On unsteady MHD flow near an infinite flat wall

The flow of an electrically conducting incompressible viscous fluid near an infinite flat wall in the presence of a magnetic field when the free stream velocity is to be expressed in power series of √ t is considered. The effect of the magnetic field strength on the velocity field induced magnetic field and skin friction is analyzed for two particular cases of the free stream velocity.     

A note on Hydromagnetic oscillatory flow along an infinite flat plate with variable suction

The two-dimensional, incompressible flow past an infinite plate of a weakly conducting fluid in the presence of a transverse magnetic field is discussed when the suction velocity normal to the plate as well as the external flow velocity vary periodically with time. Expressions for the velocity and the skin-friction in the boundary layer have been obtained in a non-dimensional form.     

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     

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.     

MHD boundary-layer flow of a micropolar fluid past a wedge with constant wall heat flux

The steady laminar magnetohydrodynamic (MHD) boundary-layer flow past a wedge with constant surface heat flux immersed in an incompressible micropolar fluid in the presence of a variable magnetic field is investigated in this paper. The governing partial differential equations are transformed into a system of ordinary differential equations using similarity variables, and then they are solved numerically by means of an implicit finite-difference scheme known as the Keller-box method. Numerical results show that micropolar fluids display drag reduction and consequently reduce the heat transfer rate at the surface, compared to the Newtonian fluids. The opposite trends are observed for the effects of the magnetic field on the fluid flow and heat transfer characteristics.     

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.     

Hydromagnetic flow over a plane wall with uniform suction

Zusammenfassung Diese Abhandlung behandelt die Strömung einer inkompressiblen, zähen und elektrisch leitenden Flüssigkeit über eine ebene Wand mit homogener Absaugung und senkrechtem Magnetfeld. Eine exakte Lösung der hydromagnetischen Gleichungen kann erhalten werden, wenn die magnetische Druckzahl kleiner als eins ist.Aus den Rechnungen findet man, dass sowohl die Reibungsschubspannung als auch die Wärmeübertragung an der Wand unabhängig sind von der hydromagnetischen Wirkung, aber dass die Grenzschichtdicke zunimmt mit der Zunahme des hydromagnetischen Einflusses.Es sei bemerkt, dass keine stationäre Lösung erhalten wird für den Fall des Ausblasens.     

On the exact solutions of laminar MHD flow over a stretching flat plate

The magnetohydrodynamic steady-state laminar flow of a viscous incompressible and electrically conducting fluid over a continuous permeable stretching surface is considered. It is shown that in the presence of a vertical inverse-linear magnetic field, we establish a sufficient condition for the existence of exact solutions of this problem with respect to the three parameters: the magnetic parameter M, the suction/injection parameter γ, and the stretching parameter ξ. Numerical results are also obtained and give the effect of the suction parameter and the magnetic parameter on the velocity.     

On MHD flow of an incompressible viscous fluid

In this paper, we apply Homotopy Perturbation Method (HPM) to find the analytical solutions of nonlinear MHD flow of an incompressible viscous fluid through convergent or divergent channels in presence of a high magnetic field. The flow of an incompressible electrically conducting viscous fluid in convergent or divergent channels under the influence of an externally applied homogeneous magnetic field is studied both analytically and numerically. The graphs are presented to reveal the physical characteristics of flow by changing angles of the channel, Hartmann and Reynolds numbers.     

Flow and heat transfer along a plane wall with periodic suction

Summary The three-dimensional incompressible laminar boundary layer past a flat plate is investigated, when suction with a slightly sinusoidal transverse suction velocity distribution at the wall is applied. For the asymptotic flow conditions far downstream the components of the wall shear stress and the heat transfer including its dependence on Prandtl number are determined.

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Zusammenfassung Es wird die dreidimensionale inkompressible, laminare Grenzschicht an der längsangeströmten Platte behandelt, bei der mit einer in Querrichtung schwach sinusförmigen Geschwindigkeitsverteilung an der Wand abgesaugt wird. Für den asymptotischen Zustand weit stromabwärts werden die Komponenten der Wandschubspannung sowie der Wärmeübergang mit dessen Abhängigkeit von der Prandtl-Zahl bestimmt.

     

Exact solutions for the flow of an Oldroyd-B fluid due to an infinite flat plate

The unsteady flow of an Oldroyd-B fluid due to an infinite flat plate, subject to a translation motion of linear time-dependent velocity in its plane, is studied by means of the Laplace transform. The velocity field and the associated tangential stress corresponding to the flow induced by the constantly accelerating plate as well as those produced by the impulsive motion of the plate are obtained as special cases. The solutions that have been determined, in all accordance with the solutions established using the Fourier transform, reduce to those for a Newtonian fluid as a limiting case. The similar solutions for a Maxwell fluid are also obtained.     

