MHD Couette Flow Research Articles

Natural convection in unsteady MHD couette flow

The combined effect of natural convection and uniform transverse magnetic field on the couette flow of an electrically conducting fluid between two parallel plates for impulsive motion of one of the plates in discussed. Under the assumption of negligible induced magnetic field and applied magnetic field being fixed relative to the fluid or plate, the governing equations have been solved exactly, and the expressions for velocity and temperature field have been presented for two different cases. A comparative study is made between the velocity field for magnetic field fixed with respect to plate and magnetic field fixed with respect to fluid.

Hydromagnetic elastico-viscous fluid flow between two parallel walls: Velocity field.-I

The effect of the elastic properties of the fluid on the MHD Couette flow of a conducting viscous fluid between two parallel walls is studied when one wall is fixed and the other is moving periodically in time. Exact solution for the velocity field in the boundary layer is obtained. Also expressions for the shear stress at different layers and the skin-friction at the two walls have been obtained.

Stability of MHD Couette flow in a narrow gap annulus

A numerical solution to the MHD stability problem for dissipative Couette flow in a narrow gap is presented under following conditions: (i) the inner cylinder rotating with the outer one stationary, (ii) co-rotating cylinders, (iii) counter-rotating cylinders, (iv) an axially applied magnetic field, and (v) conducting and non-conducting walls.

Heat transfer in unsteady MHD couette flow of an electrically conducting, viscous, incompressible rarefied gas

An analytical study is performed to examine the heat transfer characteristics on the flow of a viscous, incompressible rarefied gas in a parallel plate channel under the action of transverse magnetic field when (i) suction velocity normal to the plate is constant, (ii) the second plate oscillates in time about a constant non-zero mean, (iii) fluid is subjected to a constant heat source of absorption type. Apprximate solutions for velocity, temperature, phase, and amplitude of skin-friction and rate of heat transfer are evaluated. Mean temperature profiles, phase and amplitude of rate of heat transfer at both plates are discussed graphically followed by a quantitative discussion. Mean rate of heat transfer is tabulated in Table I.

Hall Effects in MHD Couette Flow with Heat Transfer

An exact analysis of a generalized MHD Couette flow, on taking into account the Hall current, is presented. Expressions for the axial and transverse components of velocity, the skin friction, are derived. These are shown in graphs. The exact solution to the energy equation, assuming the linear variation of the temperature along the plate, is also derived and this is shown graphically. The effects of different parameters are discussed.

Effect of Hall Current on MHD Couette Flow between Thick Arbitrarily Conducting Plate in a Rotating System

In this paper the effects of Hall current on Couette flow of an electrically conducting fluid between two parallel plates in the presence of a uniform transverse magnetic field for a rotating system has been discussed. Here, we have taken the plates to be of arbitrary conductivity and arbitrary thickness. Analytic solution has been obtained exactly and influence of different parameters viz.,Hartmann number, rotation parameter, wall conductivity parameters, Hail parameters for the liquid as well as the plates, and the thickness parameters on the primary and secondary velocity profiles, and induced magnetic field components, magnetic and viscous stresses as well as flux ratio has been examined numerically.

On Combined Effects of Coriolis Force and Hall Current on Steady MHD Couette Flow and Hear Transfer

The effects of Hall current on Couette flow and heat transfer of a conducting fluid between two plates in a rotating system are discussed. Both Hall and rotation parameters introduce secondary velocity and secondary induced magnetic field. The resultant shear stress and heat transfer from the moving plate has been calculated assuming it to be non-conducting and taking the fixed plate to be infinitely conducting. The resultant shear stress increases with increase in Hartmann number as well as rotation parameter while it decreases with increase in Hall parameter. The role of each parameter on heat transfer is always opposite to its role on shear stress. In the absence of Hall current this opposing character remains unalterned even if direction of rotation is reversed.

Hall effects on MHD Couette flow in a rotating system

The combined effect of rotation and Hall current on the MHD Couette flow have been studied. The heat transfer characteristic have also been discussed on taking the viscous and Joule dissipation into account. The primary and the secondary velocity components increase with increase in Hall parameter but the primary velocity decreases with increase in rotation parameter. It is seen that the rate of heat transfer at the stationary plate is independent of both the Hall parameter and the rotation parameter. The rate of heat transfer at the moving plate increases with increase in Hall parameter, while it decreases with increase in rotation parameter. The values of the critical Eckert number at which the direction of the heat flow changes increases with increase in Hall parameter.

MHD Couette flow of a viscous stratified fluid of large conductivity

The MHD Couette flow of a viscous stratified fluid of large electrical conductivity with suction and injection at the plane boundaries is studied when the plane boundaries are maintained at different temperatures. The Oseen type governing equations are formulated using the method suggested by Greenspan for stratified fluids. Introducing the similarity variables, the linearised equations are solved to obtain the velocity and temperature distributions. The results show that the behaviour of velocity and temperature in fluids of large conductivity is different from the behaviour of velocity and temperature for fluids of finite conductivity. The effect of the magnetic field on the load capacity is investigated for the case when the width of the channel is small.

