Flow and heat transfer of an electrically conducting third grade fluid past an infinite plate with partial slip

The effects of partial slip on the steady flow and heat transfer of an electrically conducting, incompressible, third grade fluid past a horizontal plate subject to uniform suction and blowing is investigated. Two distinct heat transfer problems are studied. In the first case, the plate is assumed to be at a higher temperature than the fluid; and in the second case, the plate is assumed to be insulated. The momentum equation is characterized by a highly nonlinear boundary value problem in which the order of the differential equation exceeds the number of available boundary conditions. Numerical solutions for the governing nonlinear equations are obtained over the entire range of physical parameters. The effects of slip, magnetic parameter, non-Newtonian fluid characteristics on the velocity and temperature fields are discussed in detail and shown graphically. It is interesting to find that the velocity and the thermal boundary layers decrease with an increase in the slip, and as the slip increases to infinity, the flow behaves as though it were inviscid.     

Unsteady flow of a fourth-grade fluid due to an oscillating plate

The governing non-linear high-order, sixth-order in space and third-order in time, differential equation is constructed for the unsteady flow of an incompressible conducting fourth-grade fluid in a semi-infinite domain. The unsteady flow is induced by a periodically oscillating two-dimensional infinite porous plate with suction/blowing, located in a uniform magnetic field. It is shown that by augmenting additional boundary conditions at infinity based on asymptotic structures and transforming the semi-infinite physical space to a bounded computational domain by means of a coordinate transformation, it is possible to obtain numerical solutions of the non-linear magnetohydrodynamic equation. In particular, due to the unsymmetry of the boundary conditions, in numerical simulations non-central difference schemes are constructed and employed to approximate the emerging higher-order spatial derivatives. Effects of material parameters, uniform suction or blowing past the porous plate, exerted magnetic field and oscillation frequency of the plate on the time-dependent flow, especially on the boundary layer structure near the plate, are numerically analysed and discussed. The flow behaviour of the fourth-grade non-Newtonian fluid is also compared with those of the Newtonian fluid.     

MHD squeezing flow of second‐grade fluid between two parallel disks

This paper examines the unsteady two‐dimensional flow of a second‐grade fluid between parallel disks in the presence of an applied magnetic field. The continuity and momentum equations governing the unsteady two‐dimensional flow of a second‐grade fluid are reduced to a single differential equation through similarity transformations. The resulting differential system is computed by a homotopy analysis method. Graphical results are discussed for both suction and blowing cases. In addition, the derived results are compared with the homotopy perturbation solution in a viscous fluid (Math. Probl. Eng., DOI: 10.1155/2009/603916 ). Copyright © 2011 John Wiley & Sons, Ltd.     

Similarity solution of free convective boundary-layer behavior at a stretching surface

In the present study, free convection and heat transfer behavior of electrically conducting fluid in the boundary layer over a vertical continuously stretching surface is investigated. The effects of free convection, magnetic field, suction/blowing at the surface and the stretching speed of the surface on the flow and heat transfer characteristics are considered. By applying one-parametric group theory to analysis of the problem, a similarity solution is found. The governing equations of continuity, momentum and energy are solved numerically by a fourth-order Runge-Kutta scheme. The numerical results, which are obtained for the flow and heat transfer characteristics, reveal the influences of the parameters. Received on 9 September 1998     

Laminar flow through porous channels with an applied magnetic field

Summary The two-dimensional steady flow of an incompressible and electrically conducting viscous fluid through a porous channel with a transverse magnetic field is discussed. It is assumed that there is constant suction at one wall and constant blowing at the other wall. A perturbation solution is obtained where the perturbation parameter is equal to the difference between the two wall velocities. The behaviour of the solution for various suction Reynolds numbers and magnetic Reynolds number is considered. Finally, the skin friction at one wall is given and is found to increase with the increase of the magnetic field.     

Flow due to non-coaxial rotation of a porous disk and a second grade fluid rotating at infinity

An exact solution for the three-dimensional flow due to non-coaxial rotation of a porous disk and a second grade fluid at infinity is obtained. It is shown that for uniform suction or uniform blowing at the disk, an asymptotic profile exists for the velocity distribution. The velocity depends on two parameters: one of them is the suction parameter or blowing parameter and the other is the visco-elastic parameter. Furthermore, it is found that when the value of the visco-elastic parameter is fixed, the velocity decreases with an increase in the value of the suction parameter and when the value of the suction parameter is fixed, the velocity increases with an increase in the value of the visco-elastic parameter.     

