This article examines the critical features of four key areas of modeling transport phenomena associated with casting processes. These include heat and species transport in a metal alloy, flow of the liquid metal, tracking of the free metal-gas surface, and inducement of metal flow via electromagnetic fields. Conservation equations that represent important physical phenomena during casting processes are presented. The article provides a discussion on how the physical phenomena can be solved. It provides information on a well-established array of general and specific computational tools that can be readily applied to modeling casting processes. The article also summarizes the key features of the conservation equations in these tools.

This article presents conservation equations for heat, species, mass, and momentum to predict transport phenomena during solidification processing. It presents transport equations and several examples of their applications to illustrate the physics present in alloy solidification. The examples demonstrate the utility of scaling analysis to explain the fundamental physics in a process and to demonstrate the limitations of simplifying assumptions. The article concludes with information on the solidification behavior of alloys as predicted by full numerical solutions of the transport equations.

This article provides a comprehensive review and critical assessment of numerical modeling of heat and mass transfer in fusion welding. The different fusion welding processes are gas tungsten arc welding, gas metal arc welding, laser welding, electron beam welding, and laser-arc hybrid welding. The article presents the mathematical equations of mass, momentum, energy, and species conservation. It reviews the applications of heat transfer and fluid flow models for different welding processes. Finally, the article discusses the approaches to improve reliability of, and reduce uncertainty in, numerical models.

In order to model macrosegregation, one must consider convection and the partitioning of segregating elements at the dendritic length scale. This article describes microsegregation with diffusion in the solid. It presents a continuum model of macrosegregation and illustrates the simulation of macrosegregation and microsegregation.

This article provides information on the classification of various composites manufacturing processes based on similar transport processes. The composites manufacturing processes can be grouped into three categories: short-fiber suspension methods, squeeze flow methods, and porous media methods. The article presents an overview of the modeling philosophy and approach that is useful in describing composite manufacturing processes.

This article provides an overview of the studies on computational modeling of the vacuum arc remelting (VAR) and electroslag remelting (ESR) processes. These models involve the axisymmetric analysis of the electromagnetic, flow, heat-transfer, and phase-change phenomena to predict the pool shape and thermal history of an ingot using two-dimensional axisymmetric models for VAR and ESR. Analysis of segregation of alloying elements during solidification that gives rise to macrolevel compositional nonuniformity in titanium alloy ingots is also described. The article discusses the important features of the control-volume-based computational method to review the unique aspects of the processes. Measurement of the properties of alloys and slags is explained and an analysis of the process variants for improving the predictive accuracy of the models is presented.

This article focuses on transport phenomena and modeling approaches that are specific to vapor-phase processes (VPP). It discusses the VPP for the synthesis of materials. The article reviews the basic notions of molecular collisions and gas flows, and presents transport equations. It describes the modeling of vapor-surface interactions and kinetics of hetereogeneous processes as well as the modeling and kinetics of homogenous reactions in chemical vapor deposition (CVD). The article provides information on the various stages of developing models for numerical simulation of the transport phenomena in continuous media and transition regime flows of VPP. It explains the methods used for molecular modeling in computational materials science. The article also presents examples that illustrate multiscale simulations of CVD or PVD processes and examples that focus on sputtering deposition and reactive or ion beam etching.

Computational fluid dynamics (CFD) is one of the tools available for understanding and predicting the performance of thermal-fluids systems. This article qualitatively describes the basic principles of CFD. The numerical methods, such as geometry description and discretization, used to solve the CFD equations are discussed. The article also demonstrates the application of CFD to a few casting problems.

This article provides an overview of experimental, analytical, and numerical tools for temperature evaluation of dry and lubricated systems. It describes the analytical methods and numerical techniques for frictional heating and temperature estimation, as well as viscous heating in full-film lubrication. The article also discusses the viscous heating temperature measurements and numerical analysis of viscous heating.

This article focuses on the various assumptions involved in the numerical modeling of welds, including the geometry of the welded structure and the weld joint, thermal stress, strain, residual stress, and the microstructure in the heat-affected and fusion zones.

This article is a comprehensive collection of formulas and numerical solutions, addressing many heat-transfer scenarios encountered in welds. It provides detailed explanations and dimensioned drawings in order to discuss the geometry of weld models, transfer of energy and heat in welds, microstructure evaluation, thermal stress analysis, and fluid flow in the weld pool.

Modeling of structure formation in casting of alloys involves several length scales, ranging from the atomic level to macroscopic scale. Intermediate length scales are used to define the microstructure of the growing phases and the grain structure. This article discusses the principles and applications of the phase field method and the cellular automaton method for modeling the direct evolution of structure at the intermediate length scales, where transport phenomena govern the spatial and temporal evolution of the structure that involves nucleation and growth.

This article focuses on the intermediate length scales, where transport phenomena govern the spatial and temporal evolution of a structure. It presents the cellular automaton (CA) and phase field (PF) methods that represent the state of the art for modeling macrostructure and microstructure. The article describes the principles of the PF method and provides information on the applications of the PF method. The CA model is introduced as a computationally efficient method to predict grain structures in castings using the mesoscopic scale of individual grains. The article discusses the coupling of the CA to macroscopic calculation of heat, flow, and mass transfers in castings and applications to realistic casting conditions.

This article discusses the three different modeling approaches for grain structures formed during solidification of metallic alloys: direct modeling of dendritic structure, direct modeling of grain structure, and indirect modeling of grain structure. The main construction bases, the scale at which it applies, and the mathematical background are presented for each modeling approach. The article concludes with a table that presents a comparison of the main inputs/outputs, approximations, numerical methods, kinetics laws, and applications for the three approaches to modeling of dendritic grain solidification.

This article presents effective stress equations that are based on the von Mises criterion, the Tresca criterion, and the Huddleston criterion. It describes the calculation of effective stresses for different cases: elastic stresses, steady-state creep stresses, stresses in a fully plastic case, and thermal stresses in a tube. The article illustrates the comparison of life predictions by the stress criteria and presents a simple mean diameter hoop stress equation, which is used for designing components. It also provides information on the multiaxial creep ductility of tubular components and multiaxial testing methods.

Computational fluid dynamics (CFD) is a computationally intensive three-dimensional simulation of thermal fluids systems where non-linear momentum transport plays an important role. This article presents the governing equations of fluid dynamics and an introduction to the CFD techniques. It introduces some common techniques for discretizing the fluid-flow equations and methods for solving the discrete equations. These include finite-difference methods, finite-element methods, spectral methods, and computational particle methods. The article describes the approaches for grid generation with complex geometries. It discusses the four-step procedures used in the CFD process for engineering design: geometry acquisition, grid generation and problem specification, flow solution, and post-processing and synthesis. The article also provides information on the engineering applications of the CFD. It concludes with a discussion on issues and directions for engineering CFD.

This article presents the governing equations for moving a solidification front, based on the balance of mass, momentum, energy, and solute. It reviews how material properties and geometry can be analyzed in the context of the governing equations. The article provides several example problems that illustrate how the hierarchy of time and length scales associated with transport leads to the important features of cast microstructures. It includes equations for estimating microsegregation in cast alloys.

This article begins with balance equations for mass, momentum, energy, and solute and the necessary boundary conditions for solving problems of interest in casting and solidification. The transport phenomena cover a vast range of length and time scales, from atomic dimensions up to macroscopic casting size and from nanoseconds for interface attachment kinetics to hours for casting solidification. The article describes how to determine which phenomena are most important at the particular length and time scale for the problem. It concludes with several examples of the application of transport phenomena in solidification, focusing on microstructure formation.