Stagnation point flow and heat transfer for a viscoelastic fluid impinging on a quiescent fluid

A theoretical study is made in the region near the stagnation point when a lighter incompressible viscoelastic fluids impinges orthogonally on the surface of another quiescent heavier incompressible viscous fluid. Similarity solutions of the momentum balance equations for both fluids are equalized at the interface. It is noted that an exact boundary layer solution is obtained for the lower lighter fluid. The velocity of the lower fluid is independent of lateral interface velocity but the velocity of the upper viscoelastic fluid increases with increasing lateral interface velocity. It is observed that lateral interface velocity increases with increasing viscoelastic parameter for fixed values of density and viscosity ratio of the two fluids. The convective heat transfer is investigated base on the similarity solutions for the temperature distribution of the two fluids. The interface temperature increases with increasing viscoelastic parameter of the upper viscoelastic fluid.     

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.     

Hydromagnetic Flow Past an Impulsively Started Infinite Vertical Plate with Variable Temperature and Mass Diffusion

An exact solution of the MHD Stokes problem for the flow of an electrically conducting, incompressible, viscous fluid past an impulsively started infinite vertical plate in the presence of variable temperature and mass diffusion is obtained. The dimensionless governing equations are solved using the Laplace-transform technique. The plate temperature and the concentration level near the plate increase linearly with time. The solutions for the velocity and skin friction are obtained for different magnetic field parameters and multiple buoyancy effects for aiding and opposing flows. It is observed that the velocity decreases in the presence of a magnetic field as compared to its absence and that the skin friction increases in the presence of aiding flows and decreases with opposing flows.__________Published in Inzhenerno-Fizicheskii Zhurnal, Vol. 78, No. 2, pp. 131–135, March–April, 2005.     

Unsteady MHD forced flow due to a point sink

Summary An analysis is performed to study the unsteady laminar incompressible boundary-layer flow of an electrically conducting fluid in a cone due to a point sink with an applied magnetic field. The unsteadiness in the flow is considered for two types of motion, viz. the motion arising due to the free stream velocity varying continuously with time and the transient motion occurring due to an impulsive change either in the strength of the point sink or in the wall temperature. The partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme in combination with the quasilinearization technique. The magnetic field increases the skin friction but reduces heat transfer. The heat transfer and temperature field are strongly influenced by the viscous dissipation and Prandtl number. The velocity field is more affected at the early stage of the transient motion, caused by an impulsive change in the strength of the point sink, as compared to the temperature field. When the transient motion is caused by a sudden change in the wall temperature, both skin friction and heat transfer take more time to reach a new steady state. The transient nature of the flow and heat transfer is active for a short time in the case of suction and for a long time in the case of injection. The viscous dissipation prolongs the transient behavior of the flow.     

BEM and FEM based numerical simulations for biomagnetic fluid flow

We investigate numerically the biomagnetic fluid flow between parallel plates imposed to a magnetic source placed below the lower plate. The biomagnetic fluid is assumed to be Newtonian, viscous, incompressible, electrically nonconducting, and has magnetization varying linearly with temperature and magnetic field intensity. Both steady and unsteady, laminar, two-dimensional biomagnetic fluid flow equations taking into care the heat transfer between the plates are solved using both finite element and dual reciprocity boundary element methods. Treatment of nonlinear terms by using only the fundamental solution of the Laplace equation, and discretization of only the boundary of the region are the advantages of dual reciprocity boundary element method giving small algebraic systems to be solved at a small expense. Finite element method is capable of giving very accurate results by discretizing the region affected by the magnetic source very finely, but it results in large sized algebraic systems requiring high computational cost. The results indicate that the flow is appreciably affected with the presence of magnetic source in terms of vortices at the magnetic source area. The lengths of the vortices, and temperature increase with an increase in the intensity of the magnetic field.     

A study of induced magnetic field with chemically reacting and radiating fluid past a vertical permeable plate

The influence of thermal radiation and chemical reaction on the steady MHD heat and mass transfer by a mixed convective flow of a viscous, incompressible, electrically conducting Newtonian fluid (an optically thin gray gas) past a vertical permeable plate was investigated with account for the induced magnetic field. The similarity solutions of the transformed nondimensional governing equations are obtained by the series solution technique. The influence of numerous parameters on the process characteristics is studied.     

MHD flow over a moving plate in a rotating fluid with magnetic field, Hall currents and free stream velocity

The non-similar boundary layer flow of a viscous incompressible electrically conducting fluid over a moving surface in a rotating fluid, in the presence of a magnetic field, Hall currents and the free stream velocity has been studied. The parabolic partial differential equations governing the flow are solved numerically using an implicit finite-difference scheme. The Coriolis force induces overshoot in the velocity profile of the primary flow and the magnetic field reduces/removes the velocity overshoot. The local skin friction coefficient for the primary flow increases with the magnetic field, but the skin friction coefficient for the secondary flow reduces it. Also the local skin friction coefficients for the primary and secondary flows are reduced due to the Hall currents. The effects of the magnetic field, Hall currents and the wall velocity, on the skin friction coefficients for the primary and secondary flows increase with the Coriolis force. The wall velocity strongly affects the flow field. When the wall velocity is equal to the free stream velocity, the skin friction coefficients for the primary and secondary flows vanish, but this does not imply separation.     

