Hall effects on MHD free-convection flow past an accelerated vertical porous plate

The effect of Hall currents on the hydromagnetic free-convection flow of an electrically conducting and incompressible viscous fluid past a uniformly accelerated infinite vertical porous plate is discussed. The magnetic Reynolds number is assumed to be small so that the induced magnetic field can be neglected. The governing equations of the flow are solved by defining a complex velocity with the help of the Laplace transform method when the Prandtl number is equal to unity. The influence of the various parameters on the unsteady flow field is presented for both the cases, cooling and heating of the porous plate by free-convection currents.     

Magnetohydrodynamic free convective effect for an incompressible viscous fluid past an infinite limiting surface

An analysis of the effect of a magnetic field on the free convective flow of an incompressible, electrically conducting and viscous fluid past an infinite vertical limiting surface, has been carried out. Also the limiting surface are unmoving, we have constant heat flux at the limiting surface, the free velocity is constant and the magnetic Reynolds number is not small. The effects of the magnetic parameter and the Grashoff number on the flow are discussed.     

Oscillatory hydromagnetic free-convection flow in the stokes problem past an infinite vertical porous plate in a rotating system,I

Rotation effect on the hydromagnetic free-convection flow of an electrically conducting, viscous, and incompressible fluid past a steadily moving vertical porous plate has been analysed in the presence of a transverse magnetic field. The free-stream velocity oscillates in time about a constant mean, while the suction velocity, normal to the porous plate, is constant. The magnetic Reynolds number of the flow is taken small enough so that the induced magnetic field can be neglected. The plate temperature is constant and the difference between the temperature of the plate and the free stream is moderately large causing the free-convection currents. The flow field is described by nonlinar coupled system of equations. With viscous dissipative heat taken into account, approximate solutions of the problem are obtained for the components of velocity field and temperature field as well as for the skin-friction components and rate of heat transfer.     

Effects of free convection on the hydromagnetic accelerated flow past a vertical porous limiting surface

The effects of free convection on the accelerated flow of a viscous, incompressible and electrically conducting fluid (e.g. of a stellar atmosphere) past a vertical, infinite, porous limiting surface (e.g. of a star) in the presence of a transverse magnetic field, is considered. The magnetic Reynolds number of the flow is taken to be small enough, so that the induced magnetic field is negligible. Expressions for velocity and skin-friction are obtained by using Laplace transform, when the Prandtl number is equal to one (P=1). Graphs showing variations of velocity and skin-friction, for different values ofG (Grashof number) andM (magnetic parameter) are plotted, and the results of them are discussed.     

MHD free-convection flow past an accelerated vertical porous plate in a rotating fluid

The three-dimensional flow of an electrically conducting and incompressible viscous fluid past a uniformly accelerated infinite vertical porous plate is studied in a rotating fluid. The flow is assumed to be at small magnetic Reynolds number so that the induced magnetic field is neglected. An exact solution has been obtained by defining a complex velocity with the help of the Laplace transform method for the Prandtl number equal to unity. The effects of rotation, magnetic and free-convection parameters are discussed for the whole problem. Also, the skin-friction components on the plate are discussed.     

Effects of mass transfer on the hydromagnetic flow past a vertical limiting surface

An analysis of a two-dimensional steady free convective flow of a conducting fluid, in the presence of a magnetic field and a foreign mass past an infinite, vertical porous and unmoving surface is carried out, when we have constant heat flux at the limiting surface and the magnetic Reynolds number of the flow is not small. If we assume constant suction at the surface, approximate solutions of coupled nonlinear equations are derived for the velocity field, temperature field, magnetic field and for their related quantities. During the course of discussion, the effectsM (magnetic parameter),Gr (Grashof number), andGm (modified Grashof number) have been presented.     

Three-dimensional simulations of shear instabilities in magnetized flows

Shear mixing is believed to be the main mechanism to provide extra mixing in stellar interiors. We present results of three-dimensional (3D) simulations of the magnetohydrodynamic Kelvin–Helmholtz instability in a stratified shear layer. The magnetic field is taken to be uniform and parallel to the shear flow. We describe the evolution of the fluid flow and the magnetic field for a range of initial conditions. In particular, we investigate how the mixing rate of the fluid depends on the Richardson number and the magnetic field strength. It is found that the magnetic field can enhance as well as suppress mixing. Moreover, we have performed two-dimensional (2D) simulations and discuss some interesting differences between the 2D and 3D results.     

