Hydromagnetic free-convection flow near a time-varying accelerated vertical plate

The effect of a uniform transverse magnetic field on the free-convection flow of an electrically conducting fluid past an exponentially accelerated infinite vertical plate is analysed for both cases, when the magnetic lines of force are fixed relative to the fluid and the plate, respectively. The Laplace transform method is used to obtain the expressions for velocity and skin-friction. The effect of a magnetic parameter is to decrease the velocity of water when the magnetic field is fixed to the fluid, while it increases the velocity field when the magnetic lines of force are fixed relative to the plate.     

Unsteady MHD flow of a viscoelastic fluid past an infinite porous plate with oscillating temperature

The unsteady flow of an electrically conducting fluid past an infinite plate with constant suction is investigated in the presence of an external magnetic field and buoyancy forces. The temperature of the plate is assumed to oscillate in time about a constant mean and the flow is considered to be free of convection. For the method of solution, we have employed a small parameter approach when this small parameter is a non-dimensional quantity which is related to the viscoelastic constant of the fluid. Analytical expressions are obtained for the temperature distribution and the velocity profile of the fluid. These analytical results clearly show that the velocity profile is strongly damped when the magnetic field is more intense. This means that the applied magnetic field causes the fluid to move slower as compared with the non-magnetic case.     

MHD free-convection flow in the stokes problem for a porous vertical plate

The effect of a uniform transverse magnetic field on the free-convection flow of an electrically-conducting fluid past an infinite, vertical, porous plate for both classes of impulsive as well as uniformly-accelerated motion of the plate is discussed. The magnetic lines of force are assumed to be fixed relative to the plate. Expressions for the velocity field and skin friction for both cases are obtained by the Laplace transform technique. The influence of the various parameters, entering into the problem, on the velocity field and skin-friction is extensively discussed with the help of graphs and tables.     

MHD free-convection flow near a vertical oscillating plate

The unsteady free-convection flow of an electrically-conducting fluid near an oscillating vertical plate of infinite extent, is studied in the presence of a uniform transverse magnetic field. Exact solutions for velocity, temperature and skin friction are obtained with the aid of the Laplace transform method, when the plate is oscillating harmonically in its own plane. The influence of various parameters, entering into the problem, is discussed for the velocity field and skin-friction.     

Hydromagnetic unsteady flow due to an unsteady plate

The unsteady flow near an infinite flat plate, which is oscillating harmonically in its own plane, is studied in the presence of a magnetic field subjected to suction or injection. The magnetic field is perpendicular to the plate and the flow of viscous incompressible and electrically conducting fluid is regarded as being initially at rest. Exact solutions for velocity and skin-friction are obtained for the magnetic field fixed to the fluid or to the plate.     

MHD free-convection and mass-transform flow through a porous medium

The effect of a uniform transverse magnetic field on the free-convection and mass-transform flow of an electrically-conducting fluid past an infinite vertical plate for uniformly accelerated motion of the plate through a porous medium is discussed. The magnetic lines of force are assumed to be fixed relative to the plate. Expression for the velocity field and skin-friction are obtained by the Laplace transform technique. The influence of the various parameters, entering into the problem, on the velocity field and skin-friction is extensively discussed.     

Note on the Helmholtz instability in stratified flows with magnetic fields

The nature of the neutral curves for the stability of a Helmholtz velocity profile in a stratified, Boussinesq fluid in the presence of a uniform magnetic field for the cases (1) an infinite fluid (2) a semi-infinite fluid with a rigid boundary is discussed.     

Oscillatory hydromagnetic flow through a porous medium in the presence of free convection and mass transfer flow

Unsteady two-dimensional hydromagnetic free convection and mass transfer flow of an electrically-conducting viscous-incompressible fluid, through a highly porous medium bounded by a vertical plane surface of constant temperature is considered. The free-stream velocity of the fluid vibrates about a mean constant value and the surface absorbs the fluid with constant velocity. Expressions for the velocity, temperature, concentration are obtained. Effects of Gr (Grashof number), Gm (modified Grashof number),K (permeability of the porous medium), (frequency parameter), andM (magnetic parameter) upon the velocity field are discussed.     

