An oscillatory hydrodynamic flow through porous medium bounded by two horizontal parallel porous plates in the presence of transverse magnetic field is investigated. Both the stationary plates are subjected to the same constant injection / suction velocities ( V ). A closed form analytical solution is obtained and the affects of different parameters (Injection / suction Parameter, Darcy number, Hartmann number, Frequency of oscillations etc.) on velocity field and skin-friction are discussed with the help of graphs in details. Key words: Oscillatory flow, Magnetic field, Injection / suction, Planner channel. 1 Introduction: The flows of fluids through porous media have attracted the attention of a number of scholars because of their possible applications in many branches of science and technology. In fact a porous material containing the fluid is a non-homogeneous medium but it may be possible to treat it as a homogeneous one, for the sake of analysis, by taking its dynamical properties to be equal to the averages of the original non-homogeneous continuum. Thus a complicated problem of the flow through a porous medium gets reduced to the flow problem of a homogeneous fluid with some additional resistance. The hydrodynamic channel flow is a classical problem for which exact solution can be obtained Schillicting [1]. Eckert [2] obtained the exact solution of Navier-Stokes equations for the flow between two parallel porous plates with constant injection/suction. In view of numerous important engineering and geophysical applications of the channel flows through porous medium, for example in the fields of chemical engineering for filtration and purification processes, in the fields of agriculture engineering f... ... middle of paper ... ...Sci. Acad. 75(1) (2009): 41-48. 14 Garg, B.P., Singh, K.D. and Pathak, Reena (2011). An analysis of radiative, free-convective and mass transfer flow past an accelerated vertical plate in the presence of transverse magnetic field, J. Rajasthan Acad. Phy. Sci. 10(1) (in press). 15 Moreau, R. “MagnetoHydrodynamics”. Kluwer Academic Publishers, Dordrecht (1990). 16 Makinde, O.D. and Mhone, P.Y. “Heat Transfer to MHD Oscillatory Flow in a Channel Filled with Porous Medium”. Rom. Journ. Phys. 50 (2005): 931-938. 17 Mehmood, A. and Ali, A. “The Effect of Slip Condition on Unsteady MHD Oscillatory Flow of a Viscous Fluid in a Planer Channel”. Rom. Journ. Phys. 52(1-2) (2007): 85-91. 18 Singh, K.D. and Garg, B.P. “Radiative Heat Transfer in MHD Oscillatory Flow through Porous Medium Bounded by Two Vertical Porous Plates”. Bull. Cal. Math. Soc.102(2) (2010) 129-138.
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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.
Darcy’s law provides an accurate description of the flow of ground water in almost all hydrogeological environments. Henri Darcy established empirically that the flux of water through a permeable formation is proportional to the distance between top and bottom of the soil column.
The shear viscosity is a transport coefficient for momentum in inhomogeneous flows. This transport coefficient, which is widely used to describe both plasmas and fluids, relates two hydrodynamic quantities: shear stress and shear rate. The shear stress Pxy is the off-diagonal element of a pressure tensor, and the shear rate γ is the transverse gradient of the flow velocity u. For a flow in the y direction,
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 Bernoulli’s equation was mainly derived for ideal fluids i.e zero viscous fluids hence they are frictionless. But all the fluids are real and has some viscosity and hence offer resistance to flow. When the fluid is flowing there will always be some losses across the sections and Bernoulli’s equation considers all the losses.
Trefil, J. S. (1975) Introduction to the physics of fluids and solids (New York: Pergamon Press).
The horizontal flow velocities show that a wake is formed aft of the cylinder as expected.
The next type of heat transfer is convection. Convection is heat transferred by a gas or liquid. Such as dumping hot water into a cold glass of water, making the water overall warmer. The last type of heat transfer is radiation.
...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.
Cengel, Y. A., & Boles, M. A. (2011). Thermodynamics: An engineering approach (7th ed.). New York, NY: McGraw-Hill.¬¬¬¬
The process of conduction between a solid surface and a moving liquid or gas is called convection. The motion of the fluid may be natural or forced. If a liquid or gas is heated, its mass per unit volume generally decreases. If the liquid or gas is in a gravitational field, the hotter, lighter fluid rises while the colder, heavier fluid sinks. For example, when water in a pan is heated from below on my stove, the liquid closest to the bottom expands and its density decreases. The hot water as a result rises to the top and some of the cooler fluid descends toward the bottom, thus setting up a circulatory motion. This is also why the heating of a room by a radiator depends less on radiation than on natural convection currents, the hot air rising upward along the wall and cooler air coming back to the radiator from the side of the bottom. Because of the tendencies of hot air to rise and of cool air to sink, radiators are positioned near the floor and air-conditioning outlets near the ceiling for maximum efficiency.