Modeling in Materials Processing

by Jonathan A. Dantzig , Charles L. Tucker

• ISBN13: 9780521779234
• ISBN10: 0521779235
• Format: Paperback
• Copyright: 2001-11-12
• Publisher: Cambridge University Press

Summary

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 new 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.

Author Biography

Jonathan A. Dantzig is Professor of Mechanical Engineering, Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign.

Table of Contents

Preface	ix
Principal Nomenclature	xi
Introduction	1	(23)
What Is a Model?	1	(1)
A Simple Pendulum	2	(4)
One-Dimensional Traffic Flow	6	(13)
Summary	19	(5)
Bibliography	19	(1)
Exercises	20	(4)
Governing Equations	24	(36)
Preliminaries	24	(5)
Mass Balance	29	(4)
Momentum Balance	33	(12)
Energy Balance	45	(7)
Summary	52	(8)
Bibliography	53	(1)
Exercises	53	(5)
Appendix	58	(2)
Scaling and Model Simplification	60	(27)
Introduction	60	(2)
Basic Scaling Analysis	62	(7)
Small Parameters and Boundary Layers	69	(7)
Classical Dimensionless Groups	76	(2)
Nondimensionalization for Numerical Solutions (Advanced)	78	(3)
Summary	81	(6)
Bibliography	81	(1)
Exercises	81	(6)
Heat Conduction and Materials Processing	87	(45)
Steady Heat Conduction in Solids	90	(3)
Transient Heat Conduction	93	(13)
Conduction with Phase Change	106	(14)
Summary	120	(12)
Bibliography	121	(1)
Exercises	121	(9)
Appendix	130	(2)
Isothermal Newtonian Fluid Flow	132	(58)
Newtonian Flow in a Thin Channel	132	(11)
Other Slow Newtonian Flows	143	(6)
Free Surfaces and Moving Boundaries	149	(12)
Flows with Significant Inertia	161	(16)
Summary	177	(13)
Bibliography	178	(1)
Exercises	178	(12)
Non-Newtonian Fluid Flow	190	(49)
Non-Newtonian Behavior	190	(2)
The Power Law Model	192	(8)
Power Law Solutions for Other Simple Geometries	200	(2)
Principles of Non-Newtonian Constitutive Equations	202	(7)
More Non-Newtonian Constitutive Equations	209	(8)
The Generalized Hele-Shaw Approximation	217	(11)
Summary	228	(11)
Bibliography	228	(1)
Exercises	229	(10)
Heat Transfer with Fluid Flow	239	(43)
Uncoupled Advection	239	(11)
Temperature-Dependent Viscosity and Viscous Dissipation	250	(9)
Buoyancy-Driven Flow	259	(16)
Summary	275	(7)
Bibliography	275	(1)
Exercises	276	(6)
Mass Transfer and Solidification Microstructures	282	(45)
Governing Equations for Diffusion	282	(3)
Solid-State Diffusion	285	(10)
Solidification Microstructure Development	295	(24)
Summary	319	(8)
Bibliography	320	(1)
Exercises	321	(6)
A Mathematical Background	327	(21)
Scalars, Vectors, and Tensors: Definitions and Notation	327	(4)
Vector and Tensor Algebra	331	(4)
Differential Operations in Rectangular Coordinates	335	(2)
Vectors and Tensors in Cylindrical and Spherical Coordinates	337	(2)
The Divergence Theorem	339	(1)
Curvature of Curves and Surfaces	339	(4)
The Gaussian Error Function	343	(5)
Bibliography	345	(1)
Exercises	345	(3)
B Balance and Kinematic Equations	348	(9)
Continuity Equation: General Form	348	(1)
Continuity Equation: Constant p	348	(1)
Rate-of-Deformation Tensor	349	(1)
Vorticity Tensor	350	(1)
General Equation of Motion	350	(2)
Navier-Stokes Equation: Constant p and μ	352	(1)
Heat Flux Vector: Isotropic Material	353	(1)
Energy Balance: General Form	354	(1)
Energy Balance: Constant p, k, and μ	355	(2)
Bibliography	356	(1)
Index	357