2 Quadratic Triangular Element 12.2.3 Two-dimensional Quadrilateral Element 12.3 Three-dimensional Element 12.3.1 Three-dimensional Tetrahedron Element 12.3.2 Three-dimensional Hexahedron Element 13. Finite Element Method: One-dimensional Steady State Problems 13.1 Finite Element Formulation using Galerkin Method 13.2 Finite Element Formulation using Variational Approach 13.3 Boundary Conditions 13.3.1 Boundary Condition of the Second Kind or Constant Surface Flux 13.3.2 Mixed Boundary Conditions 13.4 Variable Source Term 13.5 Axisymmetric Problems Problems 14. Finite Element Method: Multi-dimensional Steady State Problems 14.1 Two-dimensional Steady State Diffusion Equation 14.2 Two-dimensional Axisymmetric Problems 14.3 Three-dimensional Problems 14.4 Point Source
Problems 15. Finite Element Method: Unsteady State Problems 15.1 Discretization Scheme 15.2 One-dimensional Unsteady State Problems 15.2.1 Semi-discrete Finite Element Formulations 15.2.2 Time Approximation 15.2.3 Stability Consideration 15.3 Two-dimensional Unsteady State Diffusion Equation 15.4 Three-dimensional Unsteady State Diffusion Equation Problems 16. Finite Element Method: Convection Problems 16.1 Classification of Finite Elements Methods for Convection Problems 16.2 Velocity-Pressure or Mixed Formulation 16.2.1 One-dimensional Convection-Diffusion Problem 16.2.2 Two-dimensional Viscous Incompressible Flow 16.2.3 Unsteady Two-dimensional Viscous Incompressible Flow 16.2.4 Unsteady Three-dimensional Viscous Incompressible Flow 16.2.5 Convective Heat and Mass Transfer 16.3 Solution Methods 16.3.1 Steady State Problems 16.3.2 Unsteady State Problem Problems Appendix - A. Review of Vectors and Matrices Appendix - B. Integral Theorems Bibliography Index
PRADIP MAJUMDAR earned his M.S. and Ph.D. in mechanical engineering from Illinois Institute of Technology. He was a professor and the chair in the Department of Mechanical Engineering at Northern Illinois University. He is recipient of the 2008 Faculty of the Year Award for Excellence in Undergraduate Education. Dr. Majumdar has been the lead investigator for numerous federal and industrial projects. Dr. Majumdar authored numerous papers on fluid dynamics, heat and mass transfer, energy systems, fuel cell, Li-ion battery storage, electronics cooling and electrical devices, engine combustion, nano-structured materials, advanced manufacturing, and transport phenomena in biological systems. Dr. Majumdar is the author of three books including Computational Methods for Heat and Mass Transfer; Fuel Cells- Principles, Design and Analysis; and Design of Thermal Energy Systems (In Press). Dr. Majumdar is currently serving as an editor of the International Communications in Heat and Mass Transfer. He has previously served as the Associate Editor of ASME Journal of Thermal Science and Engineering. Dr. Majumdar has been making keynote and plenary presentations on Li-ion Battery storage, fuel cell, electronics cooling, nanostructure materials at national/international conferences and workshops. Dr. Majumdar has participated as an international expert in GIAN lecture series on fuel cell and Li-ion battery storage. Dr. Majumdar is a fellow of the American Society of Mechanical Engineers (ASME).