Heat and mass transfer in a visco–elastic fluid flow over an accelerating surface with heat source/sink and viscous dissipation

 In this paper we present a mathematical analysis of heat and mass transfer phenomena in a visco–elastic fluid flow over an accelerating stretching sheet in the presence of heat source/sink, viscous dissipation and suction/blowing. Similarity transformations are used to convert highly non-linear partial differential equations into ordinary differential equations. Several closed form analytical solutions for non-dimensional temperature, concentration, heat flux, mass flux profiles are obtained in the form of confluent hypergeometric (Kummer's) functions for two different cases of the boundary conditions, namely, (i) wall with prescribed second order power law temperature and second order power law concentration (PST), and (ii) wall with prescribed second order power law heat flux and second order power law mass flux (PHF). The effect of various physical parameters like visco–elasticity, Eckert number, Prandtl number, heat source/sink, Schmidt number and suction/blowing parameter on temperature and concentration profiles are analysed. The effects of all these parameters on wall temperature gradient and wall concentration gradient are also discussed. Received on 23 March 2000 / Published online: 29 November 2001     

Exact flow of a third-grade fluid on a porous wall

The flow of a third-grade fluid occupying the space over a wall is studied. At the surface of the wall suction or blowing velocity is applied. By introducing a velocity field, the governing equations are reduced to a non-linear partial differential equation. The resulting equation is analysed analytically using Lie group methods.     

Optimization of suction-blowing in a viscous fluid

The problem of drag minimization in a viscous fluid by means of controlled suction (blowing) is considered. In the low Reynolds number approximation matched asymptotic expansions are used to construct the second approximation and analytic solutions of the optimization problem are found for a sphere and a circular cylinder. Transition from unseparated to separated flow is accompanied by a qualitative restructuring of the optimal solution.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 27–32, May–June, 1989.     

Effects of suction or blowing on the velocity and temperature distribution in the flow past a porous flat plate of a power-law fluid

An analysis is made of the steady flow of a non-Newtonian fluid past an infinite porous flat plate subject to suction or blowing. The incompressible fluid obeys Ostwald-de Waele power-law model. It is shown that steady solutions for velocity distribution exist only for a pseudoplastic (shear-thinning) fluid for which the power-law index n satisfies 0<n<1 provided that there is suction at the plate. Velocity at a point is found to increase with increase in n. No steady solution for velocity distribution exists when there is blowing at the plate. The solution of the energy equation governing temperature distribution in the flow of a pseudoplastic fluid past an infinite porous plate subject to uniform suction reveals that temperature at a given point near the plate increases with n but further away, temperature decreases with increase in n. A novel result of the analysis is that both the skin-friction and the heat flux at the plate are independent of n.     

Viscoelastic fluid flow impinging on a wall with suction or blowing

The oblique flow of a viscoelastic fluid impinging on a porous wall with suction or blowing is studied. It is found that when suction is applied the fluid penetrates the wall while blowing causes the shifting of the stagnation point. It is also found that this shifting depends upon the magnitude of the blowing and upon the Weissenberg number.     

A novel analytic solution of MHD flow for two classes of visco-elastic fluid over a sheet stretched with non-linearly (quadratic) velocity

The laminar boundary layer flow induced in a quiescent visco-elastic fluid by a permeable stretched flat surface with non-linearly (quadratic) velocity and appropriate wall transpiration under the influence of a magnetic field is investigated. It is shown that the problem permits a complete analytic exponentially decaying solution for the set of continuity and momentum equations with both magnetic field and visco-elasticity influences for two classes of visco-elastic fluid, namely, the second grade and Walters’ liquid B fluids. The effects on both the skin friction parameter α and velocity profiles of various physical parameters such as visco-elasticity, suction/blowing parameter and magnetic parameter are studied. The results for the velocity field are presented through graphs and discussed in detail.     

The effects of the side walls on the flow of a second grade fluid in ducts with suction and injection

The effects of the side walls on the flow in ducts with suction and injection are examined. Three illustrative examples are given. The first example considers the effect of the side walls on the flow over a porous plate. The second example considers the flow between two parallel porous plates and the third example is devoted to the investigation of the flow in a rectangular duct with two porous walls. Exact solution of the governing equation using the no-slip boundary condition and an additional condition are obtained. The expression of the velocity, the volume flux and the vorticity are given. It is found that for large values of the cross-Reynolds number near the suction region the flow for a Newtonian fluid does not satisfy the boundary condition, but it does not behave in the same way for a second grade fluid. Three examples considered show that there are pronounced effects of the side walls on the flows of a second grade fluid in ducts with suction and injection.     

