Modeling in Materials Processing

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Paperback | 8 April 2002

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378 Pages

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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.

Industry Reviews

'The book is highly recommended.' Zeitschrift fuer Angewandte Mathematik und Mechanik

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Preface	p. ix
Principal Nomenclature	p. xi
Introduction	p. 1
What Is a Model?	p. 1
A Simple Pendulum	p. 2
One-Dimensional Traffic Flow	p. 6
Summary	p. 19
Bibliography	p. 19
Exercises	p. 20
Governing Equations	p. 24
Preliminaries	p. 24
Mass Balance	p. 29
Momentum Balance	p. 33
Energy Balance	p. 45
Summary	p. 52
Bibliography	p. 53
Exercises	p. 53
Appendix	p. 58
Scaling and Model Simplification	p. 60
Introduction	p. 60
Basic Scaling Analysis	p. 62
Small Parameters and Boundary Layers	p. 69
Classical Dimensionless Groups	p. 76
Nondimensionalization for Numerical Solutions (Advanced)	p. 78
Summary	p. 81
Bibliography	p. 81
Exercises	p. 81
Heat Conduction and Materials Processing	p. 87
Steady Heat Conduction in Solids	p. 90
Transient Heat Conduction	p. 93
Conduction with Phase Change	p. 106
Summary	p. 120
Bibliography	p. 121
Exercises	p. 121
Appendix	p. 130
Isothermal Newtonian Fluid Flow	p. 132
Newtonian Flow in a Thin Channel	p. 132
Other Slow Newtonian Flows	p. 143
Free Surfaces and Moving Boundaries	p. 149
Flows with Significant Inertia	p. 161
Summary	p. 177
Bibliography	p. 178
Exercises	p. 178
Non-Newtonian Fluid Flow	p. 190
Non-Newtonian Behavior	p. 190
The Power Law Model	p. 192
Power Law Solutions for Other Simple Geometries	p. 200
Principles of Non-Newtonian Constitutive Equations	p. 202
More Non-Newtonian Constitutive Equations	p. 209
The Generalized Hele-Shaw Approximation	p. 217
Summary	p. 228
Bibliography	p. 228
Exercises	p. 229
Heat Transfer with Fluid Flow	p. 239
Uncoupled Advection	p. 239
Temperature-Dependent Viscosity and Viscous Dissipation	p. 250
Buoyancy-Driven Flow	p. 259
Summary	p. 275
Bibliography	p. 275
Exercises	p. 276
Mass Transfer and Solidification Microstructures	p. 282
Governing Equations for Diffusion	p. 282
Solid-State Diffusion	p. 285
Solidification Microstructure Development	p. 295
Summary	p. 319
Bibliography	p. 320
Exercises	p. 321
Mathematical Background	p. 327
Scalars, Vectors, and Tensors: Definitions and Notation	p. 327
Vector and Tensor Algebra	p. 331
Differential Operations in Rectangular Coordinates	p. 335
Vectors and Tensors in Cylindrical and Spherical Coordinates	p. 337
The Divergence Theorem	p. 339
Curvature of Curves and Surfaces	p. 339
The Gaussian Error Function	p. 343
Bibliography	p. 345
Exercises	p. 345
Balance and Kinematic Equations	p. 348
Continuity Equation: General Form	p. 348
Continuity Equation: Constant [rho]	p. 348
Rate-of-Deformation Tensor	p. 349
Vorticity Tensor	p. 350
General Equation of Motion	p. 350
Navier-Stokes Equation: Constant [rho] and [mu]	p. 352
Heat Flux Vector: Isotropic Material	p. 353
Energy Balance: General Form	p. 354
Energy Balance: Constant [rho], [kappa] and [mu]	p. 355
Bibliography	p. 356
Index	p. 357
Table of Contents provided by Syndetics. All Rights Reserved.

Modeling in Materials Processing

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

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You Can Find This Book In

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