Flows induced by a plate moving normal to stagnation-point flow

The flow generated by an infinite flat plate advancing toward or receding from a normal stagnation-point flow is obtained as an exact reduction of the Navier?CStokes equations for the case when the plate moves at constant velocity V. Both Hiemenz (planar) and Homann (axisymmetric) stagnation flows are considered. In each case, the problem is governed by a Reynolds number R proportional to V. Small and large R behaviors of the shear stress parameters are found for both advancing and receding plates. Numerical solutions determined over an intermediate range of R accurately match onto the small and large R asymptotic behaviors. As a side note, we report an interesting exact solution for plates advancing toward or receding from an exact rotational stagnation-point flow discovered by Agrawal (1957).     

Non-orthogonal stagnation-point flow of a micropolar fluid

This paper considers the problem of steady two-dimensional flow of a micropolar fluid impinging obliquely on a flat plate. The flow under consideration is a generalization of the classical modified Hiemenz flow for a micropolar fluid which occurs in the boundary layer near an orthogonal stagnation point. A coordinate decomposition transforms the full governing equations into a primary equation describing the modified Hiemenz flow for a micropolar fluid and an equation for the tangential flow coupled to the primary solution. The solution to the boundary-value problem is governed by two non-dimensional parameters: the material parameter K and the ratio of the microrotation to skin friction parameter n. The obtained ordinary differential equations are solved numerically for some values of the governing parameters. The primary consequence of the free stream obliqueness is the shift of the stagnation point toward the incoming flow.     

Magnetohydrodynamic stagnation-point flow towards a stretching sheet

Steady two-dimensional stagnation-point flow of an incompressible viscous electrically conducting fluid over a flat deformable sheet is investigated when the sheet is stretched in its own plane with a velocity proportional to the distance from the stagnation-point. It is shown that the velocity at a point decreases/increases with increase in the magnetic field when the free stream velocity is less/greater than the stretching velocity. Temperature distribution in the flow is obtained when the surface is held at a constant temperature.     

Unsteady oscillatory stagnation-point flow of a viscoelastic fluid

The unsteady stagnation point flow of the Walters B^′ fluid is examined and solutions are obtained. It is assumed that the infinite plate at y=0 is oscillating and the fluid impinges obliquely on the plate.     

A laminar walljet on a moving wall

Summary The laminar wall jet from a momentum source at the leading edge on a wall which is moving in the same direction with uniform velocity is considered. It is shown that a solution is possible starting at the leading edge and proceeding all the way downstream. For smallx (x measures distance along the wall) we find the solution by using a natural coordinate expansion in powers ofx ^1/2. For largex, the asymptotic solution is approached through eigensolutions and the two coordinate expansions are then joined by a numerical solution of the full equations.With 2 Figures     

Unsteady axisymmetric stagnation-point flow of a viscous fluid on a cylinder

The unsteady viscous flow in the vicinity of an axisymmetric stagnation point of an infinite circular cylinder is investigated when both the free stream velocity and the velocity of the cylinder vary arbitrarily with time. The cylinder moves either in the same direction as that of the free stream or in the opposite direction. The flow is initially (t=0) steady and then at t>0 it becomes unsteady. The semi-similar solution of the unsteady Navier–Stokes equations has been obtained numerically using an implicit finite-difference scheme. Also the self-similar solution of the Navier–Stokes equations is obtained when the velocity of the cylinder and the free stream velocity vary inversely as a linear function of time. For small Reynolds number, a closed form solution is obtained. When the Reynolds number tends to infinity, the Navier–Stokes equations reduce to those of the two-dimensional stagnation-point flow. The shear stresses corresponding to stationary and the moving cylinder increase with the Reynolds number. The shear stresses increase with time for the accelerating flow but decrease with increasing time for the decelerating flow. For the decelerating case flow reversal occurs in the velocity profiles after a certain instant of time.     

Analysis of laminar film condensation from a moving vapor

Correction functions are derived which permit extension of the results of the theory based on an asymptotic friction law for uniform suction of a boundary layer to low-intensity film condensation from a moving vapor.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 32, No. 2, pp. 221–225, February, 1977.     

Axisymmetric stagnation-point flow impinging on a transversely oscillating plate with suction

The viscous fluid motion generated by axisymmetric stagnation-point flow of strain rate a impinging on a flat plate oscillating in its own plane with velocity amplitude U0 and frequency , including uniform suction of strength W0 is considered. A coordinate decomposition transforms the full Navier-Stokes equations into a primary equation describing the steady flow and a secondary equation describing the unsteady motion coupled to the primary solution. The solution to the boundary-value problem is governed by two dimensionless groups: the suction parameter S = W0 a and the frequency parameter = /a, where is the kinematic viscosity. Numerical integrations performed with a Runge-Kutta routine provide an exact solution to the Navier-Stokes equations. Values of the steady shear stress are found to agree with asymptotic results for large values of |S|, with S>0 representing suction and S<0 representing blowing. The magnitude and phase of the unsteady shear stress are given over a range of frequencies sufficient to recover analytical asymptotic results at large values of . The unsteady shear stress lags the wall motion by radians for 0 and by 5/4 radians when . Velocity profiles at selected parameter values during a period of plate oscillation are presented and discussed.     

