Search Results for energy equation

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.

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 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.

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.

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 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.

Electromagnetic problem solutions are based on the macroscopic theory of the continuous model for the electromagnetic field (EMF). It is described by a system of integral or partial differential equations for five vector quantities, namely, electric field strength, electric flux density, current density, magnetic field strength, and magnetic flux density. This article describes the behavior of the EMF by Maxwell's equations in integral or differential forms. It discusses the definition of potentials; methods of mathematical modeling; boundary conditions; and energy, power density, and electromagnetic forces.

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 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.

This article focuses on the axisymmetric 2.5-dimensional approach used in metal powder injection molding (PIM) simulations. It describes three stages of PIM simulations: filling, packing, and cooling. The article discusses the process features of numerical simulation of PIM, such as filling and packing analysis, cooling analysis, and coupled analysis between filling, packing, and cooling stages. It explains the experimental material properties and verification for filling, packing, and cooling stages in the PIM simulations. The article presents simulation results from some of the 2.5-dimensional examples to demonstrate the usefulness of the computer-aided engineering analysis and optimization capability of the PIM process.

This article focuses on the directed-energy deposition (DED) additive manufacturing (AM) technique of biomedical alloys. First, it provides an overview of the DED process. This is followed by a section describing the design and development of the multiphysics computational modeling of the layer-by-layer fusion-based DED process. A brief overview of the primary governing equations, boundary conditions, and numerical methods prescribed for modeling laser-based metal AM is then presented. Next, the article discusses fundamental concepts related to laser surface melting and laser-assisted bioceramic coatings/composites on implant surfaces, with particular examples related to biomedical magnesium and titanium alloys. It then provides a review of the processes involved in DED of biomedical stainless steels, Co-Cr-Mo alloys, and biomedical titanium alloys. Further, the article covers novel applications of DED for titanium-base biomedical implants. It concludes with a section on the forecast of DED in biomedical applications.

The primary fossil fuels are generally defined as coal, oil, natural gas, tar sands, and shale oil. This article discusses the characteristics and the types of fuels used in fossil and fuel industries. It describes the energy conversion in fuels and outlines the efficiency of a heat engine with the help of the Carnot equation.

This article discusses the application of thermodynamic in the form of phase diagrams for visually representing the state of a material and for understanding the solidification of alloys. It presents the derivation of the relationship between the Gibbs energy functions and phase diagrams, which forms the basis for the calculation of phase diagrams (CALPHAD) method. The article also discusses the calculation of phase diagrams and solidification by using the Scheil-Gulliver equation.

Ultrasonic welding (UW), as a solid-state joining process, uses an ultrasonic energy source and pressure to induce oscillating shears between the faying surfaces to produce metallurgical bonds between a wide range of metal sheets and wires. This article reviews the models of the ultrasonic welding with an emphasis on governing equations, material behavior, and heat generation of the process. It discusses the resulting factors, namely, vibration, friction, temperature, and plastic deformation as well as the bonding strength and its mechanism.

Damping is the energy dissipation properties of a material or system under cyclic stress. The vibrational and damping characteristics of composites are important in many applications, including ground-based and airborne vehicles, space structures, and sporting goods. This article describes the damping characteristics of unidirectional composites, when they are subjected to longitudinal shear, longitudinal tension/compression, and transverse tension/compression. It presents equations that govern the overall damping capacity of beams that are cut from laminated plates. The article discusses the effect of temperature on damping and provides information on the relationship between damping and strength.