Friction and heat transfer of compressible flow into an infinite lattice of flat plates

Zusammenfassung Es wird eine Analyse vorgelegt, die erlauben soll, die Bestimmung der Reibungs-und Wärmeübergangs-Kenngrössen einer kompressiblen, laminaren Strömung in einem unendlich grossen Gitter flacher Platten vorzunehmen.Die Ergebnisse weichen für niedrige Reynoldssche zahlen bedeutend von jenen einer einzelnen flachen Platte ab. Die Rechnungen führen zu vergrössertem Reibungswiderstand, verminderter Rückbildung und für den Fall, dass die Flüssigkeit die Wand erwärmt bzw. abkühlt, zu vergrösserter bzw. verkleinerter Nusselt-Zahl.     

On generalised MHD couette flow with heat transfer

In the case of short-circuited generalised MHD Couette flow the rate of heat transfer, in general, increases with the increase in the value of both the Hartmann number and the pressure gradient. Especially, at the lower stationary plate it is affected by the magnetic field, which is not observed in the case of plane MHD Couette flow.     

Free convection effects on the oscillatory flow of an incompressible viscous fluid past an infinite,vertical plate with variable suction

An analysis of a two-dimensional flow of an incompressible, viscous fluid past an infinite, vertical porous plate has been carried out under the following conditions: (i) the suction velocity normal to the plate varies periodically with time (ii) the free stream velocity oscillates in time about a constant mean (iii) the temperature difference between the constant plate temperature and the free stream temperature, causing the free convection currents in the boundary layer. Approximate solutions for the transient velocity, the transient temperature, the amplitude and the phase of the skin-friction and the rate of heat transfer are derived. The fluctuating parts of the velocity profiles, the transient velocity, the transient temperature are shown on graphs whereas the numerical values of the amplitude and the phase of the skin-friction and the rate of heat transfer are entered in tables. The results are discussed in a quantitative way.     

Couette flow of a stratified fluid with suction varying along a boundary

A viscous incompressible fluid between two plane boundaries is stratified by maintaining the planes at different temperatures. The upper plane moves with a uniform velocity. The suction/injection mechanism with constant injection velocity at the upper plane and suction velocity varying sinusoidally along the lower plane with a wave numberk is introduced at the boundaries. The steady linearised equations are solved using similarity variables for the velocity components. The wave numberk is shown to be effective in controlling the boundary layer thickness.     

MHD free convective flow past semi-infinite vertical permeable wall

In this paper,the basic equations governing the flow and heat transfer of an incompressible viscous and electrically conducting fluid past a semi-infinite vertical permeable plate in the form of partia...     

Hydromagnetic flow near an accelerated plate with suction

The two-dimensional unsteady flow of a conducting viscous incompressible fluid past, an infinite flat plate with uniform suction, is considered in the presence of a uniform magnetic field. For a constant time, it is shown that for a given Hartmann numbera, as the cross Reynolds number β (corresponding to the suction velocity of the plate) increases, the velocity at any point of the fluid decreases and the skin friction at the plate increases. The results also hold good for a given β, asa increases if the magnetic lines of force are fixed relative to the fluid and are just opposite for the magnetic lines of force fixed relative to the plate.     

Boundary layer along the initial length of a flat plate at zero incidence with homogeneous suction

An investigation has been made into the two-dimensional laminar incompressible boundary layer along the initial length of a semi-infinite flat plate at zero incidence with homogeneous suction. The momentum and the kinetic energy integral equations have been numerically integrated with the aid of a singly infinite system of boundary layer velocity profiles. The results obtained are well in agreement with the known exact solution and the process of integration is simpler to be carried out by the use of a monoparametric family of velocity profiles. The method can be used to investigate the boundary layer along a flat plate with arbitrary suction starting either at the leading edge or at some point downstream.     

Effects of chemical reaction and radiation on an unsteady MHD flow past an accelerated infinite vertical plate with variable temperature and mass transfer

This paper deals with the study of the effects of first order chemical reaction and radiation on an unsteady MHD flow of an incompressible viscous electrically conducting fluid past an accelerated infinite vertical plate with variable temperature and mass transfer. The resulting approximate dimensionless system of governing partial differential equations are integrated in closed form by the Laplace transform technique A uniform magnetic field is assumed to be applied transversely to the direction of the flow. Rosseland model of radiation has been chosen in the investigation, the expressions for the velocity field, temperature field and concentration field and skin-friction in the direction of the flow, coefficient of heat transfer and mass flux at the plate have been obtained in non-dimensional form and these are illustrated graphically for various physical parameters involved in the study. Investigation reveals that the fluid velocity is decelerated in the region adjacent to the plate, due to the effect of first order chemical reaction and the rate of heat transfer (from plate to the fluid) decreases due to the absorption of thermal radiation. The results obtained in this work are consistent with physical situation of the problem.