Magnetohydrodynamic Couette Flow and Heat Transfer in a Rotating System

The influence of electrode geometry for the MHD Couette flow in the presence of the Hall current and heat transfer of a conducting liquid in a rotating system has been studied.

Hall and Ion-Slip Effects in MHD Couette Flow with Heat Transfer

An analysis of the MHD Couette flow on taking into account the Hall and the ion-slip effects has been carried out for fully developed flow. Exact solutions to the velocity components, magnetic field components, axial and transverse components of the skin-friction, temperature and the rate of heat transfer have been derived. The numerical values of the transverse induced pressure gradient, the skin friction and the rate of heat transfer are entered in tables and the others have been shown on graphs. It has been observed that the flow may become unstable when M is small and se (Hall parameter) and si (ion-slip parameter) are large or at large value of M.

Effects of couple stresses on MHD Couette flow

An exact analysis of the effects of the couple stresses on the MHD Couette flow of an electrically conducting, viscous incompressible fluid is carried out. Closed form solutions are derived for the velocity, the current density, the skin-friction at the lower plate, the force to move the upper plate, and the coefficient of mass flux for (i) A → ∞, and (ii) 2 M/ A </> 1, where A is the couple stress parameter and M is the Hartmann number. These are shown graphically followed by a discussion. During the course of discussion the effects of A are quantitatively compared with those in the ordinary case. It is observed that in the presence of a magnetic field the skin friction is affected by the couple stresses.

Hall effects on magnetohydrodynamic couette flow and heat transfer in a rotating system

An exact solution for the MHD Couette flow and heat transfer of a conducting liquid in a rotating system has been obtained, taking into account the Hall currents. It is found that at the moving plate the resultant shear stress and the rate of heat transfer decrease with an increase in the Hall parameter.

Magnetohydrodynamic Couette Flow and Heat Transfer in a Rotating System

An exact solution for the MHD Couette flow and heat transfer of a conducting liquid in a rotating system has been obtained. It is found that at the moving plate the resultant shear stress increases and the rate of heat transfer decreases with increase in either magnetic parameter or rotation parameter.

Heat Generated by MHD Couette Flow With Porous Walls

The simultaneous effects of mass injection and magnetic field on the heat generation due to viscous dissipation is investigated analytically. The present findings are in general agreement with the temperature measurements of Chang-Yi Wang [1]. Results indicate larger reductions in maximum temperature and a significant increase in the heat take off by porous boundaries, if magnetic field is present. The most striking feature of this investigation is the marked improvement in the temperature reduction with the application of the electromagnetic force.

MHD Couette Flow with Consideration of Hall Effect

MHD Couette Flow with Consideration of Hall Effect

Hall effects on generalised MHD Couette flow with heat transfer

An analysis of a generalised magnetohydrodynamic Couette flow of a viscous, incompressible, electrically conducting fluid between two infinite parallel plates, on taking into account the transverse magnetic field and the Hall currents, is presented. Exact solutions for the velocity, the temperature, current density, the magnetic field, the skin-friction and the Nusselt number are derived. The velocity components, the current density, the magnetic field, and the skin-friction are shown on graphs and the values of the Nusselt number are entered in tables. During the course of the discussions, the effects of the Hartmann number, the Hall parameter and the axial pressure gradient are discussed.

On the instability of magnetohydrodynamic Couette flow via non-axisymmetric, oscillatory critical modes

The onset of instability of MHD Couette flow due to non-axisymmetric, oscillatory disturbances is investigated. For counter-rotating cylinders, the existence is discovered of two threshold magnetic fields. Below the first threshold, non-axisymmetric, oscillatory modes are responsible for the onset of instability in analogy with the hydrodynamic case. For values of the magnetic field between the two thresholds, the critical modes are axisymmetric and stationary. Beyond the second threshold, in the region of high magnetic field, the critical modes are again non-axisymmetric and oscillatory. For the case of a stationary inner cylinder, only the large magnetic threshold exists. For co-rotating cylinders, the assumptions are verified under which the exact solution was obtained by Hassard, Chang and Ludford (1972).

Unsteady MHD couette flow due to a change in the applied magnetic field magnitude

Unsteady MHD couette flow due to a change in the applied magnetic field magnitude

Low speed MHD Couette flow of a slightly rarefied and electrically conducting gas

The effects of an applied magnetic field on the steady, laminar, low speed plane Couette flow of a slightly rarefied and electrically conducting gas are studied. Consideration is given to the slip-flow regime, wherein the gas rarefaction begins to play its important role. The generally accepted method of analysis for slip flows is utilized, i.e. the continuum magnetohydrodynamic equations of motion are used throughout the gas, together with the first and the second order slip velocity and temperature jump boundary conditions. Considerations are further given to (1) the case of zero electric field and (2) the case of a nonconducting channel in which the net current across the channel is zero.