Observed behavior of various oxide inclusions in front of a solidifying low-carbon steel shell

The engulfment and pushing (extrusion) of inclusions during solidification play an important role in the formation of a steel structure and, as a result, for the mechanical properties of the final steel product. The aim of this study is to gain knowledge about the behavior of non-metallic inclusions at the interface between a growing solid front and a liquid phase. The focus is on the effect of the titanium and titanium oxide content on the inclusions and the different phenomena, which occurs at the solid/liquid interface. This was studied in samples of low-carbon steels de-oxidized by different combinations of Al, Ca, and Ti. For this purpose, each metal sample of 0.19 g was melted at a temperature close to 1550 °C in an argon atmosphere and solidified under different solidification rates. A direct observation of inclusion behavior during solidification was made using a confocal scanning laser microscope equipped with an infrared gold image furnace. The alloying elements in the sample varied between: C 0.002–0.044; Si 0.02–1.33; Mn 0.12–1.33; P 0.003–0.016; S 0.003–0.01; Al 0.002–0,033; Ni 0–0.28; Cr 0–0.25; Ti 0.008–0.065; Ca 0.0007–0.002; O 0.002–0.0114 and N 0.0028–0.0056 (mass%). Several types of inclusions with different morphologies were found within the sample. The morphology of the observed inclusions on the molten steel surface varied from round alumina and calcium-oxide-rich inclusion to needle-shaped titanium oxide-rich inclusions. The observed motions of the inclusions at the vicinity of the front of the solidifying steels were classified. At a low solidifying velocity and a small inclusion size, inclusions flowed away from the solidifying front. Furthermore, they also or got pushed a distance and thereafter flowed away from the interface. At a medium velocity and a slightly bigger size, inclusions tend to get pushed in front of the solidifying front. Another observation was that at a high velocity and a large particle size, inclusions tend to get engulfed or pushed and then engulfed by the progressing front. The relationship among the morphology, chemical composition of inclusions and the solidifying velocity is discussed in this article.     

Detection of moving point objects against a moving background

The temporal spectral characteristics of a dim moving point object and a moving background, as observed by a sensor array, are analyzed. This type of problem occurs in remote sensing, machine vision, and many other applications. The diffraction limitation of the sensor optics ensures that the temporal spectrum of the background moving with a finite velocity has a finite maximum bandwidth, regardless of background structure. Because the outputs of the sensor array are time sampled, its spectrum is infinitely replicated over an interval of temporal frequency equal to the reciprocal of the sampling time. If this interval is at least twice as large as the maximum background temporal frequency, there is a region with no background components in the middle of each interval. However, because the point object temporal spectrum in the sampled sensor array output is continuously distributed, this region will contain part of the point object signal. Thus, a criterion for the existence of an effective background suppression filter is that the point object fundamental frequency must be greater than the maximum background temporal frequency. When this criterion is satisfied, the amount of background leakage in the filter depends on the sharpness of its passband response and its stopband characteristics. In general, higher-order filters have sharper response and hence better performance. If the criterion is not met, all types of filter lose their effectiveness since the background signal will leak through the passband of the filter. The fundamental concepts developed here were examined for some typical parameter values. It is shown that for this system the point object can be effectively discriminated. In some cases the point object and background temporal spectral responses vary significantly with spatial position within the field of view. Because the filter's center frequency must match the point object temporal fundamental frequency, it is necessary to use an adaptive filter in these situations.     

Unsteady laminar flow over a rough surface

A model is developed for the unsteady laminar flow of athin fluid film over a substrate with roughness of the same order as the film height. The limits of large and small surface resistance and small surface-roughness are investigated and it is shown that at leading order the classical parabolic form for the velocity profile is retrieved in all cases. Empirical expressions for the depth-averaged velocity and the ratio of the average to maximum velocities are investigated and shown to agree with the present theory under certain conditions. The method is verified by comparison with experiments for steady uni-directional flow over a surface of known roughness.     

The longitudinal laminar flow of a liquid in a bundle of rods

Analog and digital methods have been applied to the problem of the longitudinal flow of a viscous incompressible liquid through bundles of rods in square or triangular array.     

The Navier-Stokes solution for laminar flow past a semi-infinite flat plate

Summary A numerical solution joining Carrier and Lin's solution near the leading edge to the boundary layer solution at large distance of the leading edge is presented. The solution is valid for any Reynolds number. Results are given for the skin friction, the integrated skin friction, the displacement thickness, the pressure along the plate and the velocity ahead of the plate. The asymptotic value of the integrated skin friction agrees very well with the exact value. The displacement thickness is already different from zero for small distances ahead of the plate.     

Radiative heat transfer to a laminar liquid flow

A calculation is presented of the temperature distribution in a laminar liquid flow moving in a circular tube. The heat exchange on the outer surface of the channel is determined by the Stefan — Boltzmann law.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 18, No. 3, pp. 487–491, March, 1970.