Modeling in materials processing

Description

While courses in materials processing cover modeling, they usually treat 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. They emphasize understanding basic physical phenomena and knowing how to include them in a model. Students will learn how to use scaling analysis as a general tool for simplifying models and for obtaining rapid estimates of results. The book also includes selected numerical methods, a wealth of practical, realistic examples, and homework exercises ''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.  Read more... 1.1 What Is a Model? 1 -- 1.2 A Simple Pendulum 2 -- 1.3 One-Dimensional Traffic Flow 6 -- 2 Governing Equations 24 -- 2.2 Mass Balance 29 -- 2.3 Momentum Balance 33 -- 2.4 Energy Balance 45 -- 3 Scaling and Model Simplification 60 -- 3.2 Basic Scaling Analysis 62 -- 3.3 Small Parameters and Boundary Layers 69 -- 3.4 Classical Dimensionless Groups 76 -- 3.5 Nondimensionalization for Numerical Solutions (Advanced) 78 -- 4 Heat Conduction and Materials Processing 87 -- 4.1 Steady Heat Conduction in Solids 90 -- 4.2 Transient Heat Conduction 93 -- 4.3 Conduction with Phase Change 106 -- 5 Isothermal Newtonian Fluid Flow 132 -- 5.1 Newtonian Flow in a Thin Channel 132 -- 5.2 Other Slow Newtonian Flows 143 -- 5.3 Free Surfaces and Moving Boundaries 149 -- 5.4 Flows with Significant Inertia 161 -- 6 Non-Newtonian Fluid Flow 190 -- 6.1 Non-Newtonian Behavior 190 -- 6.2 Power Law Model 192 -- 6.3 Power Law Solutions for Other Simple Geometries 200 -- 6.4 Principles of Non-Newtonian Constitutive Equations 202 -- 6.5 More Non-Newtonian Constitutive Equations 209 -- 6.6 Generalized Hele-Shaw Approximation 217 -- 7 Heat Transfer with Fluid Flow 239 -- 7.1 Uncoupled Advection 239 -- 7.2 Temperature-Dependent Viscosity and Viscous Dissipation 250 -- 7.3 Buoyancy-Driven Flow 259 -- 8 Mass Transfer and Solidification Microstructures 282 -- 8.1 Governing Equations for Diffusion 282 -- 8.2 Solid-State Diffusion 285 -- 8.3 Solidification Microstructure Development 295 -- A Mathematical Background 327 -- A.1 Scalars, Vectors, and Tensors: Definitions and Notation 327 -- A.2 Vector and Tensor Algebra 331 -- A.3 Differential Operations in Rectangular Coordinates 335 -- A.4 Vectors and Tensors in Cylindrical and Spherical Coordinates 337 -- A.5 Divergence Theorem 339 -- A.6 Curvature of Curves and Surfaces 339 -- A.7 Gaussian Error Function 343 -- B Balance and Kinematic Equations 348 -- B.1 Continuity Equation: General Form 348 -- B.2 Continuity Equation: Constant [rho] 348 -- B.3 Rate-of-Deformation Tensor 349 -- B.4 Vorticity Tensor 350 -- B.5 General Equation of Motion 350 -- B.6 Navier-Stokes Equation: Constant [rho] and [mu] 352 -- B.7 Heat Flux Vector: Isotropic Material 353 -- B.8 Energy Balance: General Form 354 -- B.9 Energy Balance: Constant [rho], [kappa] and [mu] 355