The past few decades have brought significant advances in the computational methods and in the experimental techniques used to study transport phenomena in materials processing operations. However, the advances have been made independently and with competition between the two approaches. Mathematical models are easier and less costly to implement, but experiments are essential for verifying theoretical models.In Mathematical and Physical Modeling of Materials Processing Operations, the authors bridge the gap between mathematical modelers and experimentalists. They combine mathematical and physical modeling principles for materials processing operations simulation and use numerous examples to compare theoretical and experimental results.The modeling of transport processes is multi-disciplinary, involving concepts and principles not all of which can be associated with just one field of study. Therefore, the authors have taken care to ensure that the text is self-sustaining through the variety and breadth of topics covered. Beyond the usual topics associated with transport phenomena, the authors also include detailed discussion of numerical methods and implementation of process models, software and hardware selection and application, and representation of auxiliary relationships, including turbulence modeling, chemical kinetics, magnetohydrodynamics, and multi-phase flow. They also provide several correlations for representing the boundary conditions of fluid flow, heat transfer, and mass transfer phenomena.Mathematical and Physical Modeling of Materials Processing Operations is ideal for introducing these tools to materials engineers and researchers. Although the book emphasizes materials, some of the topics will prove interesting and useful to researchers in other fields of chemical and mechanical engineering.

Table of Contents:
INTRODUCTION
Introductory Remarks
Mathematical Modeling
Physical Models
Pilot Plant
BUILDING BLOCKS OF MATHEMATICAL MODELS
Introduction
General Philosophy of Model Development
Some Basic Physical Situations of Relevance to Modeling
SCIENCE BASE OF MATHEMATICAL MODEL DEVELOPMENT
Introduction
Fluid Flow Phenomena
Heat Transfer
Diffusion and Mass Transfer
Multiphase Flow
SUBSIDIARY RELATIONSHIPS USED IN MATHEMATICAL MODELING
Introduction
Chemical Equilibria and Chemical Kinetics
Electromagnetic Flow Phenomena
Non-Newtonian Rheology of Semisolid Slurry Systems
Turbulence Modeling
Useful Correlations
Determination of Physical Properties
SCALING, SCOPING, AND ASYMPTOTIC SOLUTIONS
Introduction
Scaling
Scoping and Asymptotic Solutions
NUMERICAL TECHNIQUES
Introduction
Linear Equations
Nonlinear Equations
Functional Approximation
Numerical Differentiation
Numerical Integration
Ordinary Differential Equations
Partial Differential Equations
Finite Difference Method
Finite Element Method
Orthogonal Collocation
Boundary Integral Method
Optimization
IMPLEMENTATION AND VERIFICATION OF PROCESS MODELS
Introduction
Hardware
Software
Artificial Intelligence
The Future of Modeling Implementations
Verification of Models
MATHEMATICAL MODELING CASE STUDIES
Introduction
Scaling and Scoping-Electrolytic Deposition
Simulations of Fluid Flow and Heat Transfer in Coextrusion
Infiltration Processing of Silicon Carbide
Stoichiometry Driven Marangoni Convection in GaAs Growth
Czochralski Crystal Growth
Flow Characteristics in Gas-Agitated Bath
BASIC ELEMENTS OF PHYSICAL MODELING
Principles of Physical Modeling
Flow Visualization Technique
Measurement of Turbulent Phenomena
Bubble Characteristics
Measurement of Interfacial Phenomena
Measurement of Heat and Mass Transfer
PHYSICAL MODELING EXAMPLES
Bubbling and Jetting
Mixing
Swirl Motion of Bubbling jet
Bubble Characteristics
Liquid Flow Characteristics in a Bath Agitated by Gas Injection
Heat Transfer Between Bubbles and Molten Metal
Heat Transfer Between Solid Body and Molten Metal
Mass Transfer Between Bubbles and Liquid
Mass Transfer Between a Solid Body and Liquid
Entrainment of Top Slag by Lower Molten Metal
Effects of Top Slag on Liquid Flow Characteristics
Turbulence Structure in Bottom Blown Bath with Top Slag Using Conditional Sampling
APPENDICES
Dimensionless Numbers Useful in Process Metallurgy
Fluid Flow Equations in Various Coordinate Systems
Components of the Stress Tensor for Newtonian Fluids in Various Coordinate Systems
The Viscous Dissipation Term for Newtonian Fluids in Various Coordinate Systems

Plus each chapter includes references