You are previewing Modeling in Materials Processing.
O'Reilly logo
Modeling in Materials Processing

Book Description

Mathematical modeling and computer simulation are useful tools for improving materials processing. While courses in materials processing have covered modeling, they have traditionally been devoted to one particular class of materials, that is, polymers, metals, or ceramics. This text offers a different approach, presenting an integrated treatment of metallic and non-metallic materials. The authors show that a common base of knowledge - specifically, the fundamentals of heat transfer and fluid mechanics - provides a unifying theme for these seemingly disparate areas. Emphasis is placed on understanding basic physical phenomena and knowing how to include them in a model. The book also treats selected numerical methods, showing the relationship between the physical system, analytical solution, and the numerical scheme. A wealth of practical, realistic examples are provided, as well as homework exercises. Students, and practising engineers who must deal with a wide variety of materials and processing problems, will benefit from the unified treatment presented in this book.

Table of Contents

  1. Cover
  2. Title Page
  3. Copyright Page
  4. Contents
  5. Preface
  6. Principal Nomenclature
  7. 1 Introduction
    1. 1.1 What Is a Model?
    2. 1.2 A Simple Pendulum
    3. 1.3 One-Dimensional Traffic Flow
    4. 1.4 Summary
    5. Bibliography
    6. Exercises
  8. 2 Governing Equations
    1. 2.1 Preliminaries
    2. 2.2 Mass Balance
    3. 2.3 Momentum Balance
    4. 2.4 Energy Balance
    5. 2.5 Summary
    6. Bibliography
    7. Exercises
    8. Appendix
  9. 3 Scaling and Model Simplification
    1. 3.1 Introduction
    2. 3.2 Basic Scaling Analysis
    3. 3.3 Small Parameters and Boundary Layers
    4. 3.4 Classical Dimensionless Groups
    5. 3.5 Nondimensionalization for Numerical Solutions (Advanced)
    6. 3.6 Summary
    7. Bibliography
    8. Exercises
  10. 4 Heat Conduction and Materials Processing
    1. 4.1 Steady Heat Conduction in Solids
    2. 4.2 Transient Heat Conduction
    3. 4.3 Conduction with Phase Change
    4. 4.4 Summary
    5. Bibliography
    6. Exercises
    7. Appendix
  11. 5 Isothermal Newtonian Fluid Flow
    1. 5.1 Newtonian Flow in a Thin Channel
    2. 5.2 Other Slow Newtonian Flows
    3. 5.3 Free Surfaces and Moving Boundaries
    4. 5.4 Flows with Significant Inertia
    5. 5.5 Summary
    6. Bibliography
    7. Exercises
  12. 6 Non-Newtonian Fluid Flow
    1. 6.1 Non-Newtonian Behavior
    2. 6.2 The Power Law Model
    3. 6.3 Power Law Solutions for Other Simple Geometries
    4. 6.4 Principles of Non-Newtonian Constitutive Equations
    5. 6.5 More Non-Newtonian Constitutive Equations
    6. 6.6 The Generalized Hele-Shaw Approximation
    7. 6.7 Summary
    8. Bibliography
    9. Exercises
  13. 7 Heat Transfer with Fluid Flow
    1. 7.1 Uncoupled Advection
    2. 7.2 Temperature-Dependent Viscosity and Viscous Dissipation
    3. 7.3 Buoyancy-Driven Flow
    4. 7.4 Summary
    5. Bibliography
    6. Exercises
  14. 8 Mass Transfer and Solidification Microstructures
    1. 8.1 Governing Equations for Diffusion
    2. 8.2 Solid-State Diffusion
    3. 8.3 Solidification Microstructure Development
    4. 8.4 Summary
    5. Bibliography
    6. Exercises
  15. A Mathematical Background
    1. A.1 Scalars, Vectors, and Tensors: Definitions and Notation
    2. A.2 Vector and Tensor Algebra
    3. A.3 Differential Operations in Rectangular Coordinates
    4. A.4 Vectors and Tensors in Cylindrical and Spherical Coordinates
    5. A.5 The Divergence Theorem
    6. A.6 Curvature of Curves and Surfaces
    7. A.7 The Gaussian Error Function
    8. Bibliography
    9. Exercises
  16. B Balance and Kinematic Equations
    1. B.1 Continuity Equation: General Form
    2. B.2 Continuity Equation: Constant p
    3. B.3 Rate-of-Deformation Tensor
    4. B.4 Vorticity Tensor
    5. B.5 General Equation of Motion
    6. B.6 Navier-Stokes Equation: Constant p and ?
    7. B.7 Heat Flux Vector: Isotropic Material
    8. B.8 Energy Balance: General Form
    9. B.9 Energy Balance: Constant p, k, and ?
    10. Bibliography
  17. Index