The effect of an oblique magnetic field on the surface instability of a finite conducting fluid layer

Summary The effect of an oblique magnetic field on the growth rate of Rayleigh-Taylor instability (RT) at the interface of a finite thickness layer of a viscous electrically conducting fluid in the presence of surface tension has been studied analytically. The effects of aligned and transverse magnetic fields on the coupled differential equations for the velocity and the magnetic field are discussed separately. The numerical results reveal that the nature and strength of the magnetic field and the layer thickness exacerbate or ameliorate the instability characteristic of such a layer.     

Unsteady flow and heat transfer of a viscous fluid in the stagnation region of a three-dimensional body with a magnetic field

The unsteady incompressible flow and heat transfer of a viscous electrically conducting fluid in the vicinity of a stagnation point of a general three-dimensional body have been studied when the velocity in the potential flow varies arbitrary with time. The magnetic field is applied normal to the surface. The effects of viscous dissipation and Ohmic heating are included in the analysis. Both nodal-point region (0?c?1, where c=b/a is the ratio of the velocity gradients in y and x directions in the potential flow) and saddle-point region (−1?c<0) are considered. The semi-similar solution of the Navier-Stokes equations and the energy equation are obtained numerically using an implicit finite difference scheme. Also a self-similar solution is found when the velocity in the potential flow, the magnetic field and the wall temperature vary with time in a particular manner. The asymptotic behaviour of the self-similar equations for large η is obtained which enables us to find the upper limit of the unsteady parameter λ. One interesting result is that the magnetic field tends to delay or prevent flow reversal in y-component of the velocity. The surface shear stresses in x and y directions and the surface heat transfer increase with the magnetic field as well as with the accelerating free stream velocity.     

The flow of conducting fluids through circular pipes having finite conductivity and finite thickness under uniform transverse magnetic fields

The steady flow of viscous, incompressible, electrically conducting fluids through circular pipes in the presence of an applied uniform transverse magnetic field is considered. In this analysis, the finite conductivity and wall thickness of the pipe have been taken into account. An exact solution and its numerical calculation have been presented. Some interesting results have been obtained.     

On the magnetohydrodynamic flow between eccentrically rotating disks

The steady flow of an incompressible, viscous, electrically conducting fluid between two parallel, infinite, insulated disks rotating with different angular velocities about two noncoincident axes has been investigated; under the application of a uniform magnetic field in the axial direction. The solutions for the symmetric and asymmetric velocities are presented. The interesting feature arising due to the magnetic field is that in the central region the flow attains a uniform rotation with mean angular velocity at all rotation speeds for sufficiently large Hartmann number. In this case the flow adjusts to the rotational velocities of the disks mainly in the boundary layers near the disks. The forces on the disks are found to increase due to the presence of the applied magnetic field.     

Unsteady three-dimensional MHD-boundary-layer flow due to the impulsive motion of a stretching surface

Summary The development of velocity and temperature fields of an incompressible viscous electrically conducting fluid, caused by an impulsive stretching of the surface in two lateral directions and by suddenly increasing the surface temperature from that of the surrounding fluid, is studied. The partial differential equations governing the unsteady laminar boundary-layer flow are solved numerically using an implicit finite difference scheme. For some particular cases, closed form solutions are obtained, and for large values of the independent variable asymptotic solutions are found. The surface shear stresses inx-andy-directions and the surface heat transfer increase with the magnetic field and the stretching ratio, and there is a smooth transition from the short-time solution to the long-time solution.     

Effects of mass transfer on a resonance instability in the laminar boundary layer flow over a rotating-disk

In this paper the linear stability properties of the magnetohydrodynamic flow of an incompressible, viscous and electrically conducting fluid are investigated for the boundary-layer due to an infinite permeable rotating-disk. The fluid is subjected to an external magnetic field perpendicular to the disk. The interest lies also in finding out the effects of uniform suction or injection. In place of the traditional linear stability method, a theoretical approach is adopted here based on the high-Reynolds-number triple-deck theory. It is demonstrated that the nonstationary perturbations evolve in accordance with an eigenrelation analytically obtained.     

Universal stability of thermo-magneto-micropolar fluid motions

Criteria for universal stability of the unsteady motion of an incompressible, electrically conducting linear micropolar fluid with heat transfer in the presence of an arbitrary magnetic field, and in an arbitrary time dependent domain are established. The model of the micropolar fluid employed is essentially the one proposed by Eringen. The interaction between the flow field and the magnetic field is manifested through the Lorentz force and the coupling between the flow and temperature field arises through the Boussinesq equation of state.The stability method employed is an energy technique due to James Serrin. Certain uniqueness theorems for the unsteady and steady flows of thermo-magneto-micropolar fluid are also established.The theorems established for the stability and uniqueness are universal in the sense that they may be applied to any geometry of bound domains and any distribution of the basic field variables.     

