Incompressible Stagnation Point Research Articles

Features of Cattaneo‐Christov heat flux model for Stagnation point flow of a Jeffrey fluid impinging over a stretching sheet: A numerical study

AbstractThe present work focuses on a two‐dimensional steady incompressible stagnation point flow of a Jeffery fluid over a stretching sheet. The Cattaneo‐Christov heat flux model is incorporated into this study. Simulation is conducted via the Runge‐Kutta fourth‐order cum shooting method for the transformed system of nonlinear equations. The influence of the governing parameters on the dimensionless velocity, temperature, skin friction, streamlines, and isotherms is incorporated. A significant outcome of the current investigation is that an increase in the relaxation time parameter uplifts temperature; however, a gradual decrease is observed in the velocity field. Another important outcome of the present analysis is that the momentum boundary layer augments due to an increase in the Deborah number; however, a decrease is observed in the temperature. Furthermore, it is also observed that the skin friction coefficient escalates with an increase in the relaxation time parameter for the assisting flow, but a reverse trend is observed for the opposing flow.

Effects of unsteady expansion/contraction of Wang's cylinder problem with suction near a stagnation point

AbstractThe unsteady viscous incompressible stagnation point flow over an expanding/contracting cylinder with heat and mass transfer is studied in this article. The governing partial differential equations are transformed into a couple nonlinear ordinary differential equations by using similarity transformation. These obtained nonlinear ordinary differential equations are solved numerically by using spectral method. There exist unique, dual, and triple solutions in the presence of unsteadiness parameter S for different values of velocity ratio parameter. The ranges for which the unique, dual, and triple solutions exist are shown through graphs and in tabular form. It is observed that the temperature and thermal boundary layer thickness decrease by increasing the absolute values of S in expanding cylinder case. However, this behavior is opposite in contracting cylinder case. © 2014 Curtin University of Technology and John Wiley & Sons, Ltd.

A new look at driven magnetic reconnection at the terrestrial subsolar magnetopause

The physics of steady driven magnetic reconnection at Earth's subsolar magnetopause is addressed. Three‐dimensional, global magnetohydrodynamics (MHD) simulations of the magnetopause are compared with analytical solutions of the resistive MHD equations [Sonnerup and Priest, 1975] corresponding to magnetic field annihilation driven by an incompressible stagnation point flow. The simulations demonstrate that under steady southward interplanetary magnetic field conditions and when the plasma resistivity is spatially uniform, subsolar magnetopause reconnection occurs in long, thin Sweet‐Parker current sheets via a flux pileup mechanism [Sonnerup and Priest, 1975; Priest and Forbes, 1986] (rather than in Petschek slow shock configurations). Magnetic energy piles up upstream of the magnetopause current sheet to accommodate the sub‐Alfvénic solar wind inflow. The scaling of the pileup with Lundquist number, S, is consistent (approximately ∝ S1/4) with that predicted by the analytical, incompressible stagnation point flow solutions (though there are small corrections due to plasma compressibility in the simulations). Since there is a finite energy in the magnetosheath available to drive the magnetic pileup (and associated rapid magnetic reconnection), we expect the pileup to saturate and the reconnection rate to drop as the upstream plasma pressure drops to accommodate the pileup. Thus we expect the reconnection to stall, the rate vanishing in the limit S → ∞. We discuss the role of Hall electric fields in allowing the magnetic pileup to saturate before the reconnection begins to stall, permitting Alfvénic reconnection to occur in thin current sheets in the limit S → ∞.

Fast reconnection of weak magnetic fields

Fast magnetic reconnection refers to annihilation or topological rearrangement of magnetic fields on a timescale that is independent (or nearly independent) of the plasma resistivity. The resistivity of astrophysical plasmas is so low that reconnection is of little practical interest unless it is fast. Yet, the theory of fast magnetic reconnection is on uncertain ground, as models must avoid the tendency of magnetic fields to pile up at the reconnection layer, slowing down the flow. In this paper it is shown that these problems can be avoided to some extent if the flow is three dimensional. On the other hand, it is shown that in the limited but important case of incompressible stagnation point flows, every flow will amplify most magnetic fields. Although examples of fast magnetic reconnection abound, a weak, disordered magnetic field embedded in stagnation point flow will in general be amplified, and should eventually modify the flow. These results support recent arguments against the operation of turbulent resistivity in highly conducting fluids.

