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.     

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     

Fluctuating flow of a Maxwell fluid past a porous plate with variable suction

The problem dealing with the two-dimensional flow of an incompressible viscoelastic Maxwell fluid past an infinite porous plate is investigated. It is assumed that the suction velocity is normal to the plate and oscillates about a mean value. The external free-stream velocity varies periodically in time. The resulting differential equation subject to the relevant boundary and initial conditions is numerically solved by means of a numerical technique, in which a coordinate transformation is employed to transform the semi-infinite physical space to a bounded computational domain. The effects of various values of the emerging parameters, e.g. the elasticity parameter, the oscillation amplitude and frequency of the external flow and the suction velocity, on the time series of velocity, especially on the boundary-layer structure near the plate, are discussed. The nature of the shear stress engendered due to the flow is also investigated.     

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.     

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.     

Free convection flow of a second order fluid past a hot vertical plate

Laminar free convection flow of a second order fluid past a hot vertical plate with varying wall temperature has been studied in this paper. Exact solutions for the velocity and temperature fields have been obtained. The effects of elastic coefficient on the velocity and temperature fields, rate of heat transfer and the skin-friction have been studied.     

Hydromagnetic rotating flow of a fourth‐order fluid past a porous plate

The rotating flow in the presence of a magnetic field is a problem belonging to hydromagnetics and deserves to be more widely studied than it has been to date. In the non‐linear regime the literature is scarce. We develop the governing equations for the unsteady hydromagnetic rotating flow of a fourth‐order fluid past a porous plate. The steady flow is governed by a boundary value problem in which the order of differential equations is more than the number of available boundary conditions. It is shown that by augmenting the boundary conditions based on asymptotic structures at infinity it is possible to obtain numerical solutions of the nonlinear hydromagnetic equations. Effects of uniform suction or blowing past the porous plate, exerted magnetic field and rotation on the flow phenomena, especially on the boundary layer structure near the plate, are numerically analysed and discussed. The flow behaviours of the Newtonian fluid and second‐, third‐ and fourth‐order non‐Newtonian fluids are compared for the special flow problem, respectively. Copyright © 2004 John Wiley & Sons, Ltd.     

Steady two-dimensional flow past a normal flat plate

A vorticity/stream function formulation is used to obtain a numerical simulation of steady two-dimensional flow of a viscous incompressible fluid past a normal flat plate for a range of Reynolds numbers. A method of Fornberg [J. Fluid Mech. 98, 819 (1980)] is used to determine upstream and downstream boundary conditions on the stream function. Special care is taken in the neighbourhood of the singularities in vorticity at the plate edges and this is very important because any errors introduced are swept downstream and severely affect such quantities as the length and width of the attached eddies. The computed results are compared with those of a laboratory experiment in which a plane strip is drawn through water and ethylene glycol for the range of Reynolds numbers for which the experimental flow is stable.     

On MHD flow along an infinite flat wall with constant suction

Exact solutions of the Navier-Stokes equations are derived by a Laplace-transform technique for two-dimensional, incompressible flow of an electrically conducting fluid past an infinite porous plate under the action of a transverse magnetic field subject to the conditions: (i) the magnetic Prandtl number P_m is unity, and (ii) the Alfven velocity is less than the suction velocity. It is assumed that the flow is independent of the distance parallel to the plate and that the velocity component normal to the plate is constant. General formulae are derived for the velocity distribution and the magnetic field in terms of the given external velocity. The skin-friction is obtained and some special cases are considered.     

On unsteady flow of an infinite expanse of a visco-elastic Maxwell liquid bounded by a flat plate under the influence of an impulsive force

The equations of motion of the title problem are solved using Laplace transforms.     

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     

Effect of the chemical reaction and radiation absorption on the unsteady MHD free convection flow past a semi infinite vertical permeable moving plate with heat source and suction

Analytical solutions for heat and mass transfer by laminar flow of a Newtonian, viscous, electrically conducting and heat generation/absorbing fluid on a continuously vertical permeable surface in the presence of a radiation, a first-order homogeneous chemical reaction and the mass flux are reported. The plate is assumed to move with a constant velocity in the direction of fluid flow. A uniform magnetic field acts perpendicular to the porous surface, which absorbs the fluid with a suction velocity varying with time. The dimensionless governing equations for this investigation are solved analytically using two-term harmonic and non-harmonic functions. Graphical results for velocity, temperature and concentration profiles of both phases based on the analytical solutions are presented and discussed.     

Boundary-layer on a flat plate with homogeneous suction

Zusammenfassung Zur Berechnung einer laminaren Grenzschicht an einer ebenen Platte mit gleichmässiger Absaugung ist als Ansatz für das Geschwindigkeitsprofil ein Polynom 6. Grades benutzt und mit Hilfe der v. Kármánschen Integralbedingung eine Lösung erhalten worden. Das Verfahren gibt eine gute Annäherung für die verschiedenen Grenzschichtparameter und die Ergebnisse sind in enger Übereinstimmung mit den numerischen Ergebnissen von Iglisch. Darüber hinaus liefert der Fall ohne Absaugung eine ausgezeichnete Übereinstimmung mit der exakten Blasius-Lösung.     

Subsonic triple deck flow past a flat plate with an elastic stretch

The steady laminar subsonic flow past a flat plate having a stretch of an elastic membrane, the pressure on the other side of which is adjustable, is studied within the framework of the triple deck theory. The resulting lower deck problem is supplemented with a membrane equation relating the pressure difference across the membrane to its curvature. By pressurizing or depressurizing the membrane, it assumes the form of a hump or a dent that alters the flow characteristics. Numerical solutions obtained, in either case, give plausible account of the interaction between the membrane and the flow.     

Hydromagnetic effects on the three-dimensional flow past a porous plate

Hydromagnetic effects on the three-dimensional flow of an electrically conducting viscous incompressible fluid past a porous plate with periodic suction has been analysed. The uniform flow is subjected to a transversely applied magnetic field. The mathematical analysis is presented for the hydromagnetic boundary layer flow neglecting the induced magnetic field. Approximate solutions for the components of velocity field and the skin-frictions due to them are obtained and discussed with the help of a graph and tables.     

Exact solution for flow in a porous pipe with unsteady wall suction and/or injection

This paper presents an extension of the exact solution of the steady laminar axisymmetric flow in a straight pipe of circular cross section with porous wall, given by R.M. Terrill, to the case of unsteady wall injection and/or suction. The cases of the pulsating parabolic profile and of the developed pulsating flow are investigated as examples. The pulsating flow in porous ducts has many applications in biomedical engineering and in other engineering areas.     

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.