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.     

The three-dimensional breakup of a magnetic layer

Three-dimensional numerical simulations of the instability of a layer of magnetic field caused by magnetic buoyancy are carried out over a range of parameter values. The layer breaks up into a number of interlocking magnetic flux tubes that become increasingly three-dimensional, although strongly arched flux tubes are not observed. The introduction of background rotation has the principal effect of suppressing the instability. The α -effect, which measures the twist of the flux tubes induced by the rotation, is found to be positive (in the northern hemisphere) but small in magnitude.     

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.     

The magnetic field transfer in the solar convective zone

The large-scale azimuth magnetic field is pumping to the bottom of the solar convective zone due to the diamagnetic action of turbulent conductive fluids. When the field at the bottom is of about 10³ G, an equilibrium is established between diamagnetic pumping and buoyancy.If, in addition to the density gradient, an additional anisotropy exists (for instance, due to rotation), another mechanism of the magnetic field transfer appears, the efficiency of which greatly depends on the magnitude of the anistropy parameter.     

Disc structure around strongly magnetic accretors: a full disc solution with buoyancy diffusivity

A full numerical solution is found for the effect of a strongly magnetic star on its accretion disc, for the case of magnetic buoyancy diffusion. As in the previously considered case of turbulent diffusion, the disc becomes disrupted when magnetic and viscous stresses become comparable. A magnetically induced temperature elevation leads to electron scattering opacity and radiation pressure becoming significant far from the stellar surface, with consequent viscous instability and vertical disruption of the disc. This, together with the previous turbulent case, suggests that such a disruption mechanism owing to strongly magnetic accretors is generally operable.     

Model calculations of the rising motion of a prominence loop

Model calculations are presented for the rising motion of the top section of a prominence loop, which is represented by a straight flux rope immersed in a coronal medium permeated with a bipolar magnetic field. Initially the prominence is at rest, in equilibrium with the surrounding coronal medium. When the magnetic monopoles that account for the source current for the bipolar field strengthen, the upward hydromagnetic buoyancy force overcomes the downward gravitational force so that the prominence is initiated into rising motion. The illustrative examples show that prominences can move away from the solar surface by the action of the hydromagnetic buoyancy force, which is preponderant with the diamagnetic force due to the current carried by the prominence interacting with the coronal magnetic field produced by the photospheric currents, if the changes in the photospheric magnetic field are sufficiently large.     

Double maxima of 11-year solar cycles

We propose a scenario to explain the observed phenomenon of double maxima of sunspot cycles, including the generation of a magnetic field near the bottom of the solar convection zone (SCZ) and the subsequent rise of the field from the deep layers to the surface in the royal zone. Five processes are involved in the restructuring of the magnetic field: the Ω-effect, magnetic buoyancy, macroscopic turbulent diamagnetism, rotary ?ρ-effect, and meridional circulation. It is found that the restructuring of magnetism develops differently in high-latitude and equatorial domains of the SCZ. A key role in the proposed mechanism of the double maxima is played by two waves of toroidal fields from the lower base of the SCZ to the solar surface in the equatorial domain. The deep toroidal fields are excited by the Ω-effect near the tachocline at the beginning of the cycle. Then these fields are transported to the surface due to the combined effect of magnetic buoyancy, macroscopic turbulent diamagnetism, and the rotary magnetic ?ρ-flux in the equatorial domain. After a while, these magnetic fragments can be observed as bipolar sunspot groups at the middle latitudes in the royal zone. This first, upward-directed wave of toroidal fields produces the main maximum of sunspot activity. However, the underlying toroidal fields in the high-latitude polar domains are blocked at the beginning of the cycle near the SCZ bottom by two antibuoyancy effects — the downward turbulent diamagnetic transfer and the magnetic ?ρ-pumping. In approximately 1 or 2 years, a deep equatorward meridional flow transfers these fields to low-latitude parts of the equatorial domain (where there are favorable conditions for magnetic buoyancy), and the belated magnetic fields (the second wave of toroidal fields) rise to the surface. When this second batch of toroidal fields comes to the solar surface at low latitudes, it leads to the second sunspot maximum.     

Transient MHD free convection in a rotating system

The classical Rayleigh problem has been extended to the case of the hydromagnetic free-convective flow of an electrically-conducting and incompressible viscous fluid past an infinite vertical naturally permeable wall in a rotating system. The applied transverse magnetic field is fixed with the moving wall and the magnetic Reynolds number of the flow is taken small so that the induced magnetic field can be neglected in comparison to the applied magnetic field. The permeable wall starts moving from rest in the still fluid and thus arises an initial value problem whose solution has been obtained by the Laplace transform method for two important cases impulsive as well as accelerated start of the plate. Mathematical expression for skin friction components have been also obtained in a closed form. Asymptotic behaviour of the solution is analysed for both the cases, and some interesting particular cases have also been encountered. Influence of various physical parameters occurring into the problem has been discussed with the aid of graphs and tables.     

