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.     

Laminar hydromagnetic thermal boundary layer in fluctuating flow past a limiting surface with variable suction

An analysis of the temperature field in the case of the two-dimensional hydromagnetic flow of a viscous incompressible and electrically conducting fluid, (e.g., of a stellar atmosphere), past a porous, infinite, limiting surface in the presence of a transverse magnetic field, is considered when (i) the free stream velocity oscillates in time about a constant mean; (ii) the suction velocity normal to the limiting surface oscillates in magnitude but not in direction about a non-zero mean; and (iii) there is no heat transfer between the fluid and the wall. Approximate solution is obtained of the energy equation and are given expressions for the temperature field and for the temperature at the limiting surface, when the magnetic Prandtl numberP _m =1 and the magnetic parameterM<1. They are shown graphically followed by a discussion.Research supported by the Alexander S. Onassis Foundation.     

The effects on the flow field of retaining the Joule heating and viscous dissipation term in the energy equation for the hydromagnetic free-convective oscillatory flow past a porous limiting surface,I

With viscous dissipation and Joule heating taking into account the hydromagnetic two-dimensional oscillating free-convection flow, of a viscous, incompressible and electrically conducting fluid, past an infinite vertical porous limiting surface, is studied. For the solution of the problem it is considered that, the free-stream velocity, the plate temperature and the induced magnetic field are oscillating in the time about constant mean values. The flow is subjected to a constant suction velocity, through the porous surface, and a magnetic field of uniform strength is applied transversely to the direction of the flow. Analytical expressions for the flow field are obtained by solving the coupled non-linear system of equations which describe the flow. The influence of the various parameters entering into the problem is also extensively discussed signifying the importance of retaining the Joule heating and viscous dissipation term in the energy equation.     

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.     

Hydromagnetic free-convection effects on the oscillatory flow in the Stokes' problem past a vertical limiting surface,I

This paper presents an approximate solution to a two-dimensional free-convection flow of a viscous, incompressible fluid past an infinite vertical, porous, limiting surface under the following conditions: (i) the fluid is electrically conducting; (ii) the limiting surface is electrically non-conducting; (iii) the free-stream velocity oscillates in time about a constant mean; (iv) suction velocity normal to the limiting surface is constant; (v) the limiting surface temperature is constant; (vi) the limiting surface is moved impulsively in its own plane with velocityU ₀; (vii) there exist free-convection currents due to the difference between the limiting surface temperature and the free-stream temperature; (viii) a uniform transverse magnetic field is applied. The mean velocity, mean temperature, mean induced magnetic field and related quantities are shown graphically, followed by a discussion.     

Magnetohydrodynamic free convection effects on the stokes problem for an incompressible viscous fluid past an infinite vertical limiting surface

An analysis of the transverse magnetic field effects on the free convective flow of an incompressible, electrically conducting viscous fluid past an infinite non-conducting and non-magnetic, vertical limiting surface (e.g., of a star), has been carried out. The limiting surface is assumed to move after receiving an initial impulse. Exact solutions to equations governing the flow are derived with the help of the Laplace transform technique. The velocity, the induced magnetic field, the skin-friction and the electric current density are shown graphically. The effects of the Grashof numberG, the Prandtl numberP, and the magnetic parameterM are described during the course of discussion.     

Free convection effects on the hydromagnetic oscillatory flow in the stokes problem past an infinite porous vertical limiting surface with constant suction,II

Unsteady hydromagnetic boundary layer flow of a viscous incompressible and electrically conducting fluid past an infinite vertical non-conducting porous limiting surface in presence of a transverse magnetic field, is considered when the limiting surface is moving impulsively in its own plane and is subjected to a constant suction. The free stream oscillates in time about a constant mean value and the magnetic Reynolds number is taken to be small enough so that the induced magnetic field is negligible. As the mean steady flow has been presented in Part I, only the solutions for the transient velocity profiles, transient temperature profiles, the amplitude and the phase of the skin friction and the rate of the heat transfer are presented in this work. The influence of the various parameters entering into the problem, especially of the magnetic parameterM, is extensively discussed. A comparative study with hydrodynamic case (M=0) is also made.     

Parallel velocity shear instabilities in an inhomogeneous plasma

The stability of an inhomogeneous anisotropic plasma flowing along a straight magnetic field has been investigated. Both the flow velocity and the plasma density are spatially varying in a direction perpendicular to the magnetic field. The stability of an interface between an inhomogeneous anisotropic plasma flowing along the magnetic field and the non-conducting compressible gas of uniform density flowing parallel to the interface has also been discussed. The effect of gyroviscosity and inhomogeneity on the Kelvin-Helmholtz shear instability has been discussed in certain limiting situations.     

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.     

Free convection effects on the hydromagnetic oscillatory flow in the stokes problem past an infinite porous vertical limiting surface with constant suction-I

In this work an analysis of Stokes' problem for a two-dimensional unsteady hydromagnetic free convection flow, of an incompressible viscous electrically conducting fluid, past an infinite vertical porous limiting surface is presented, when the free stream velocity oscillates in time about a constant mean value. The flow is subjected to a constant suction, through the porous wall, and the difference between the 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. Analytical expressions for the velocity field, the temperature field and for their related quantities are obtained. The influence of the various parameters entering into the problem is extensively discussed. A comparative study with hydrodynamic case is also made wherever necessary.     

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.     

