http://www.cfd-online.com/W/index.php?title=Special:Contributions/Zahidmath&feed=atom&limit=50&target=Zahidmath&year=&month=CFD-Wiki - User contributions [en]2015-07-02T21:34:03ZFrom CFD-WikiMediaWiki 1.16.5http://www.cfd-online.com/Wiki/User:ZahidmathUser:Zahidmath2005-11-25T08:54:37Z<p>Zahidmath: </p>
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<div>Hello Wikians,<br />
I am Zahid Shareef from Pakistan. I did my MPhil in Fluid Mechanics and presently working at Allama Iqbal Open University, Islamabad, Pakistan. I can be contacted by zahidmath@yahoo.com.</div>Zahidmathhttp://www.cfd-online.com/Wiki/Steady_flowSteady flow2005-11-25T08:49:58Z<p>Zahidmath: </p>
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<div>A steady flow is characterized by constant values of all flow variables at any location in space. If <math>\phi</math> is any flow quantity like velocity, pressure, etc., then in steady flow<br />
<br />
:<math><br />
\frac{\partial \phi}{\partial t}(x,y,z,t) \equiv 0<br />
</math><br />
<br />
Hence all flow quantities depend only on the spatial location<br />
<br />
:<math><br />
\phi(x,y,z,t) = \phi(x,y,z)<br />
</math><br />
Where as a flow in which flow/fluid properties keep on changing w.r.t. time, is termed as unsteady flow.</div>Zahidmathhttp://www.cfd-online.com/Wiki/ContinuumContinuum2005-11-22T09:35:50Z<p>Zahidmath: </p>
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<div>[[Continuum]]<br />
Fluids are characterized by the fact that intramolecular distances are much larger than the size of the molecules. In such a discontinuous medium, the terms velocity, acceleration, density and pressure etc. at a point have no meaning. For instance, density is equal to zero at point, if that point does not coincide with a molecule and would be very large if it does coincide with a molecule. Similarly velocity is zero for the first case and equal to the velocity of the molecule in the second case.<br />
In the mathematical description of fluid flow, it is therefore necessary to assume that the flow quantities such as velocity and pressure vary continuously from one point to another. Once we make the assumption that the fluid itself is continuous in its properties, we may describe these properties with continuous functions of space and time and may apply differential equations in the analysis of processes. Equations derived on the basis of this assumption have withstood the test of time and the treatment of a fluid medium as a continuum has firmly been established.</div>Zahidmathhttp://www.cfd-online.com/Wiki/Introduction_to_numerical_methodsIntroduction to numerical methods2005-11-21T07:05:19Z<p>Zahidmath: </p>
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<div><p>[[Fluid]]s could be regarded as substances those on application of external force deform or show very little resistance to deformation. This deformation in the cases of liquid and gases is substantial. Both obey common laws of motion and both for most practical computational purposes can be regarded as continuum. Forces can be considered as body forces, example: forces due to gravity or they can be considered as surface forces example: surface tension.</p><br />
<p><br />
Based on speed and nature of flow, flows could be categorized into: <br><br />
*[[Laminar flow]] <br><br />
*[[Turbulent flow]] <br><br />
Or it could be categorized into: <br><br />
*[[Subsonic flow]] <br><br />
*[[Supersonic flow]] <br><br />
Based upon their [[Mach number]]. This Mach number could be used to determine whether the flow shall be considered as [[Incompressible flow ]] or [[Compressible flow]] for computational purposes. For the flows of Mach number smaller than 0.3, we can safely assume them as incompressible for all computational purposes. </p><br />
<p><br />
Based upon the degree of effect upon the viscosity on the flow, the flows could be classified as [[Viscous flow]] or [[Inviscid flow]] in nature. Fluids obeying [[Newtonâ€™s law]] are called [[Newtonian fluid | Newtonian fluids]]. <br />
Further based upon the phases of flow, the flows can be considered as [[multiphase]] or single phase flows. </p><br />
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== Control Volume Approach ==<br />
<p> <br />
Conservation laws can be applied to given quantity of fluid. However, it is more convenient to apply them on a small spatial region, called Control volume. For this purposes the geometry under consideration is subdivided into smaller sub-regions. Together they are called mesh or grid. And the approach used is called Control volume approach for solving the flow problem. <br><br />
The figure 1.1 shows one such computational domain. <br><br />
<br />
[[Image:Img_nm_intro_01.jpg]] <br><br />
Figure 1.1 <br><br />
</p><br />
== Conservation Principles ==<br />
== Conservation of scalar quantities ==<br />
== Simple Flows ==<br />
=== [[Incompressible flow]] ===<br />
=== [[Inviscid flow | Euler or inviscid flow]] ===<br />
=== [[Potential flow]] ===<br />
=== [[Stokes flow | Stokes or creeping flow]] ===<br />
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<i> Return to [[Numerical methods | Numerical Methods]] </i></div>Zahidmathhttp://www.cfd-online.com/Wiki/Newtonian_fluidNewtonian fluid2005-11-16T11:06:42Z<p>Zahidmath: </p>
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<div>Division of fluids in Newtonian and non-Newtonian fluids is done on the basis of relation between stress and strain.<br />
In Newtonian fluids the realtion between stress and corresponding rate os strain in direct and linear.</div>Zahidmathhttp://www.cfd-online.com/Wiki/Non-Newtonian_fluidNon-Newtonian fluid2005-11-16T11:03:20Z<p>Zahidmath: </p>
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<div>Fluids for which stress and rate of strain are directly but non-linearly rated to each other are called non-Newtonian fluids. Blood, mud, paints and polymers are some of the examples of non-Newtonian fluids.</div>Zahidmath