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 using Runge Kutta fourth order method. The effects of the physical parameters like fluid particle interaction parameter, ratio of free stream velocity parameter to stretching sheet velocity parameter, Prandtl number and Eckert number on the …show more content…
To our knowledge, no attempts have been made to analyze three dimensional stagnation- point flow of a dusty fluid towards stretching sheet.
The objective of the present study is to investigate the three-dimensional stagnation point flow of a dusty fluid towards a stretching sheet by solving Navier–Stokes and energy equations for both of fluid and particle flow. A similarity solution for governing equations is derived in this problem. The obtained ODEs are solved numerically using Runge Kutta fourth order method.
Velocity and temperature profiles are presented for different values of fluid particle interaction parameter, ratio of free stream velocity parameter to stretching sheet velocity parameter, Prandtl number and Eckert number for the both of fluid and dust. Also a comparison of the obtained numerical results is made with three and two- dimensional formula and some existing literature and good agreement is
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p, ρ, ρp, and μ are fluid pressure, density of the fluid, density of the dust phase and viscosity of the fluid, respectively. Also in energy equations, T and Tp are the temperature of the fluid and temperature of the dust phase, and k is the thermal conductivity of fluid.
The terms Fpi, Qp and (vpi-v)Fpi, represent respectively the particles force on fluid along i direction (the drag force due to the interaction between the fluid and dust phases), the heat transferred from particle phase to fluid phase and the dissipation work due to particles moving relative to the fluid per unit volume, that are expressed as follows:
where σ is particle radius, Kp is thermal conductivity of particle, N is number density of the dust phase, τv is the relaxation time of the of dust phase that express the time required by the particle cloud (dust) to reduce its velocity relative to the fluid, and τT is the thermal equilibrium time that express the time required by the particle cloud to reduce its temperature relative to the
They just forgot to mention the other effects of fluids in nature. “The influence of the fluid on a body moving through it depends not only on the body’s velocity but also on the velocity of the fluid,” this is called relative velocity ( ). The relative velocity of a body in a fluid has an effect on the magnitude of the acting forces. For example, as a long distance runner is running into a head wind, the force of the fluid is very strong. If the runner is running with the help of a tail wind, the current’s force is reduced and may even be unnoticeable.
The Water vapor Transmission Rate (WVTR) of the treated and untreated PP samples was calculated by Mocon Permatran, according to the standard of ASTM F 1249 – 90. The tests were carried out at 35 ºC under the condition of 100% RH. It was repeated for three times and the average mean values were reported. All specimens were conditioned at ambient conditions.
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.
On earth, substances tend to exist in one of three phases; either a solid, liquid, or gas. While solids and liquids have defining factors such as volume, and for solids only, a shape, gases exhibit neither of these. Gases naturally take the shape of and expand into the volume of the container, and change when placed in different surroundings. As gases are constantly moving around and colliding with the walls, they exert a force, or pressure, on the walls of its container. Pressure is one of the characteristic behaviors that gases exhibit, but due to their nature, various factor effect the pressures that a gas can exert. Towards the end of the eighteenth century, scientist began to stumble upon these various factors that affect gases, especially
A representation of the slow decrease in flux that can result from consolidation of the fouled layer is presented in figure 2.4.
Introduction to Aerodynamics Aerodynamics is the study of the motion of fluids in the gas state and bodies in motion relative to the fluid/air. In other words, the study of aerodynamics is the study of fluid dynamics specifically relating to air or the gas state of matter. When an object travels through fluid/air there are two types of flow characteristics that happen, laminar and turbulent. Laminar flow is a smooth, steady flow over a smooth surface and it has little disturbance. Intuition would lead to the belief that this type of air flow would be desirable.
The comparison between the vapour compression and vapour absorption systems are given in Table 1
The Equation Of State These three gas laws that were proposed by Boyle, Amontons and Charles can be summarised as follows: For a fixed mass of gas pV = constant if T = constant (i) p/T = constant if V = constant (ii) V/T = constant if p = constant (iii)
eddy currents that , along with hairs, cilia and mucus, help remove dust in the inhaled air
where p is the density of the fluid (in runner’s case: air); v is the velocity of the runner; A is the cross-sectional area perpendicular to the runner’s velocity; and D is the dimensionless quantity called the drag coefficient.
This chart shows the relationship between the fanning friction factor and the Reynolds number over a wide range of flow rates, from which the roughness parameter (e/D) for the piping system can be estimated.
...he principle numbers of Froude, Reynolds and Weber. Mathematical model predicts the heat and mass transfer in numerical framework for both transports phenomena of relevance to the industry continuous casting tundish system. Additionally, it has an excellent agreement outlet temperature respond the step input temperatures in the inlet stream of water in the tundish model. The simulations of 8x8 grid and 16x16 grid are applied to obtain significant difference between the TAV maps in which both grids are computed by software represent the specific flow of the fluid in the model and the steel caster as the actual size system. Therefore, the physical and mathematical modeling is used as a guidance to build a model before the prototype is constructed in terms of calculation, measurement and determination of specific fluid flow, heat and mass transfer in the water model.
On a more scientific note I am interested in mechanics of fluids. This interest was enforced last year when I had the opportunity to attend a lecture on fluid mechanics at P&G. At the conference I greatly expanded my knowledge regarding the physical aspect of fluids and their properties. In last year's AS course we have met a topic in this field. I will be applying ideas and knowledge gathered from last year for this investigation.
From the graph 2, it is seen clearly that the relationship between purity and boil-up rate is inversely proportional to each other. In order to achieve a good separation and high purity between the liquid and the vapour must be brought to an intimate contact by counter-current flow. Increasing the vapour flow actually means decreasing the interaction time between the down flowing liquid and up flowing vapour inside the column. Hence, if ...
As discussed in class, submission of your solutions to this exam will indicate that you have not communicated with others concerning this exam. You may use reference texts and other information at your disposal. Do all problems separately on clean white standard 8.5” X 11” photocopier paper (no notebook paper or scratch paper). Write on only one side of the paper (I don’t do double sided). Staple the entire solution set in the upper left hand corner (no binders or clips). Don’t turn in pages where you have scratched out or erased excessively, re-write the pages cleanly and neatly. All problems are equally weighted. Assume we are working with “normal” pressures and temperatures with ideal gases unless noted otherwise. Make sure you list all assumptions that you use (symmetry, isotropy, binomial expansion, etc.).