In classical fluid dynamics, the Navier-Stokes equations for incompressible viscous fluids and its special (limiting) case the Euler equations for inviscid fluids are sets of non-linear partial differential equations that describes the spatiotemporal evolution of a fluid (gas). Both equations are derived from conservative principles and they model the behavior of some macroscopic variables namely: mass density, velocity and temperature. The evolution of a fluid (gas) can also be described by the
etc. Pressure as being three dimensional and velocity of fluid were explained thanks to Euler equations, but the equations were not enough to clarify the viscosity (friction) in a flow field. In the next century, Euler equations were developed by Claude-Louis Navier and George Stokes independently, and then new equations were derived and nowadays they are known as Navier-Stokes equations. These equations provided to describe internal friction acting in a flow field, but could not explain friction
results indicate that thermal forces have a dramatic effect on the flow of silicon melt. The simulation results are in reasonable agreement with the predictions of the theoretical approach. Kew words: Simulation and modeling; Thermal analysis; Navier-Stokes equations; Solar energy materials; Finite element analysis; 1. INTRODUCTION The unsustainable nature of fossil fuels as an energy source, from the point of view of future availability and environmental impact, has spurred an interest in diversification
The science of fluid mechanics is neither new nor biblical; however, most of the progress in this field was made in the 20th century. Therefore it is appropriate to open this text with a brief history of the discipline, with only a very few names mentioned. As far as we can document history, fluid dynamics and related engineering were always integral parts of human evolution. Ancient civilizations built ships, sails, irrigation systems, and flood-management structures, all requiring some basic understanding
Abstract: The existing solutions of Navier–Stokes and energy equations in the literature regarding the problem of stagnation-point flow of a dusty fluid over a stretching sheet are only for the case of two dimensional. In this research, the steady axisymmetric three–dimensional stagnation point flow of a dusty fluid towards a stretching sheet is investigated. The governing equations are transformed into ordinary differential equations by presentation a similarity solution and then are solved numerically
other related areas. The models used were usually described using partial differential equation, integral and integrodifferential equations, variational and probability theory methods, potential theory, the theory of functions of complex variable. Some of the dominant western mathematicians and scientist who succeeded in studying and describing the physical world by mathematical modeling are Lord Kelvin, George Stokes, James Clerk Maxwell, and Guthrie Tait. The pioneers in this area of study made several
this subject was not well quantified; instead, textbooks were comprised of endless tables and figures demonstrating phenomena. When Daniel Bernoulli, Claude Navier and George Stokes introduced mathematics to the realm of fluid flow, new research was possible, but this work was highly theoretical and required extensive use of differential equations (Eckert 15). Ludwig Prandtl was the man who quantified many fluid flow principles and created his own theories about boundary separation and airfoil dynamics
analyze the industrial and non-industrial application. Historically, methods were first developed to solve the linearized potential equations. Two-dimensional (2D) methods, using conformal transformations of the flow about a cylinder to the flow about an airfoil were developed in the 1930s. The fundamental basis of almost all CFD problems are the Navier–Stokes equations, which define any single-phase (gas or liquid, but not both simultaneously) fluid flow. CFD analysis is widely used in industries
Heat indulgence techniques are the prime concern to remove the waste heat produced by Electronic Devices, to keep them within permitted operating temperature limits. Heat indulgence techniques include heat sinks, fans for air cooling, and other forms of cooling such as liquid cooling. Heat produced by electronic devices and circuitry must be self-indulgent to improve reliability and prevent premature failure. Integrated circuits such as CPUs, chipset, graphic cards, and hard disk drives are susceptible
paper ... ...ons and CFD results of the BWB configuration are represented, including aerodynamic advantages and aerodynamics features of BWB configuration. Israel Aircraft Industries pioneers, Peigin and Epstein [16] used NES multiblock code (a Navier-Stokes solver) with the aim of developing an aircraft with minimum drag. The baseline geometry used in this project was same as Qin et al. [15] with lift coefficient of 0.41 and Mach Number 0.85. The resulted design eliminated the shock and the initial
