Unsteady flow past a flat plate with suction

A solution is given for the transient response for laminar boundary layer flow past a flat plate to a step-function change in suction velocity. An arbitrary but constant suction velocity normal to the plate is allowed prior to step-change. Using the Laplace transform technique the solutions for the unsteady velocity profile and shear stress are obtained and are graphically sketched when the suction velocity doubles in the stepchange. The results show clear evidence of boundary-layer contraction when suction velocity is increased.     

Molecular modellingof flow past an inclined flat plate

Molecular flow past an inclined plate is simulated on a scientific personal computer. Wake flow and turbulent effects are described and discussed for various fluid speeds.     

Stresses in an elastic plate lying over a base due to strip-loading

The closed-form analytic expressions for the stresses at any point of an elastic plate coupling in different ways to a base as a result of a two-dimensional shear strip-loading are obtained. The contact between the horizontal layer and the base is either smooth-rigid or rough-rigid or welded. The variations of the shear stresses with the horizontal distance have been studied numerically. It is found that the effect of different boundary conditions on the stress field is significant and the stresses for an elastic layer lying over an elastic half-space differ considerably from those of an entire homogeneous elastic half-space.     

Numerical study of unsteady flow of a second order liquid past a porous infinite flat plate with uniform suction

The two-dimensional unsteady flow of a second order visco-elastic liquid of finite depth over an infinite porous flat plate has been studied. The suction velocity normal to the plate is taken to be uniform and directed towards the plate and the external flow velocity is considered to be exponentially decaying with time. The governing equation of motion has been solved numerically over an IBM 1130 electronic computer. Shearing stress at the plate has also been sought.     

Modeling a swimming fish with an initial boundary value problem: Unsteady maneuvers of an elastic plate with internal force generation

In order to model unsteady maneuvers in swimming fish, we develop an initial-boundary value problem for a fourth-order hyperbolic partial differential equation in which the fish's body is treated as an inhomogeneous elastic plate. The model is derived from the three-dimensional equations of elastic dynamics, and is essentially a simple variant of the classical Kirchhoff model for a dynamic plate. The model incorporates body forces generating moment to simulate muscle force generation in fish. The initial-boundary value problem is reduced to a beam model in one spatial dimension and formulated computationally using finite differences. Interaction with the surrounding water is represented by nonlinear viscous damping. Two example applications using simple but physically reasonable physiological parameters are presented and interpreted. One models the acceleration from rest to steady swimming, the other a rapid turn from rest.     

Magnetohydrodynamic shear flow along a flat plate with uniform suction or blowing

An analysis is made of the steady shear flow of an incompressible viscous electrically conducting fluid past an electrically insulating porous flat plate in the presence of an applied uniform transverse magnetic field. It is shown that steady shear flow exists for suction at the plate only when the square of the suction parameter S is less than the magnetic parameter Q. In this case the velocity at a given point increases with increase in either the magnetic field or suction velocity. The shear stress at the plate increases with increase in either S or the free-stream shear-rate parameter σ₁ or Q. The analysis further reveals that solution exists for steady shear flow past a porous flat plate subject to blowing only when the square of the blowing parameter S₁ is less than Q. It is found that the induced magnetic field at a given location decreases with increase in Q. Further the wall shear stress decreases with increase in S₁. No steady shear flow is possible for blowing at the plate when S₁² > Q. Received: June 16, 2004; revised: October 24, 2004     

Steady supersonic flow past an almost straight wedge with large vertex angle

This paper studies the problem on the steady supersonic flow at the constant speed past an almost straight wedge with a piecewise smooth boundary. It is well known that if each vertex angle of the straight wedge is less than an extreme angle determined by the shock polar, the shock wave is attached to the tip of the wedge and constant states on both side of the shock are supersonic. This paper is devoted to generalizing this result. Under the hypotheses that each vertex angle is less than the extreme angle and the total variation of tangent angle along each edge is sufficiently small, a sequence of approximate solutions constructed by a modified Glimm scheme is proved to be convergent to a global weak solution of the steady problem. A sequence of the corresponding approximate leading shock fronts issuing from the tip is shown to be convergent to the leading shock front of the obtained solution. The regularity of the leading shock front is established and the asymptotic behaviour of the obtained solution at infinity is also studied.     

Boundary collocation method for a cracked rectangular plate with double external tension

In this article, the boundary collocation method is employed to investigate the problems of a central crack in a rectangular plate which applied double external tension on the outer boundary under the assumption that the dimensions of the plate are much larger than that of the crack. A set of stress functions has also been proposed based on the theoretical analysis which satisfies the condition that there is no external force on the crack surfaces. It is only necessary to consider the condition on the external boundary. Using boundary collocation method, the linear algebra equations at collocation points are obtained. The least squares method is used to obtain the solution of the equations, so that the unknown coefficients can be obtained. According to the expression of the stress intensity factor at crack tip, we can obtain the numerical results of stress intensity factor. Numerical experiments show that the results coincide with the exact solution of the infinite plate. In particular, this case of the double external tension applied on the outer boundary is seldom studied by boundary collocation method.     

