Thus current work presents a theoretical study on the stagnationpoint flow of nanofluid over an exponentially stretching sheet. In earlier releases, the exit stagnation pressure was assumed to be atmospheric. Stagnation point flow this animation depicts the particle trajectories and streamlines which are the same in this case for an inviscid stagnation point flow. These authors studied the problems of stagnation point flow in micropolar fluids with no slip effects at the boundary. Continue this line forward until it hits the airfoil. Is there a specific method to do this apart from getting the point with the highest pressure value. Numerical simulation of heat transfer in mhd stagnation point flow of. Stagnation point in dynamic flow physics stack exchange. The velocity of the external flow is assumed to vary linearly with the distance from the stagnationpoint. Part 2, author neice, s e and rutowski, r w and chan, j k, abstractnote an experimental investigation of the heattransfer rates at the stagnation point of a. The study of laminar flow of heat and mass transfer over a moving surface in bionanofluid is of considerable interest because of its importance for industrial and technological processes such as fabrication of bionano materials and thermally enhanced media for bioinspired fuel cells. So obviously, only the static pressure will contribute, not the dynamic pressure. In those cases when flows have stagnation points, a strong correlation between the alignment of vorticity vector and the local manifolds the principal directions of the strain tensors of the stagnation points has been observed. The fluid is electrically conducting in the presence of a uniform magnetic field.
Hiemenz 2 discovered that stagnationpoint flow can be analyzed by the navierstokes ns equations through similarity solution in which the. The purpose of this paper is to analyse numerically the steady stagnationpoint flow of a viscous and incompressible fluid over continuously nonaligned stretching or shrinking surface in its own plane in a waterbased nanofluid which contains three different types of nanoparticles, namely, cu, al2o3 and tio2. The central stagnation point is marked with a pale blue circle. Governing equations the 2dimensional navierstokes equations for stagnationpoint flow shown in figure 1 can be written as 5. The diagram for the stagnation point over a pitot probe looks very similar. The study of two dimensional stagnation point flow of maxwell fluid over a shrinking sheet is reported by motsa et al. Abstracttwodimensional stagnationpoint flow in three different aspect ratios is studied by solving the full navierstokes equations with the computational fluid dynamics cfd software of starcd and results are compared with those obtained from the similarity solution. What happens to the fluid flow velocity and concentration in a tube that branches out.
Chen 1998 considered laminar mixed convection adjacent to vertical, continuously stretching sheet. Axisymmetric rotational stagnation point flow impinging radially a. Numerical solutions of nonalignment stagnationpoint flow. Stagnationpoint pressure distribution and wall shear stress iaeng. Moreover, the partial slip effect on stagnation point flow of an incompressible fluid by a shrinking sheet is analyzed by bhattacharyya et al. Stagnationpoint pressure distribution and wall shear. Numerical results are obtained using boundary value problem solver bvp4c in matlab for several values of the governing parameters. Boundary layer flow near a stagnation point on a permeable. Fluidflow will enable you to simulate the flow of compressible and incompressible fluids. For an ideal fluid the flow against an infinite flat plate in the plane y. Which contains the location data,velocity vectors along with temperature, pressure, total pressure and data for turbulence modeling. Meijiau huang, in parallel computational fluid dynamics 1998, 1999. This class of solutions, describing the fluid flow near the stagnation region. Mehmood r, nayak m k, akbar n s and makinde o d 2019 effects of thermaldiffusion and diffusionthermo on oblique stagnation point flow of couple stress casson fluid over a stretched horizontal riga plate with higher order chemical reaction j.
The stagnation point flow of a nanofluid towards a permeable stretchingshrinking sheet using the buongiornos model is studied. The black oxide of iron, magnetite fe3o4 which acts as magnetic materials and water as a base fluid are considered. Physics stack exchange is a question and answer site for active researchers, academics and students of physics. This paper is an analytical study of the fluid flow and heat transfer in the stagnation zone of an unsubmerged liquid.
Oblique stagnationpoint flow of an incompressible viscoelastic fluid towards a stretching surface international journal of nonlinear mechanics, vol. While the selfsimilar model provides a useful gross flow field estimate this approach must be. With zero circulation the stagnation points lie at o. Mhd stagnationpoint flow and heat transfer with effects. The velocity at every point in any flow field is zero in one direction actually, in an infinite number of directions, in 3d flow namely, the direcitions perpendicular to the velocity vector.
In this article, stagnation point flow of a maxwell fluid over a shrinking porous. No endeavor has been made on mhd stagnation point flow of cross fluid model. Navierstokes equations for pressure in twodimensional stagnationpoint flow and the. Mhd stagnation point slip flow due to a nonlinearly. Stagnation point flow represents a fluid flow in the immediate neighborhood of solid surface at which fluid approaching the surface divides into different streams or a counterflowing fluid streams encountered in experiments. The resulting coupled equations of nonlinear ordinary differential equations were. In stagnation point reflectometry, the solution of the adsorptives is injected in front of the incident point of the laser beam fig. On series solutions for mhd plane and axisymmetric flow. The steady twodimensional stagnationpoint flow and heat transfer past a permeable stretchingshrinking sheet with effects of viscous dissipation, joule heating and partial velocity slip in the presence of a magnetic field is investigated. For inviscid flow i would define a stagnation point as where the velocity is zero. Processes free fulltext stagnation point flow with.