Lagrangian invariants in the equilibrium conditions of an ideal rotating fluid

It is shown that the velocity distribution and equilibrium conditions of the self-gravitating configurations from an ideal fluid are closely related with the presence of freezing-in vector fields determined by means of scalar potentials, whose total derivative is equal to zero. Ignorance of integrals of motion connected with the existence of freezing-in fields did not allow one to obtain the complete equilibrium conditions by variational method and, especially, led to the divergence in Lyapunov's and Riemann's results. This defect is eliminated in the paper and the equilibrium conditions and velocity distribution are considered by a single approach in the models of: (1) homogeneous fluid; (2) compressible fluid; (3) fluid with a magnetic field; (4) ideal fluid in the PNA of GR.     

Cosmic shear in inflationary models of Bianchi types VIII and IX

Two exact solutions of Einstein's field equations of vacuum are presented and investigated. We will regard the term vacuum fluid as the limiting case of scalar field with an almost constant potential. Considering the four velocity of this fluid we find, that in both solutions there is an anisotropic expansion of the cosmic fluid, but the fluid has vanishing vorticity.We investigate whether shear could prevent the transition into an inflationary era in these models, and the effect of shear on a scalar field is also considered. It is found that shear will speed up the rollover of the scalar field in some Bianchi type-VIII models.Possible initial conditions are discussed in light of the group structures of the models.     

Heat and mass transfer on MHD heat generating flow through a porous medium in a rotating fluid

The problem of the free-convection flow of a viscous heat generating fluid through porous media in a rotating frame of reference is considered for the case when a strong magnetic field is imposed in a direction which is perpendicular to the free-stream and makes an angle to the vertical direction. Analytical expressions for the velocity field and temperature are given, and the influences of the various parameters on the velocity field are discussed.     

Intermittency of magnetic turbulence in slow solar wind

We investigate the properties of intermittency of magnetic turbulence by using magnetic field data collected by the Helios spacecraft in the inner heliosphere. Clear scaling laws for magnetic structure functions are visible in periods where the velocity of the bulk plasma is low. Within these periods we found that intermittency of magnetic turbulence is high with respect to velocity field. A comparison with fluid flows where passive scalars are more intermittent than velocity, yields to consider the magnetic field like a “passive vector”.     

Magnetohydrodynamic flow of a non-Newtonian fluid past a porous plate

This article studies the laminar flow of an electrically conducting non-Newtonian fluid (Rivlin-Encksen type) past an infinite porous flat plate to a step function change in suction velocity in the presence of a transverse magnetic field. The Laplace transform technique has been employed to solve the basic differential equations. The solutions of the velocity profile and skin-friction are obtained and the effects of the visco-elastic parameter, the magnetic field and the time parameter on the fluid flow have been studied in several tables.     

Green's functions of the induction equation on regions with boundary. II. Spherical regions

In an earlier paper the evolution of a magnetic field was considered which permeates an electrically conducting fluid and its non-conducting surroundings. It was shown how the tensorial Green's function of the initial value problem posed by the governing equations can be constructed. The present paper gives a more detailed analysis of the case where the fluid occupies the interior of a sphere. The construction is carried out for arbitrary motions of the fluid. More special results are derived for differential rotation with angular velocity depending only on the radius, and explicit expressions of Green's functions are given for rigid body rotation.     

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.     

Unsteady magnetohydrodynamic free-convection flows in a rotating fluid

The three-dimensional free-convection flow near an infinite vertical plate moving in a rotating fluid in the presence of a transverse magnetic field is studied in the case when the plate temperature undergoes a thermal transient. An exact solution has been obtained by defining a complex velocity with the help of the Laplace-transform technique, when the plate is moving with a velocity which is an arbitrary function of time. Three special cases of physical interest are also 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.     

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.     

Equilibrium of self gravitating polytropic cylinders with a magnetic field

The equations of hydromagnetics for a self-gravitating fluid of infinite conductivity are examined in the axisymmetric case in terms of toroidal and poloidal scalars. The stationary state with non-zero poloidal velocity scalar admits and analytical solution for polytropic cylinder of infinite length with a prevalent toroidal magnetic field. The case when the poloidal velocity scalar is zero is also considered.     

Hydromagnetic free-convection laminar flow of an elasto-viscous fluid past an infinite plate

The effect of a transverse magnetic field on unsteady free-convection flow of an electrically conducting elasto-viscous fluid (Walters liquidB') past an impulsively started infinite vertical plate is discussed. The Laplace transform technique is used to obtain the expressions for velocity and shearing stress. The influence of the various parameters, entering in the problem, on the velocity field and shearing stress is extensively discussed.