Numerical simulation of solitary blood waves in an elastic tube subjected to a localised deformation

In order to well apprehend what really happens in a locally deformed elastic tube, a numerical analysis of the liquid flow in such a media has been undertaken. A cylindrical tube with constant rigidity subjected to a localised dilatation is first considered and results obtained help to understand the behaviour and the developing process of aneurysm. The analysis of the effects of stenoses on blood flow is also done.     

Application of parameter differentiation for flow of a third grade fluid past an infinite porous plate

This article investigates the analytic solution for the flow of a third grade fluid past an infinite porous plate. The method of parameter differentiation is used to linearized the governing flow equation. The solution of the obtained linear equation is developed by differential transform method in combination with the method of superposition. The obtained results are compared with existing results in the literature and an excellent agreement is found. This shows that the parameter differentiation is a powerful technique for solving nonlinear problems. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010     

A note on the flow induced by a constantly accelerating plate in an Oldroyd-B fluid

The velocity field and the adequate tangential stress that is induced by the flow due to a constantly accelerating plate in an Oldroyd-B fluid, are determined by means of Fourier sine transforms. The solutions corresponding to a Maxwell, Second grade and Navier–Stokes fluid appear as limiting cases of the solutions obtained here. However, in marked contrast to the solution for a Navier–Stokes fluid, in the case of an Oldroyd-B fluid oscillations are set up which decay exponentially with time.     

Propagation of waves in a micropolar elastic layer with stretch immersed in an infinite liquid

The effect of liquid on the propagation of waves in a micropolar elastic layer with stretch has been investigated. The frequency and wave velocity equations for symmetric and antisymmetric vibrations are derived. Propagation of monochromatic waves in a micropolar elastic layer with stretch is discussed. Results of this analysis reduce to those without stretch.     

On the flow of an unsteady,compressible boundary layer over a semi-infinite flat plate whose temperature is varied with time

Zusammenfassung Es wird die Grenzschicht untersucht, die sich in laminarer, kompressibler Strömung an einer ebenen Platte unter der Annahme einstellt, dass sich diese nach einer Seite ins Unendliche ausdehnt und von der Ruhe aus gleichförmig beschleunigt wird. Die Temperatur der Platte wird in vorgeschriebener Weise mit der Zeit geändert, und der Effekt dieser Änderung kurz nach dem Beginn der Bewegung wird für Punkte berechnet, die weit vom Plattenrand entfernt sind.

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The computer time for this project was supported byNational Aeronautics and Space Administration Grant NsG-398.     

Electro-thermo-mechanical torsional buckling of a piezoelectric polymeric cylindrical shell reinforced by DWBNNTs with an elastic core

The effect of partially filled poly ethylene (PE) foam core on the behavior of torsional buckling of an isotropic, simply supported piezoelectric polymeric cylindrical shell made from polyvinylidene fluoride (PVDF), and subjected to combined electro-thermo-mechanical loads has been analyzed using energy method. The shell is reinforced by armchair double walled boron nitride nanotubes (DWBNNTs). The core is modeled as an elastic environment containing Winkler and Pasternak modules. Using representative volume element (RVE) based on micromechanical modeling, mechanical, electrical and thermal characteristics of the equivalent composite were determined. Critical buckling load is calculated using strains based on Donnell theory, the coupled electro-thermo-mechanical governing equations and principle of minimum potential energy. The results indicate that buckling strength increases substantially as harder foam cores are employed i.e. as E_c/E_s is increased. The most economic in-fill foam core is at η = 0.6, as cost increases without much significant improvement in torsional buckling at higher η’s.     

Stagnation point flow and heat transfer over a non-linearly moving flat plate in a parallel free stream with slip

An analysis is presented for the steady boundary layer flow and heat transfer of a viscous and incompressible fluid in the stagnation point towards a non-linearly moving flat plate in a parallel free stream with a partial slip velocity. The governing partial differential equations are converted into nonlinear ordinary differential equations by a similarity transformation, which are then solved numerically using the function bvp4c from Matlab for different values of the governing parameters. Dual (upper and lower branch) solutions are found to exist for certain parameters. Particular attention is given to deriving numerical results for the critical/turning points which determine the range of existence of the dual solutions. A stability analysis has been also performed to show that the upper branch solutions are stable and physically realizable, while the lower branch solutions are not stable and, therefore, not physically possible.     

