Search Results for mass equation

This article focuses on the basic turbulent flow, and the thermal, mass-transfer, and hydrodynamic phenomena for use in modeling physical processes during induction melting. It provides a discussion on transport phenomena equations that includes the approximation of convective terms in the transport equation and computational schemes for the fluid dynamics equation. The aspects of computational algorithms for specific magnetohydrodynamic problems with mutual influence of the magnetic field and melt flow due to the changing shape of the free surface are also considered. The article illustrates the application of the basic equations and approaches formulated for electromagnetic field and melt turbulent flow for the numerical study of an induction crucible furnace.

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 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.

This article provides an overview of common quenching media, the factors involved in the mechanism of quenching, and process variables, namely, surface condition, mass and section size of the workpiece, and flow rate of the quenching liquid. It describes the methods of quenchant characterization using hardening-power and cooling-power tests. The article discusses the fundamentals involved in heat-transfer coefficient and heat flux of quenching processes. This discussion is followed by various actual examples of applications of these methods using simplified equations. Quenchant evaluation, classification, selection, and maintenance are reviewed in detail. The article addresses the various reasons for quench oil variability and complications due to aging and contamination.

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.

Fluid flow is important because it affects weld shape and is related to the formation of a variety of weld defects in gas tungsten arc (GTA) welds. This article describes the surface-tension-driven fluid flow model and its experimental observations. The effects of mass transport on arc plasma and weld pool are discussed. The article reviews the strategies for controlling poor and variable penetration and describes the formation of keyhole and fluid flow in electron beam and laser welds. It also explains the fluid flow in gas metal arc welding and submerged arc welding, presenting its transport equations.

Molten salts, or fused salts, can cause corrosion by the solution of constituents of the container material, selective attack, pitting, electrochemical reactions, mass transport due to thermal gradients, and reaction of constituents and impurities of the molten salt with the container material. This article describes a test method performed using thermal convection loop for corrosion studies of molten salts. It discusses the purification of salts that are used in the Oak Ridge molten salt reactor experiment. The article also reviews the corrosion characteristics of nitrates/nitrites and fluoride salts with the aid of illustrations and equations.

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 is a comprehensive collection of the thermodynamic equations and property relations of the first and second laws of thermodynamics that are applicable to closed-system consisting of several homogeneous and heterogeneous phases.

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.

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.

This article is a comprehensive collection of fluid dynamic equations for properties of fluids, fluid statics, fluid motion, dimensional analysis, and boundary layer flow. It presents equations for analyzing problems in fluid mechanics, continuity equation, momentum equation, and energy equation for solving various problems related to fluid dynamics.

Computational fluid dynamics (CFD) provides an efficient, alternate, virtual approach for simulating and analyzing quenching processes with an impact on component design, manufacturing process, and quality. This article provides domain insights for quenching researchers and CFD practitioners for the modeling of the industrial quenching process and for supporting the diverse multifunctional needs in an industry, ranging from primary metallurgical companies (steel, aluminum, and other alloys), original equipment manufacturers, engineering companies, captive and commercial heat treating facilities, quench system manufacturers, and quench fluid suppliers. It describes the governing differential equations for the fluid flow and heat-transfer phenomena during quenching. The article also discusses different modeling categories to determine a CFD methodology for quenching.

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 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.

The control of the solidification process of cast iron requires understanding and control of the thermodynamics of the liquid and solid phases and of the kinetics of their solidification, including nucleation and growth. This article addresses issues that allow for the determination of probability of formation and relative stability of various phases. These include the influence of temperature and composition on solubility of various elements in iron-base alloys; calculation of solubility lines, relevant to the construction of phase diagrams; and calculation of activity of various components. It discusses the role of alloying elements in terms of their influence on the activity of carbon, which provides information on the stability of the main carbon-rich phases of iron-carbon alloys, that is, graphite and cementite. The article reviews the carbon solubility in multicomponent systems, along with saturation degree and carbon equivalent.