Most of the large dams designed with complicated geometry in which physical models have been used extensively. Overflow design guidelines has been used for standard geometries, which are fairly simple. For more complex geometries, physical and numerical models studied here was helpful. The disadvantages with the physical models are high costs and that it can take fairly long time to get the results. In this paper we used a numeric method that is called volume of fluid (VOF) to calculate flow rates
(4) The balance of linear momentum for the viscous fluid through porous media according to Brinkman-Darcy equation is , (5) The basic assumptions that lead to the Brinkman-Darcy equation were illustrated by Rajagopal [23], and can be summarize in the following points: 1- The porous medium is a solid and thus the balance of linear momentum of the porous medium can be ignored. 2- The interactive
Magnetohydrodynamics (MHD) is the study of the interaction between magnetic fields and moving conducting fluids. The idea of magnetohydrodynamics phenomenon was first conceived by Michael Faraday in the year 1832 in his Backerian Lecture to the Royal society. In Great Britain he did an experiment at the waterloo Bridge for measuring the current from the flow of the river Thamus in earth’s magnetic field. This experiment in a way outlined the basic idea behind MHD generation over the years after that
2.1 The Continuous Casting The Continuous Casting is a highly efficient manufacturing process, whereby molten metal is solidified into long, semi-finished shapes with constant cross section for subsequent processing in the finishing mills. Every year around 1 billion tons of steel, 20 million tons of aluminium and over 1 million tons of nickel, copper and other metals are produced all over the world in this manner. Continuous casting is distinguished from other solidification processes by its “steady
decade. The profile of a plane diffuser with given upstream width and length had been optimized to obtain the maximum static pressure rise by (Cabuk & Modi, 1992). The steady-state Navier–Stokes equation was used to model the flow through the diffuser considering 2-D, incompressible and laminar flow. A set of ad joint equations had been solved to get the direction and relative magnitude of change in the diffuser profile that leads to a higher pressure rise (Haftka & Madsen,
Roadside barrier are commonly used as a tool to reduce the pollution dispersion which exist in residential area which are nearby to industrial or highway. In this study, 2 dimensional computational fluid dynamic has been conducted to simulate the roadside barrier impact on near road air pollution. Different height of the barrier and the velocity input will be evaluate Keywords: Air pollution, Barrier, CFD modeling 1.0 Introduction In recent year, air pollution has been rapidly increasing caused
Magnetohydrodynamics (MHD) is the study of the interaction between magnetic fields and moving conducting fluids. The idea of magnetohydrodynamics phenomenon was first conceived by Michael Faraday in the year 1832 in his Backerian Lecture to the Royal society. He infact carried out an experiment at the waterloo Bridge in Great Britain for measuring the current from the flow of the river Thamus in earth’s magnetic field. This experiment in a way outlined the basic concept behind MHD generation over
What is FEA? Finite element analysis (FEA) is a computerized method for predicting how a product reacts to real-world forces, vibration, heat, fluid flow, and other physical effects. Traditionally, a branch of Solid Mechanics. Nowadays, a commonly used method for multiphysics problems. Integrates Finite Element Analysis (FEA) in every 3D design of an machine. FEA visualizations ensure proper design by eliminating unnecessary costs and weight in a machine, while maximizing the structural strength
This paper first reviews the metallurgical process of continuous steel slab casting in terms of fluid flow, heat and mass transfers in the manufacture production. Finally, this paper reviews the physical and mathematical modelling in physical experiment and mathematical models, which has been used to study in the process. Keywords: Continuous Casting, Steel, Slab, Physical Modelling, Tundish, Mathematical Modelling, Fluid Flow, Heat Transfer, Mass Transfer, Instruction, Report 1. Introduction Continuous
Chapter 1 INTRODUCTION In thermodynamics Refrigeration is the major application area, in which the heat is transferred from a lower temperature region to a higher temperature region. The devices which produce refrigeration are known as Refrigerators and the cycle on which it operates are called refrigeration cycles. Vapour compression refrigeration cycle is the most regularly used refrigeration cycle in which the refrigerant is alternately vaporized and condensed and in the vapor