Dynamical behavior of strong magnetic fields in the solar convection zone

Magnetic buoyancy is thought to play an important role in the dynamical behavior of the Sun's magnetic field in the convection zone. Magnetic buoyancy is commonly thought to cause inescapable rapid loss of toroidal flux from much of the convection zone, thereby suppressing effective operation of a solar dynamo. This paper re-examines the detailed character of magnetic buoyancy, especially as it is influenced by the magnetic field's effect on heat transport and temperature gradients in the convection zone. It is suggested that suppression of convective heat transport across strong magnetic flux tubes can alter the temperature within the tubes and can subdue, or even reverse, the effect of magnetic buoyancy.     

Instability by magnetic buoyancy

Recent developments in the theory of instability by magnetic buoyancy are discussed in an astrophysical context and, where appropriate, extended to provide a more unified picture. Emphasis is placed on the effects of density stratification and rotation, which are usually stabilizing. In one strongly-stratified and rapidly-rotating parameter régime, however, it is possible to render a magnetic field configuration unstable by increasing the statically-stable stratification, although increasing it beyond a certain limit eventually stabilizes the system, as one would intuitively expect.We find that stratification exerts a strongly stabilizing influence in the solar radiative interior, despite the high thermal diffusivity . Rotation plays a rather minor role. We emphasize the importance of a doubly-diffusive parameter D _* involving the ratio of to , the magnetic diffusivity, and find that magnetic buoyancy instability typically requires field strengths in excess of about 50 000 G. The development time ties in with the rise-time of buoyant flux tubes in a stably-stratified environment calculated by Parker (1974, 1975). A reasonable gradient of molecular weight in the central core could only stabilize a (mainly) toroidal field strong enough to affect the neutrino flux if the magnetic diffusivity were rather smaller than is usually supposed, for otherwise such a field would be subject to either a doubly-diffusive magnetic instability, which would initially take the form of overstable buoyancy oscillations, or rapid ohmic decay.In the solar convection zone we find that the rotation of the Sun has an extremely strong and suppressing influence on magnetic buoyancy instability, and that this is only likely to occur for large field strengths of about 1000 G in the top half of the zone.     

A mean electromotive force induced by magnetic buoyancy instabilities

For a variety of reasons, based on results from magnetoconvection, self-consistent dynamo calculations and helioseismology, it seems plausible that the bulk of the solar magnetic field is located in the overshoot zone. Furthermore, it has also been suggested that the solar dynamo is operating in this region. The aim of this paper is then to show that it is possible to obtain a mean electromotive force (EMF), and hence an α -effect, in the convectively stable overshoot zone, which is driven by magnetic buoyancy instabilities.
By investigating the stability of a layer of magnetic field embedded between two non-magnetic layers of plasma we are able to show the following: first, that magnetic buoyancy instabilities indeed give rise to a mean EMF and, secondly, that the electromotive force is largest in the region where the magnetic layer is unstable, i.e. where the field strength decreases fastest with height.
Moreover, the influence of the rotation rate and the magnetic field strength on the magnetic buoyancy instability has been investigated in order to determine for which values of these parameters dynamo action might occur.     

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 solar corona as a minimum energy system?

This paper is an exploration of the possibility that the large-scale equilibrium of plasma and magnetic fields in the solar corona is a minimum energy state. Support for this conjecture is sought by considering the simplest form of that equilibrium in a dipole solar field, as suggested by the observed structure of the corona at times of minimum solar activity. Approximate, axisymmetric solutions to the MHD equations are constructed to include both a magnetically closed, hydrostatic region and a magnetically open region where plasma flows along field lines in the form of a transonic, thermally-driven wind. Sequences of such solutions are obtained for various degrees of magnetic field opening, and the total energy of each solution is computed, including contributions from both the plasma and magnetic field. It is shown that along a sequence of increasingly closed coronal magnetic field, the total energy curve is a non-monotonic function of the parameter measuring the degree of magnetic field opening, with a minimum occurring at moderate field opening.For reasonable choices of model parameters (coronal temperature, base density, base magnetic field strength, etc.), the morphology of the minimum energy solution resembles the observed quiet, solar minimum corona. The exact location energy minimum along a given sequence depends rather sensitively on some of the adopted parameter values. It is nevertheless argued that the existence of an energy minimum along the sequences of solutions should remain a robust property of more realistic coronal wind models that incorporate the basic characteristics of the equilibrium corona- the presence of both open and closed magnetic regions.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Heat and mass transfer in convective flow of an incompressible rarefied visco-elastic fluid in presence of transverse magnetic field

Analytical study is performed to examine heat and mass transfer characteristics of natural convection flow of an incompressible, rarefied visco-elastic fluid past an infinite vertical porous plate with constant suction in the presence of transverse magnetic field under combined buoyancy force effects of thermal and mass diffusion. The effects of various parameters on mean velocity and mean skin-friction are shown graphically followed by a comparative study of Newtonian and non-Newtonian (visco-elastic). rarefied states.     