Effects of the hydromagnetic free convection on the oscillatory flow of a viscous incompressible fluid past a porous limiting surface

The unsteady two-dimensional free convection flow of a viscous incompressible and electrically conducting fluid past an infinite non-conducting and non-magnetic porous limiting surface (e.g. of a star) through which suction with uniform velocity occurs is considered when the free-stream velocity, the temperature of the limiting surface and the induced magnetic field are oscillating in the time about a constant mean value. Expressions, in closed form for the velocity, the skin-friction, the displacement thickness, the induced magnetic field and the electrical current density are obtained by the help of the two-sided Laplace transform technique, when the magnetic Prandtl numberP _m, and the Prandtl numberP are equal to one, and the magnetic parameterM is smaller to one. During the course of analysis the effects of magnetic parameterM, Grashof numberG and non-dimensional frequency are discussed.     

The velocity field in hydromagnetic oscillatory flow past an impulsively started porous limiting surface with variable suction

This paper considers the two-dimensional hydromagnetic oscillatory flow of a viscous, incompressible and electrically conducting fluid, past a porous, infinite, limiting surface subjected to variable suction and moving impulsively with a constant velocity in the presence of a transverse magnetic field. Approximate solutions are obtained for the velocity field and expressions are given for the velocity, the induced magnetic field, the skin friction, and the electric current density for the magnetic Prandtl numberP _m =1 and the magnetic parameterM<1. Variations of the above quantities are presented graphically, and the paper is concluded with a quantitative discussion.     

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.     

The Evershed motion in sunspots

The Evershed motion is postulated as a steady, laminar flow of material along a limiting field line which separates the umbral magnetic field from the penumbral. Assuming that the Evershed flow starts from the spot-base with a velocity which is adequate to carry the convective flux at that level, the velocity at the surface comes out to be of the order of 1 km/sec, in good agreement with the observed Evershed velocity.Supported in part by the National Science Foundation [GP-5391] and the Office of Naval Research [Nonr-220 (47)].     

Hydromagnetic free convection and mass transfer flow of non-Newtonian fluid through a porous medium bounded by an infinite vertical limiting surface with constant suction

An analysis of a two-dimensional steady-free convection and mass transfer flow of an incompressible, viscous, and electrically conductive non-Newtonian fluid through a porous medium bounded by a vertical infinite limiting surface (plane wall) has been presented in the presence of a transverse magnetic field. Approximate solutions to the coupled nonlinear equations governing the flow are derived and expression for the velocity, temperature, concentration, the rate of heat transfer, and the skin-friction are derived. Effects of Gr (Grashof number), Gm (modified Grashof number),M ^* (non-Newtonian parameter),N (magnetic parameter), and permeabilityK of the porous medium on the velocity, the skin-friction and the rate of heat transfer are discussed when the surface is subjected to a constant suction velocity.     

Turbulent dynamo action in a shear flow

We consider the mean electromotive force and a dynamo-generated magnetic field, taking into account the stretching of turbulent magnetic field lines by a shear flow. Calculations are performed by making use of the second-order correlation approximation. In the presence of shear, the mirror symmetry of turbulence can be broken; thus turbulent motions become suitable for the generation of a large-scale magnetic field. Regardless of the shear law, turbulence can lead to a rapid amplification of the mean magnetic field. The growth rate of the mean magnetic field depends on the length-scale: it is faster for the fields with smaller length-scale. The mechanism considered is qualitatively different from the alpha dynamo, and can generate only a magnetic field that is inhomogeneous in the direction of flow. In contrast to the alpha dynamo, this mechanism also allows the generation of two-dimensional fields. The suggested mechanism may play an important role in the generation of magnetic fields in accretion discs, galaxies and jets.     

Dynamic equilibrium plasma configurations and physics of the magnetosphere

The impossibility is demonstrated of the limiting transition to a fluid at rest within an area, limited by a specific tangential discontinuity of the 1st, 2nd, or 3rd kind and described by the equations of ideal magnetic hydrodynamics with isotropic or anisotropic pressure. Within the framework of the concept of dynamic equilibrium plasma configuration, evaluations are obtained for the thicknesses of the layer of return flow, electrical field of convection in the magnetosphere and the jump of magnetic field at the magnetopause.     

Calculating the plasma deformation tensor and kinetic vorticity from magnetic field time series: Applications to the solar wind

It is shown that the magnetic induction equation reduces to an autoregressive model equation. Assuming weakly ergodic field variations in steady mean plasma flow, this model permits the estimation of the mean flow deformation tensor, velocity divergence and kinetic vorticity from magnetic field time series. Applications, made to hourly-averaged, in-ecliptic interplanetary magnetic field (IMF) measurements from Ulysses spacecraft, showed that the direction of maximum deformation rate was, for most of the time, aligned to the mean field, while the vorticity tended to become perpendicular to the mean radial direction at large heliodistances.     

Active region magnetic fields

The tilt angles of sunspot groups are defined, using the Mount Wilson data set. It is shown that groups with tilt angles greater than or less than the average value (&amp;#x2248; 5 deg) show different latitude dependences. This effect is also seen in synoptic magnetic field data defining plages. The fraction of the total sunspot group area that is found in the leading spots is discussed as a parameter that can be useful in studying the dynamics of sunspot groups. This parameter is larger for low tilt angles, and small for extreme tilt angles in either direction. The daily variations of sunspot group tilt angles are discussed. The result that sunspot tilt angles tend to rotate toward the average value is reviewed. It is suggested that at some depth, perhaps 50 Mm, there is a flow relative to the surface that results from a rotation rate faster than the surface rate by about 60 m/sec and a meridional drift that is slower than the surface rate by about 5 m/sec. This results in a slanted relative flow at that depth that is in the direction of the average tilt angle and may be responsible for the tendency for sunspot groups (and plages) to rotate their magnetic axes in the direction of the average tilt angle.