Modeling in materials processing Jonathan A. Dantzig, Charles L. Tucker, III.

Includes bibliographies and index.

What Is a Model? A Simple Pendulum One-Dimensional Traffic Flow Governing Equations Mass Balance Momentum Balance Energy Balance Scaling and Model Simplification Basic Scaling Analysis Small Parameters and Boundary Layers Classical Dimensionless Groups Nondimensionalization for Numerical Solutions (Advanced) Heat Conduction and Materials Processing Steady Heat Conduction in Solids Transient Heat Conduction Conduction with Phase Change Isothermal Newtonian Fluid Flow Newtonian Flow in a Thin Channel Other Slow Newtonian Flows Free Surfaces and Moving Boundaries Flows with Significant Inertia Non-Newtonian Fluid Flow Non-Newtonian Behavior Power Law Model Power Law Solutions for Other Simple Geometries Principles of Non-Newtonian Constitutive Equations More Non-Newtonian Constitutive Equations Generalized Hele-Shaw Approximation Heat Transfer with Fluid Flow Uncoupled Advection Temperature-Dependent Viscosity and Viscous Dissipation Buoyancy-Driven Flow Mass Transfer and Solidification Microstructures Governing Equations for Diffusion Solid-State Diffusion Solidification Microstructure Development A Mathematical Background Scalars, Vectors, and Tensors: Definitions and Notation Vector and Tensor Algebra Differential Operations in Rectangular Coordinates Vectors and Tensors in Cylindrical and Spherical Coordinates Divergence Theorem Curvature of Curves and Surfaces Gaussian Error Function Balance and Kinematic Equations Continuity Equation: General Form Continuity Equation: Constant [rho] Rate-of-Deformation Tensor Vorticity Tensor General Equation of Motion Navier-Stokes Equation: Constant [rho] and [mu] Heat Flux Vector: Isotropic Material Energy Balance: General Form Energy Balance: Constant [rho], [kappa] and [mu]

"Mathematical modeling and computer simulation have been widely embraced in industry as useful tools for improving materials processing. Although 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 nonmetallic 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. Thus, chapters explain how to decide which physical phenomena are important in specific applications, and how to develop analytical models. A unique feature is the use of scaling analysis as a rational way to simplify the general governing equations for each individual process. The book also treats selected numerical methods, showing the relationship among the physical system, analytical solution, and the numerical scheme. A wealth of practical, realistic examples are provided, as well as homework exercises. Students, and practicing engineers who must deal with a wide variety of materials and processing problems, will benefit from the unified treatment presented in this book."--BOOK JACKET.

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