Effects of mass transfer on free convective flow of a dissipative,incompressible fluid past an infinite vertical porous plate with suction

An analysis of the mass transfer effects on the free convective flow of an incompressible, dissipative, viscous fluid past an infinite, vertical porous plate with constant suction, has been carried out. Approximate solutions to coupled non-linear equations governing the flow are derived. The velocity and the temperature profiles are shown graphically for air (P=0·71). The effects of Gr (Grashof number), Gc (the modified Grashof number), Sc (Schmidt number), E (Eckert number) are discussed qualitatively during the course of discussion. It is observed that due to the addition of the foreign mass, there is a rise in the velocity and a fall in the temperature. But the skin-friction increases when Sc?1 and it decreases when Sc ～1. The rate of heat transfer increases for Sc<1 and decreases for Sc>1.     

Computational treatment of free convection effect on flow of elastico-viscous fluid past an accelerated plate with constant heat flux

Effect of free convection on the visco-elastic fluid (Walter - B’ type) flow past an infinite vertical plate accelerating in its own plane with constant heat flux is examined analytically. It is found that for given values of Grashof number, Prandtl number and Newtonian parameter; flow velocity at any point increases with the increase in time and non-Newtonian parameter, however, it decreases with both, the heating and cooling of the plate.     

Dependence of the solution of a semi‐discrete von Mises equation with respect to the pressure for an inverse problem

We study precisely the solution of a semi‐discrete von Mises problem with known pressure to generalize a method for an inverse problem: the problem with known displacement. We prove the boundedness of the diffusive term, the uniqueness and the continuity of the solution with respect to the pressure and a coercivity property. However, the estimate of the diffusive term is not sharp enough for the inverse problem. We highlight a special behaviour of this term due to the combination of the nonlinearity with the degeneracy of the diffusion coefficient. Copyright © 2013 John Wiley & Sons, Ltd.     

Hall effect on unsteady MHD Couette flow and heat transfer of a Bingham fluid with suction and injection

The unsteady magnetohydrodynamic flow of an electrically conducting viscous incompressible non-Newtonian Bingham fluid bounded by two parallel non-conducting porous plates is studied with heat transfer considering the Hall effect. An external uniform magnetic field is applied perpendicular to the plates and the fluid motion is subjected to a uniform suction and injection. The lower plate is stationary and the upper plate moves with a constant velocity and the two plates are kept at different but constant temperatures. Numerical solutions are obtained for the governing momentum and energy equations taking the Joule and viscous dissipations into consideration. The effect of the Hall term, the parameter describing the non-Newtonian behavior, and the velocity of suction and injection on both the velocity and temperature distributions are studied.     

Mathematical modelling of unsteady flow of a Sisko fluid through an anisotropically tapered elastic arteries with time-variant overlapping stenosis

In the present investigation, we have studied the influence of heat and chemical reactions on blood flow through anisotropically tapered elastic artery with time-variant overlapping stenosis. The nature of blood in small arteries are analyzed mathematically by considering it as a Sisko fluid. The analysis is carried out for an artery with a mild stenosis. Analytical expressions for the axial velocity, the stream function, the temperature distribution, the concentration of fluid, the pressure gradient, the resistance impedance and the wall shear stress distribution have been computed numerically and the results were studied for various values of the physical parameters, such as the Sisko parameter b^∗, the power index n, the taper angle ?  , the maximum height of stenosis δ^∗${\delta }^{\ast }$, the Soret number S_r, the Brickmann number B_r, the total mass of the vessel and the surrounding tissues M and the longitudinal contributions of the viscous and elastic constraints to the total tethering C and K respectively. The obtained results show that the magnitude of the axial velocity is higher for a Newtonian fluid than that for a Sisko fluid and it decreases by increasing of the power index n also the transmission of axial velocity curves through a tethered tube is substantially higher than that through the free tube. The wall shear stress distribution and resistance impedance profiles with the time have an oscillation form through the tapered overlapping stenosed arteries and this oscillation decaying as the time increases. The temperature profile increase by increasing the Sisko parameter b^∗ and the power index n   but the concentration profile has an opposite behavior as compared to the temperature profile. For a fixed flux, the magnitude of the pressure drop for a shear-thinning fluid (n<1)$(n<1)$ is much larger than that through a shear-thickening (n>1)$(n>1)$. The stream lines separate and the trapping bolus appear by increasing the maximum height of the stenosis δ^∗${\delta }^{\ast }$. The trapping bolus increase in size toward the line center of the tube as the power index n increases and it appear gradually by increasing the Sisko parameter b^∗. Finally the size of trapped bolus for the stream lines in the free isotropic tube is smaller than those in the tethered tube.