Asymptotic stability of linearly evolving non-stationary modes in a uniform hydromagnetic field over a rotating-disk flow with suction and injection

In this paper the linear stability properties of the magnetohydrodynamic flow of an incompressible, viscous and electrically conducting fluid are investigated for the boundary-layer due to an infinite permeable rotating-disk. The fluid is subjected to an external magnetic field perpendicular to the disk. The interest lies also in finding out the effects of uniform suction or injection. In place of the traditional linear stability method, a theoretical approach is adopted here based on the high-Reynolds-number triple-deck theory. It is demonstrated that the nonstationary perturbations evolve in accordance with an eigenrelation analytically obtained.     

Hydromagnetic couette flow of an Oldroyd-B fluid in a rotating system

The motion of electrically conducting, Oldroyd-B and incompressible fluid between two infinitely extended non-conducting parallel plates under a uniform transverse magnetic field, fixed relative to the fluid has been considered. The lower plate is at rest and the upper plate is oscillating in its own plane. The governing partial differential equation of this problem, subject to boundary conditions are solved analytically. The expressions for the steady and unsteady velocity fields for the conducting Oldroyd-B fluid are obtained. The graphs are plotted for different values of dimensionless parameters of the problem and the analysis of the results showed that the flow field is appreciably influenced by the applied magnetic field, the rotation and the material parameters of the fluid.     

Instability growth rate of a charged interface between immiscible electrically conducting liquids

It is shown by means of a numerical analysis of the dispersion equation that two types of aperiodic instability may occur at a charged planar interface between two viscous incompressible immiscible electrically conducting liquids, for which the growth rates increase or decrease, respectively as the conductivity ratio of the media increases. Pis’ma Zh. Tekh. Fiz. 23, 38–40 (August 26, 1997)     

MHD flow between two parallel plates with heat transfer

Summary In the present paper, the steady flow of an electrically conducting, viscous, incompressible fluid bounded by two parallel infinite insulated horizontal plates and the heat transfe through it are studied. The upper plate is given a constant velocity while the lower plate is kept stationary. The viscosity of the fluid is assumed to vary with temperature. The effect of an external uniform magnetic field as well as the action of an inflow perpendicular to the plates together with the influence of the pressure gradient on the flow and temperature distributions are reported. A numerical solution for the governing non-linear ordinary differential equations is developed.     

On the flow of an electrically conducting nonlocal viscous fluid between parallel plates in the presence of a transverse magnetic field in magnetohydrodynamics

A continuum theory is constructed for the flow of an electrically conducting nonlocal viscous fluid between two nonconducting parallel plates. The flow is subject to the influence of a transverse magnetic field. The effects of long range or nonlocal interactions at a material point in the fluid arising from all material points in the rest of the fluid are taken into account by means of a nonlocal influence function. Equations of motion governing the nonlocal viscous flow are derived from localized forms of global balance laws and constitutive equations appropriate for electromagnetically active media. These field equations are analytically solved for the nonlocal velocity and the nonlocal stress fields. The effects of varying the magnetic field strength on the shear stress are investigated. The effects of such variations on the shear stress exerted on the walls of microscopic channels are also determined. Numerical computations are provided for these results.     

Hydromagnetic flow past a rotating porous plate in a conducting fluid rotating about a noncoincident parallel axis

Summary The hydromagnetic flow of an incompressible viscous electrically conducting fluid past a porous plate is investigated when the plate rotates with a uniform angular velocity about an axis normal to the plate and the fluid at infinity rotates with the same angular velocity about a non-coincident parallel axis. It is shown that in the presence of a uniform magnetic field parallel to the axis of rotation the boundary layer thickness decreases with an increase in either the suction at the plate or the magnetic parameter M. In the presence of suction at the plate, the velocity component u in the direction normal to the plane containing the axis of rotation of the plate and that of the fluid increases with an increase in M, while the velocity component v in the transverse direction parallel to the plane of the plate decreases with an increase in M. For a fixed value of M, at a given location u increases with an increase in the suction parameter S while v decreases with increasing S. For a fixed value of M, at a given location both u and v decrease with an increase in the blowing parameter S₁. Further, for a fixed value of S₁, at a given position u increases with an increase in M but v decreases with increasing M. It is shown that no torque is exerted by the fluid on the plate, and non-coaxial rotations of the plate and the fluid at infinity have no influence on the torque.The solution of the heat transfer equation reveals that for given values of the suction parameter S, Prandtl number P and Eckert number E, the temperature at a given point in the flow increases with increasing M. On the other hand, for fixed values of M, P and E, the temperature at a given point decreases with increasing S. No steady distribution of temperature exists when there is blowing at the plate.