Hydromagnetic free convection effects on the oscillatory flow past an impulsively started porous limiting surface: I

Unsteady two-dimensional free convection flow of an electrically conducting, viscous, incompressible fluid, past an infinite vertical porous limiting surface in the presence of a transverse magnetic field is studied, when the limiting surface is moved impulsively with a constant velocity, either in the direction of the flow or in the opposite direction. The magnetic Reynolds number of the flow is not taken to be small enough so that the induced magnetic field is not negligible. The obtained results, for the mean steady flow phenomena, are discussed with the aid of graphs and tables for different values of the dimensionless parameters entering into the problem.     

Unsteady hydromagnetic flow past a porous spherical or cylindrical surface

The problem of unsteady hydromagnetic axial flow near the porous surface of a sphere or a cylinder is studied numerically. The fluid is considered to be electrically conducting, viscous and incompressible subjected to a magnetic field. Results are presented for the case of injected or sucked fluid with a constant velocity through the porous surfaces. The magnetic Prandtl number is set equal to one, while the magnetic Reynolds number is taken to be small enough so that the inducted magnetic field is negligible.     

Hall effects on an oscillatory MHD flow in the Stokes problem past an infinite vertical porous plate,I

Hall effects on the hydromagnetic free convection flow of an electrically conducting incompressible viscous fluid past a steadily moving vertical porous plate has been analysed when the free stream oscillates in magnitude. The flow is subjected to a constant suction, through the porous plate, and the difference between wall temperature and the free-stream is moderately large causing the free convection currents. The mathematical analysis is presented for the hydromagnetic boundary layer flow without taking into account the induced magnetic field. This is a valid assumption for small magnetic Reynolds number. Approximate solutions for the components of velocity field and temperature field and their related quantities are obtained. The influence of various parameters entering into the problem is extensively discussed with the help of graphs and tables.     

Hydromagnetic free convection flow in the stokes problem for a porous vertical limiting surface with constant suction

This paper provides a comprehensive analysis of the effects of a uniform transverse magnetic field on the free-convection flow of a viscous incompressible and electrically conductive fluid (e.g., of a stellar atmosphere) past an impulsively started, infinite, porous, vertical limiting surface (e.g., of a star) with a constant suction. The magnetic Reynolds number is assumed small so that the induced magnetic field is considered negligible. Exact solution of the equations governing the flow is obtained in closed form with the help of the Laplace transform technique when the Prandtl numberP=1. Expressions are given for the velocity field, for the temperature field and for their related quantities. The results thus obtained are discussed quantitatively in the last section of this paper.     

Seismology of Oscillating Flux Tube with Twisted Magnetic Field and Plasma Flow

Transverse oscillations of a thin coronal loop in a zero-beta plasma in the presence of a twisted magnetic field and flow are investigated. The dispersion relation is obtained in the limit of weak twist. The twisted magnetic field modifies the phase difference and asymmetry of standing kink oscillations caused by the flow. Using data from observations the kink speed and flow speed have been determined. The presence of the twisted magnetic field can cause underestimation or overestimation of the flow speed in coronal loops depending on the direction of the flow and twisted magnetic field, but a twisted magnetic field has little effect on the estimated value of the kink speed.     

Hydromagnetic flow past a continuously moving semi-infinite plate for large suction

The similarity solution for hydromagnetic flow of an incompressible viscous electrically conducting fluid past a continuously moving semi-infinite porous plate in the presence of a magnetic field has been obtained for the case of small magnetic Reynolds number. The perturbation method has been used to solve the similarity equations at large suction. The resulting equations have been solved by analytical method. The effect of the magnetic parameter is to increase the skin-friction coefficient while it has no significant effect on the Nusselt number.     

Do mean‐field dynamos in nonrotating turbulent shear‐flows exist?