An exact solution for the flow of a non-newtonian fluid past an infinite porous plate

Summary The flow of an incompressible fluid of second grade past an infinite porous plate subject to either suction or blowing at the plate is studied. It is found that existence of solutions is tied in with the sign of material moduli and in marked contrast to the Classical Newtonian, fluid solutions can be exhibited for the blowing problem.

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Sommario Si studia la corrente di un fluido incomprimibile di secondo grado che lambisce una lastra porosa da cui è succhiato o soffiato. Si trova che l'esistenza delle soluzioni è legata al segno dei moduli del materiale e, in netto contrasto col fluido newtoniano classico, si possono trovare soluzioni per il problema del soffiamento.

     

NUMERICAL STUDY ON THE FLOW AROUND A CIRCULAR CYLINDER WITH SURFACE SUCTION OR BLOWING USING VORTICITY-VELOCITY METHOD

A vorticity-velocity method was used to study the incompressible viscous fluid flow around a circular cylinder with surface suction or blowing. The resulted high order implicit difference equations were effeciently solved by the modified incomplete LU decomposition conjugate gradient scheme (MILU-CG). The effects of surface suction or blowing ' s position and strength on the vortex structures in the cylinder wake, as well as on the drag and lift forces at Reynoldes number Re = 100 were investigated numerically. The results show that the suction on the shoulder of the cylinder or the blowing on the rear of the cylinder can effeciently suppress the asymmetry of the vortex wake in the transverse direction and greatly reduce the lift force; the suction on the shoulder of the cylinder, when its strength is properly chosen , can reduce the drag force significantly , too.     

Fluctuating flow of an elastico-viscous fluid along an infinite porous plate with an applied magnetic field

The problem of oscillating free stream flow of an elastico-viscous, incompressible, and electrically conducting fluid along an infinite plate with suction varying periodically with time, is considered in the presence of a transverse magnetic field. The effect of the elasticity of the fluid, the magnetic fluid, and the fluctuation of suction velocity on the velocity and the skin friction is examined.     

Optimal control of viscous flow at high reynolds numbers

The most promising and most highly developed method for reducing drag in aerodynamics remains control of the flow by blowing and suction. In practice the main control problems remain the reduction of separation and the protracting of the transition of the boundary layer. These problems are solved mainly by experimental methods [1]. Meanwhile the main theoretical question remains unanswered: what is the theoretical minimum drag attainable by control through blowing (or suction)? In the present study an answer is given to this question for the cage of laminar flow round a body by a viscous incompressible fluid at high Reynolds numbers.     

Laminar flow through channels with porous walls and with an applied transverse magnetic field

Summary The problem of two-dimensional steady laminar flow of a viscous incompressible and electrically conducting fluid through a channel with two equally porous walls in the presence of a transverse magnetic field has been extended to include all values of Hartmann number and small suction velocity at the walls. Expressions for the velocity components, the pressure and the wall friction in terms of the Hartmann number and the suction Reynolds number are given. It is found that the pressure drop in the major flow direction and the wall friction decrease with the increase in suction and increase with the increase in the strength of the magnetic field.     

Aerodynamic jet steering using steady blowing and suction

An aerodynamic jet steering scheme using a combination of blowing and suction near the exit plane of the primary jet is demonstrated. Previous studies involving synthetic jet actuators have shown that jet steering or vectoring is achieved when primary jet fluid is drawn into the suction slot, and that the vectoring force increases with primary jet speed. These studies were limited by the high-actuation frequencies required to maintain vectoring at high primary jet speeds. The present steady technique does not suffer from this limitation, and requires suction and blowing flow rates which are a small fraction of that of the primary jet. This arrangement is studied experimentally and numerically. The results are presented primarily in terms of turning angle. It is found that for sufficient blowing flow rates (similar to the suction flow rate) the resultant turning angle increases linearly with the suction flow rate regardless of Reynolds number (up to 21,000). For insufficient blowing, the jet may be turned in the opposite direction.The authors would like to thank Ari Glezer for the loan of the primary jet facility, and Terry Zollinger for fabricating of the actuator and butterfly valve.     

Flow through a porous annulus

Summary The problem of laminar flow through a porous annulus with constant velocity of suction at the walls and with swirl is reduced to the solution of four non-linear differential equations. The significance of each of these equations is discussed. By taking the swirl to be zero series solutions are obtained for (i) small suction or blowing (ii) when the total flow into the channel through the walls is small. Finally the asymptotic behaviour of the flow for large suction or blowing is discussed.