In fluid dynamics, a stagnation point is a point in a flow field where the local velocity of the fluid is zero. Mhd stagnationpoint flow over a stretchingshrinking. A stagnation point of a body in a moving airstream is a point where. It is assumed that at time t 0 the surface starts to move with the velocity u w x, t. Abstractin this paper, we have studied the heat transfer characteristics of stagnation point flow of an mhd flow over a nonlinearly moving plate with momentum and thermal slip effects in presence of nonuniform heat sourcesink. Consider the unsteady stagnationpoint flow and heat transfer of a third grade fluid in the region y 0 driven by an impulsively started stretchingshrinking surface, as shown in fig. The stagnationzone characteristics of an impinging liquid jet are of great interest because the maximum heat transfer coefficient occurs in that region. Stagnationpoint flow of a jeffrey nanofluid over a. The stagnation flow is about the fluid motion near the stagnation point. In the numerical procedure scheme we choose maple17 software which. Pr is fixed at pr 7, using the bvp4c function from matlab software. Stagnation point article about stagnation point by the. For inviscid flow, the velocity normal to a boundary must be zero. In this region, net fluid velocity along either axis is zero.
Stagnation points exist at the surface of objects in the flow field, where the fluid is brought to rest by the object. At that point, the flow has most kinetic energy and it loses more of it in the first collide that makes pressure. It can be located in the stagnation region of flow passing any shape of body, i. This investigation presents a mathematical model describing the momentum, heat and mass transfer characteristics of magnetohydrodynamic mhd flow and heat generatingabsorbing fluid near a stagnation point of an isothermal twodimensional body of an axisymmetric body. The two dimensional stagnation point flow of cold ferrofluid against a hot wall under the influence of the uniform magnetic field of. Stagnationpoint flow has been found in numerous applications in engineering and technology 1. I am trying to find the stagnation point of a fluid flow from a complex potential. Abstracttwodimensional stagnation point flow in three different aspect ratios is studied by solving the full navierstokes equations with the computational fluid dynamics cfd software of starcd and results are compared with those obtained from the similarity solution. The question i want to ask would need all this info and it would take very long to write it. The governing differential equations are transformed into the ordinary differential equations using suitable similarity transformations. Numerical simulation of fluid flow over a shrinking porous sheet by.
Stagnationpoint heat transfer during impingement of. A stagnation point occurs whenever a flow impinges on a solid object. Stagnationpoint flow towards a stretchingshrinking sheet. The viscous flow near a stagnation point when the external. Numerical and series solutions for stagnationpoint flow.
The series expressions of velocity, temperature and nanoparticles concentration are developed by homotopy analysis method ham developed by liao 30. The governing partial differential equations are first transformed into ordinary differential equations, before being solved numerically using the. Citeseerx stagnationpoint pressure distribution and. Using bernoullis equation, you can easily see that the term 12 rhov2,is zero at p since v is zero.
Approximate model for turbulent stagnation point flow. The pressure at a point in a fluid is called the static pressure. Hence, the present work deals with the unsteady bionanofluid flow, heat and mass transfer past an impermeable. Keeping this into view, in this study we investigated the stagnation point flow, heat and mass transfer behaviour of. With every passing day the heat transfer enhancement in the convectional base fluids plays a major role in several industrial and engineering processes. The strain rate experienced by the trapped macromolecule is controlled by changing the velocity of the pumped solution. I want to calculate the location of the stagnation point in this flow field. A steady mixed convection boundary layer flow near a stagnation point on a permeable vertical surface immersed in a nanofluid is investigated. Unsteady stagnationpoint flow and heat transfer of a. The paper investigates the numerical solution of problem of magnetohydrodynamic mhd micropolar fluid flow with heat and mass transfer towards a stagnation point on a vertical plate.
Stagnation point flow of radiative oldroydb nanofluid. The fluid pressure, the heat transfer and the rate of mass deposition are highest in the stagnation area. The governing equations are transformed to a nonsimilar ordinary differential equation subject to nonlinear boundary conditions. Close to the stagnation point, it flows very slowly and the closer you get, the slower it flows. Mathematical solution on mhd stagnation point flow of. The point, at which resultant velocity of the fluid becomes zero, will be termed as stagnation point and the value of pressure at stagnation point will be called as stagnation pressure. Axisymmetric stagnationpoint flow of a thirdgrade fluid.
This study presents a numerical investigation on the magnetohydrodynamic mhd stagnation point flow of a ferrofluid with newtonian heating. The governing equations have been transformed into nonlinear ordinary differential equations by applying the. Usually there are other important features of the flow. Download this handout and complete it as you watch the videos.
Numerical solution of mhd flow of micropolar fluid with. The point where it hits the airfoil is the stagnation point. For incompressible fluids, if the local flow velocity at a point p is zero, then p is a stagnation point in fluid flow. Mhd stagnation point flow of a micropolar fluid over a. Hence, the changes in reflectivity are measured at a point where the hydrodynamic conditions are well controlled. In this study, we consider both strong concentrations n 0 and weak concentrations n 12. The stagnationpoint flow of a thirdgrade fluid over a disk lubricated with a power law fluid is discussed in this article. This gives a motivation for a further study on the correlation. This is a configuration favorable for measuring fast adsorption kinetics.
This paper concerns the stagnation point flow and heat transfer of a viscous and incompressible fluid passing through a flat riga plate with the effects of velocity slip and radiation. Sharma and singh 46 investigated stagnation point flow past a linearly stretching sheet with additional effects of variable thermal conductivity, heat sourcesink, and mhd. When the flows from above and below meet, there will be a line dividing both. Understanding what a stagnation point is in compressible flow. Calculating the stagnation point of a flow field cfd. Although the fluid is stagnant everywhere on the solid surface due to noslip condition. Pitot tube, assumption of hydrostatic pressure distribution.
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