A plane‐shear flow in a fluid with forced turbulence is considered. If the fluid is electrically‐conducting then a mean electromotive force (EMF) results even without basic rotation and the magnetic diffusivity becomes a highly anisotropic tensor. It is checked whether in this case self‐excitation of a large‐scale magnetic field is possible (so‐called W̄ × J̄ ‐dynamo) and the answer is NO. The calculations reveal the cross‐stream components of the EMF perpendicular to the mean current having the wrong signs, at least for small magnetic Prandtl numbers. After our results numerical simulations with magnetic Prandtl number of about unity have only a restricted meaning as the Prandtl number dependence of the diffusivity tensor is rather strong. If, on the other hand, the turbulence field is strati.ed in the vertical direction then a dynamo‐active α ‐effect is produced. The critical magnetic Reynolds number for such a self‐excitation in a simple shear flow is slightly above 10 like for the other – but much more complicated – flow patterns used in existing dynamo experiments with liquid sodium or gallium. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Magnetic field dragging and the vertical structure of thin accretion discs

The presence of an imposed vertical magnetic field may drastically influence the structure of thin accretion discs. If the field is sufficiently strong, the rotation law can depart from the Keplerian one. We consider the structure of a disc for a given eddy magnetic diffusivity but neglect details of the energy transport. The magnetic field is assumed to be in balance with the internal energy of the accretion flow. The thickness of the disc as well as the turbulent magnetic Prandtl number and the viscosity, α , are the key parameters of our model. The calculations show that the radial velocity can reach the sound speed for a magnetic disc if the thickness is comparable to that of a non-magnetic one. This leads to a strong amplification of the accretion rate for a given surface density. The inclination angle of the magnetic field lines can exceed the critical value 30° (required to launch cold jets) even for a relatively small magnetic Prandtl number of order unity. The toroidal magnetic fields induced at the disc surface are smaller than predicted in previous studies.     

Photometry of the fast-rotating late-type star W92 in NGC 2264

The effect of a uniform transverse magnetic field on the free-convection flow of an electrically conducting fluid past a uniformly accelerated infinite vertical porous plate is discussed. Finite-difference method has been used to obtain the solution of the governing equations when the Prandtl number is not equal to unity. The velocity profiles have been shown graphically for both cases, cooling and heating of the porous plate. The numerical values of the skin-friction are entered in table and the effects of the various parameter are discussed on the flow field.     

Hydromagnetic flow near an oscillating wall

The flow of a viscous incompressible and electrically conducting fluid produced by harmonically oscillating wall of infinite extent in presence of a transverse magnetic field is considered. Exact solutions for velocity, induced magnetic field, electrical current density and skin-friction are obtained when the magnetic Prandtl number is unity. It is shown that the velocity has a phase lag with respect to the oscillations of the wall. This phase lag is found to be significantly affected by the applied magnetic field.On study-leave from Defence Science Laboratory, Delhi, India.     

Numerical treatment of hydromagnetic thermal boundary-layer flow of an infinite porous limiting surface

The finite difference approximation technique using the explicit method is used for solving the unsteady flow of an electrically conducting viscous and incompressible fluid, subjected to a normal homogenous magnetic field. The flow is confined on one side of a non-magnetic infinite limiting surface (wall) which is initially at rest and then is suddenly accelerated in its own plane with a velocity which is a general function of time. The wall is porous and we assume that the Prandtl number of the fluid corresponds to the case of water and that the magnetic Prandtl number is equal to one. Quantitative discussion of the results is presented for the case of uniformly accelerated motion of the wall.     

Axisymmetry vs. nonaxisymmetry of a Taylor‐Couette flow with azimuthal magnetic fields

The instability of a supercritical Taylor‐Couette flow of a conducting fluid with resting outer cylinder under the influence of a uniform axial electric current is investigated for magnetic Prandtl number Pm = 1. In the linear theory the critical Reynolds number for axisymmetric perturbations is not influenced by the current‐induced axisymmetric magnetic field but all axisymmetric magnetic perturbations decay. The nonaxisymmetric perturbations with m = 1 are excited even without rotation for large enough Hartmann numbers (“Tayler instability”). For slow rotation their growth rates scale with the Alfvén frequency of the magnetic field but for fast rotation they scale with the rotation rate of the inner cylinder. In the nonlinear regime the ratio of the energy of the magnetic m = 1 modes and the toroidal background field is very low for the non‐rotating Tayler instability but it strongly grows if differential rotation is present. For super‐Alfv´enic rotation the energies in the m = 1 modes of flow and field do not depend on the molecular viscosity, they are almost in equipartition and contain only 1.5 % of the centrifugal energy of the inner cylinder. The geometry of the excited magnetic field pattern is strictly nonaxisymmetric for slow rotation but it is of the mixed‐mode type for fast rotation – contrary to the situation which has been observed at the surface of Ap stars. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)