Search Results for species conservation equation

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.

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 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.

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.

A potential pH diagram is a graphical representation of the relations, derived from the Nernst equation, between the pH and the equilibrium potentials (E) of the most probable electrochemical reactions occurring in a solution containing a specific element. This article describes three types of reactions for calculation and construction of E-pH diagrams: electrochemical reactions of pure charge (electron) transfer; reactions involving both electron and solvated proton transfer; and acid-base reactions of pure solvated proton transfer. It illustrates the practical use of E-pH diagrams for temperature aqueous solutions and adsorbed species and in prediction of corrosion of nickel and copper.

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.

This article describes the Schottky defect and the Frenkel defect in oxides. It provides information on the p-type metal-deficit oxides and n-type semiconductor oxides. The article discusses diffusion mechanisms and laws of diffusion proposed by Fick. It explains the oxide texture of amorphous and epitaxy oxide layers and presents equations for various oxidation reaction rates. The article reviews different theories to describe the oxidation mechanism. These include the Cabrera-Mott, Hauffe-IIschner, Grimley-Trapnell, Uhlig, and Wagner theories.

This article discusses the fundamental aspects of phase-field microstructure modeling. It describes the evolution of microstructure modeling, including nucleation, growth, and coarsening. The article reviews two approaches used in the modeling nucleation of microstructure: the Langevin force approach and explicit nucleation algorithm. Calculation of activation energy and critical nucleus configuration is discussed. The article presents the deterministic phase-field kinetic equations for modeling growth and coarsening of microstructure. It also describes the material-specific model inputs, chemical free energy and kinetic coefficients, for phase-field microstructure modeling. The article provides four examples that illustrate some aspects of phase-field modeling.

There is a need for models that predict the percentage and size of porosity formed during solidification in order to effectively predict mechanical properties. This article provides an overview of equations that govern pore formation. It reviews the four classes of models, highlighting both the benefits and drawbacks of each class. These classes include criteria functions, analytical models, continuum models, and kinetic models. The article also tabulates the criteria functions for porosity prediction.

This article describes various methods of electrochemical analysis, namely coulometry, electrogravimetry, voltammetry, electrometric titration, and nanometer electrochemistry. The discussion covers the general uses, sample requirements, application examples, advantages, and limitations of these methods. Some of the factors pertinent to electrochemical cells are also provided. In addition, the article provides information on various potentiometric membrane electrodes used to quantify numerous ionic and nonionic species.

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.

Aluminum wrought products, castings, welds, and fasteners are used in many structural applications where they are required to safely support a load. It is useful to design aluminum structural components with its structural properties in mind from conceptualization rather than attempting to mimic components of other materials. This article discusses design specifications, design requirements and methods, and material properties used in aluminum structural design. These properties include tensile yield strength and tensile ultimate strength, welding, and ductility. The article describes various factors that affect the strength of two categories of aluminum structural components, namely members and connections. Design requirements for aluminum bolts, rivets, screws, and pins are provided. The article concludes with a discussion on the considerations for serviceability, namely deflections and vibrations.

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.

Ultraviolet/visible (UV/VIS) absorption spectroscopy is a powerful yet cost-effective tool that is widely used to identify organic compounds and to measure the concentration of principal and trace constituents in liquid, gas, and solid test samples. This article emphasizes the quantitative analysis of elements in metals and metal-bearing ores. The instrumentation required for such applications consists of a light source, a filter or wavelength selector, and some type of visual or automated sensing mechanism. The article examines common sensing options and provides helpful information on how to set up and run a variety of UV/VIS absorption tests.

Electronic structure methods based on the density functional theory (DFT) are used as a powerful tool for assessing the mechanical thermodynamic and defect properties of metal alloys. This article presents the origins of the electronic structure methods and their strengths and limitations. It describes the basic procedures for calculating essential structural properties in metal alloys. The article reviews the approximations and computational details of the pseudopotential plane wave methods used in metal systems. It provides information on the applications of DFT methods in metal alloy systems. The article discusses the calculations of a variety of structural, thermodynamic, and defect properties, with particular emphasis on structural metal alloys and their derivatives.

Computational fluid dynamics (CFD) is reserved for computationally intensive three-dimensional simulations of thermal fluids systems where nonlinear momentum transport plays an important role. This article presents the governing equations of fluid dynamics and an introduction to the CFD techniques for their solution. It introduces discretization techniques that are used by finite-difference, finite-volume, finite-element, spectral, and some particle methods. Associated concepts of numerical stability and accuracy are also reviewed. The article describes two approaches for grid generation with complex geometries: the use of unstructured grids and the use of special differencing methods on structured grids. The article describes the four-step procedures of the CFD process: geometry acquisition, grid generation and problem specification, flow solution, and post-processing and synthesis. It provides information on the applications of the engineering CFD. Issues and directions for the engineering CFD are also described.