MHD stagnation-point flows at a current sheet including viscous and resistive effects: general two-dimensional solutions

Exact solutions are presented of two-dimensional steady-state incompressible stagnation point flows at a current sheet separating two colliding plasmas. They describe the process of resistive field annihilation (zero reconnection) where the magnetic field in each plasma is strictly parallel to the current sheet, but may have different magnitudes and direction on its two sides. The flow in the (x, y) plane toward the current sheet, located at x = 0, may have an arbitrary angle of incidence and an arbitrary amount of divergence from or convergence towards the stagnation point. We find the most general form of the solution for the plasma velocity and for the magnetic field. For the z compenents of the flow and field, solutions in the form of truncating power series in y are found. The cases obtained in this study contain the solutions obtained by Parker, Sonnerup & Priest, Gratton et al. and Besser, Biernat & Rijnbeek as special cases. The role of viscosity in determining the flow and field configurations is examined. When the two colliding plasmas have the same viscosity and density, it is shown that viscous effects usually are important only in strongly divergent or convergent viscous flows with viscous Reynolds number of the order of unity or smaller. For astrophysical applications the viscous Reynolds number is usually high and the effects of viscosity on the interaction of plasmas of similar properties are small. The formulation of the stagnation-point flow problem involving plasmas of different properties is also presented. Sample cases of such flows are shown. Finally, a possible application of the results from this study to the earth's magnetopause is discussed briefly.

Heat transfer in squish gaps

It is shown that the flow in planar and annular squish gaps of internal combustion engines at the near end of the compression stroke resembles an unsteady stagnation point flow. When the ratio of the diffusion time across the boundary layer to the characteristic time of the outer flow is constant, as is the case when the final squish gap height is zero, then the compressible unsteady stagnation boundary-layer flow is self-similar. For a nonvanishing final gap height, the flow is nonsimilar but is treated locally in time as a quasisimilar flow. This quasisimilar flow may be computed by expanding the solution in powers of the above-mentioned ratio. The first term in this expansion is the steady compressible stagnation point boundary-layer flow. The reported heat-transfer rates have been measured in a single-stroke compression device. These agree well with only the first term in the expansion. Even steady incompressible stagnation point heat-transfer rates are found to correlate the experimental data satisfactorily.

Accurate transonic wave drag prediction using simple physical models

A new method is presented to compute the transonic wave drag of airfoils. Coupled with an inverse boundary-layer procedure, the calculated results have an accuracy comparable to experiments. The method is robust and easy to handle without the necessity of tuning; hence, it is an excellent engineering tool for supercritical airfoil design. The inviscid flowfield is assumed to be governed by the full potential equation except at the shock. The solution is obtained by a finite-difference method. At shock points, a shock operator is introduced; it satisfies the kinematic Prandtl relation for normal and oblique shocks, which is the consistent condition for the velocity potential. For each streamline behind the shock, an entropy correction is calculated by the Rankine-Hugoniot equations. The wave drag is given by integrating the entropy rise along the shock. The computational mesh, formed by incompressibl e stream and potential lines, allows easy coupling of the boundary-layer solution at the airfoil and wake. The H-type singularity at the incompressible stagnation point is handled by a finite-volume procedure. For better physical pressure and drag solutions, the condition of the normal shock has to be altered due to the boundary layer. Therefore, an analytic model of the inviscid interference region was developed and the essential features are embedded in the numerical procedure.

非圧縮性よどみ点流れの周辺

非圧縮性よどみ点流れの周辺

Oscillating stagnation point flow

A solution of the Navier-Stokes equations is given for an incompressible stagnation point flow whose magnitude oscillates in time about a constant, non-zero, value (an unsteady Hiemenz flow). Analytic approximations to the solution in the low and high frequency limits are given and compared with the results of numerical integrations. The application of these results to one aspect of the boundary layer receptivity problem is also discussed.