Thermal and mass diffusion on MHD natural convective flow of a rarefied gas along vertical porous plate

The flow of an electrically conducting incompressible rarefied gas due to the combined buoyancy effects of thermal and mass diffusion past an infinite vertical porous plate with constant suction has been studied in the presence of uniform transverse magnetic field. The problem has been solved for velocity, temperature, and concentration fields. It has been observed that mean velocity and the mean temperature are affected by the Grashof numbersG ₁ andG ₂, the slip parameterh ₁, temperature jump coefficienth ₂, concentration jump coefficienth ₃ and magnetic field parameterM. The amplitude and the phase of skin-friction and the rate of heat transfer are affected by frequency in addition to the above parameters. They are shown graphically. The numerical values of the mean skin-friction and the mean rate of heat transfer are also tabulated.     

Dynamo-generated magnetic fields at the surface of a massive star

Spruit has shown that an astrophysical dynamo can operate in the non-convective material of a differentially rotating star as a result of a particular instability in the magnetic field (the Tayler instability). By assuming that the dynamo operates in a state of marginal instability, Spruit has obtained formulae which predict the equilibrium strengths of azimuthal and radial field components in terms of local physical quantities. Here, we apply Spruit's formulae to our previously published models of rotating massive stars in order to estimate Tayler dynamo field strengths. There are no free parameters in Spruit's formulae. In our models of 10- and  50-M_⊙  stars on the zero-age main sequence, we find internal azimuthal fields of up to 1 MG, and internal radial components of a few kG. Evolved models contain weaker fields. In order to obtain estimates of the field strength at the stellar surface, we examine the conditions under which the Tayler dynamo fields are subject to magnetic buoyancy. We find that conditions for Tayler instability overlap with those for buoyancy at intermediate to high magnetic latitudes. This suggests that fields emerge at the surface of a massive star between magnetic latitudes of about 45° and the poles. We attempt to estimate the strength of the field which emerges at the surface of a massive star. Although these estimates are very rough, we find that the surface field strengths overlap with values which have been reported recently for line-of-sight fields in several O and B stars.     

A dynamical model of prominence loops

A dynamical model of prominence loops is constructed on the basis of the theory of hydromagnetic buoyancy force. A prominence loop is regarded as a flux rope immersed in the solar atmosphere above a bipolar region of the photospheric magnetic field. The motion of a loop is partitioned into a translational motion, which accounts for the displacement of the centroidal axis of the loop, and an expansional motion, which accounts for the displacement of the periphery of the loop relative to the axis. The translational motion is driven by the hydromagnetic buoyancy force exerted by the surrounding medium of the solar atmosphere and the gravitational force exerted by the Sun. The expansional motion is driven by the pressure gradient that sustains the pressure difference between internal and external gas pressures and the self-induced Lorentz force that results from interactions among internal currents. The main constituent of the hydromagnetic buoyancy force on a prominence loop is the diamagnetic force exerted on the internal currents by the external currents that sustain the pre-existing magnetic field. By spatial transformation between magnetic and mechanical stresses, the diamagnetic force is manifested through a mechanical force acting at various mass elements of the prominence. For a prominence loop in equilibrium, the gravitational force is balanced by the hydromagnetic buoyancy force and the Lorentz force of helical magnetic field is balanced by a gradient force of gas pressure.     

The effect of finite electrical and thermal conductivities on magnetic buoyancy in a rotating gas

A horizontal magnetic field if increasing in strength downwards can cause a horizontal layer of electrically conducting fluid to become unstable, a phenomenon known as ‘magnetic buoyancy’, and sometimes thought to have relevance to magnetic A stars, and to sunspot creation. Analyses that assume infinite thermal and electrical conductivities (and zero viscosity) predict that modes of zero horizontal wave-length, in the direction perpendidular to the field, are maximally unstable but are stabilised by even small Coriolis forces. It is shown here, however, that when proper allowance is made for the finite (though large) conductivities of the fluid the layer may experience a ‘conductive instability’ that grows on the ohmic time-scale and is maximally unstable to a mode of non-zero horizontal extent.     

Unsteady magnetic boundary-layer flow of power-law non-Newtonian conducting fluid through a porous medium past an infinite porous flat plate

In this paper, the nonsteady flow of non-Newtonian power-law conducting fluid through a porous medium past an infinite porous plate is investigated. The system is stressed by a constant transverse magnetic field. The velocity outside the boundary layer depends exponentially on time. The rheological effects are shown and discussed on the shear stress in terms of rheological parameter of power-law fluid. The approximate solution in a closed form were obtained by using the Galerkin method. Also the effect of the magnetic field and permeability parameter are discussed.     

Expulsion of magnetic flux from the core and its dissipation in the crust of a neutron star

We construct a model for the magnetic-field evolution of an isolated neutron star by assuming that its core is a type II superconductor and that the field penetrates the core in the form of magnetic lines (fluxoids). We consider the fluxoid expulsion from the core and the field dissipation in a conducting crust. The magnetic-field evolution is calculated self-consistently by taking into account the inverse effect of crustal magnetic line bending on the fluxoid velocity in the core. We consider the evolution of two magnetic configurations, in which the bulk of the magnetic flux passes through the neutron-star core and crust. The buoyancy of fluxoids and the force from the neutron vortexes are mainly responsible for their expulsion from the core in the former and latter cases, respectively.