Effects of mass transfer on the unsteady free convection flow past an accelerated vertical porous plate with variable suction

An exact analysis of the effects of mass transfer on the flow of a viscous incompressible fluid past an uniformly accelerated vertical porous and non-porous plate has been presented on taking into account the free convection currents. The results are discussed with the effects of the Grashof number Gr, the modified Grashof number Sc, the Schmidt number Sc, and the suction parametera for Pr (the Prandtl number)=0.71 representating air at 20°C.Nomenclature a suction parameter - C species concentration - C species concentration at the free stream - g acceleration due gravity - Gc modified Grashof number (vg^*(C –C )/U ₀ ³ ) - Pr Prandtl number (C _p/K) - T temperature of the fluid near the plate - T dimensionless temperature near the plate ((T-T )/(T -T )) - U(t) dimensionless velocity of the plate (U/U ₀) - v normal velocity component - v ₀ suction/injection velocity - x, y coordinate along and normal to the plate - v kinematic viscosity (/gr) - C _p specific heat at constant pressure - C _w species concentration at the plate - C non-dimensional species concentration ((C-C )/(C _w -C )) - Gr Grashof number (g(T _w -T )/U ₀ ³ ) - D chemical molecular diffusivity - K thermal conductivity - Sc Schmidt number (/D) - T _w temperature of the plate - T free stream temperature - t time variable - t dimensionless time (tU ₀ ² /) - U ₀ reference velocity - u velocity of the fluid near the plate - u non-dimensional velocity (u/U ₀) - v dimensionless velocity (v/U ₀) - v ₀ non-dimensionalv ₀ (v ₀ /U₀)=–at^–1/2 - y dimensionless ordinate (yU ₀/) - density of the fluid - coefficient of viscosity     

The role of loop footpoints rotation in single loop flares

We consider that single loop flares can be caused by the rotation of loop footpoints. Choosing a typical geometry for this case we find from MHD equations self-consistent expressions and a set equations governing behaviour of all physical quantities. Numerical simulations have revealed that under the determined conditions for the initial azimuthal velocity and current the pinch instability takes place. The most important parameters of the problem are the plasma and the ratio of the initial values of longitudinal and poloidal components of the magnetic field-B ₁. Thus, calculations show that the critical pinch time increases with the increase ofB ₁ and decreases with the increase of plasma . So the most effective flares are probable for the most high loops with strong currents. ForB ₁=10 and =0.01 the critical pinch time is 2.5 s. The critical twist angle for magnetic field depends on the initial one. For low intial twist which corresponds to bigB ₁ the critical one is more less. For exampleB ₁=30 gives 1.8 (when ratio of loop length and radius is 10). Geometrical analysis shows that the present model can explain (for high photospheric rotation) single loop flares taking place on different parts of the loop as on the top of it as closer to one of the footpoints. It depends on the relative rotation momentum of loop footpoints. Subject headings: MHD-Sun:flares.     

Wall temperature oscillation on convection flow in a rotating fluid with hall and ion-slip currents

An analysis of Hall and ion-slip current effects on the MHD free-convection flow of a partiallyionised gas past an infinite vertical porous plate in a rotating frame of reference is carried out. A strong magnetic field is applied perpendicular to the plate and the plate temperature oscillates in time about a constant non-zero mean. The problem has been solved for the velocity and temperature fields and the effects of _e (the Hall parameter), _i (the ion-slip parameter),E _r (rotation parameter), and have been discussed and shown graphically.     

The equivalent width of the Hβ emission line and the evolution of the Hii regions

The synthetic equivalent width (W _H) of the line H in emission is obtained for Hii regions opaque to the Lyman photon flux, with embedded OB associations with different initial chemical compositions and initial mass functions. The variation ofW _H as a function of the evolution of the ionizing stars is analysed. The observations ofW _H for M33, M101, and M51 by Searle (1971) are discussed.     

Hall effects on natural convective flow in slip flow regime

Hall effects on the flow of electrically conducting rarefied gas due to combined buoyant effects of thermal and mass diffusion past an infinite porous plate with constant suction in the presence of strong transverse magnetic field have been investigated. The equations governing the flow poblem have been solved for primary, secondary velocities and temperature. The effects of Hall current, magnetic field and the effect of rarefication have been discussed graphically followed by a discussion.Nomenclature x,y coordinate system - u velocity inx direction - v ₀ suction velocity - w velocity inz direction - E Eckert number - G, G^* Grashof numbers - h ₁ velocity slip coefficient - h ₂ temperature jump coefficient - h ₃ concentration jump coefficient - M, m magnetic field parameter, Hall parameter - Pr Prandtl number - Sc Schmidt number - T, T _w, T temperature in flow regime, plate temperature, temperature outside the boundary layer very away from the plate - C, C _w, C concentration of the gas in flow, concentration at the plate, concentration far away from the plate - thermal conductivity - D coefficient of chemical molecular diffusion - coefficient of kinematic viscosity - coefficient of viscosity - electrical conductivity - C _p specific heat of gas at constant pressure density     

Kelvin-Helmholtz instability of composite plasma in an oblique magnetic field with resistivity

Analytic structure of high-density steady isothermal spheres is discussed using the TOV equation of hydrostatic equilibrium which satisfies an equation of state of the kind:P = K _g , = _g c ².Approximate analytical solutions to the Tolman-Oppenheimer-Volkoff (TOV) equations of hydrostatic equilibrium in (, ), (,U) and (u, v) phase planes in concise and simple form useful for short computer programmes or on small calculator, have been given. In Figures 1, 2, and 3, respectively, we display the qualitative behaviours of the ratio of gas density _g to the central density _gc , _g / _gc ; pressureP to the _gc ,P/ _gc ; and the metric componente ^–, for three representative general relativistic (GR) isothermal configurations =0.1, 0.2, and 0.3. Figure 4 shows the solution curve (, ) for =0.1, 0.2, and 0.3 (=0 represents the classical (Newtonian) curve). Numerical values of physical quantitiesv (=4r ² P ^*(r)), in steps ofu (=M(r)/r)=0.03, and the mass functionU, in steps of =0.2 (dimensionless radial distance), are given, respectively, in Tables I and II. Other interesting features of the configurations, such as ratio of gravitational radius 2GM/c ² to the coordinate radiusR, mass distributionM(r)/M, pressure (or density) distributionP/P _c , binding energy (B.E.), etc., have also been incorporated in the text. It has further been shown that velocity of sound inside the configurations is always less than the velocity of light.Part of the work done at Azerbaijan State University, Baku, U.S.S.R., and Mosul University, Mosul, Iraq, 1985-1986     

Finite Larmor radius and Hall effects on thermosolutal instability of a plasma

The thermosolutal instability of a plasma with finite Larmor radius and Hall effects is studied. When the instability sets in as stationary convection, finite Larmor radius effects are always stabilizing forx(=k ² d ²/² greater than two and forx less than two, they have a stabilizing or destabilizing influence depending on the Larmor radius parameterN in the presence of Hall currents. On the other hand the Hall currents have both stabilizing and destabilizing effects on the thermosolutal instability forx less than two and forx greater than two depending on the Hall parameterM. The stable solute gradient is found to have a stabilizing effect on stationary convection. The case of overstability is also considered wherein the sufficient conditions for the non-existence of overstability are derived.     

A strong limitation on the rapidity of flux-pile-up reconnection

The reconnection rate which can be achieved in the steady-state flux-pile-up regime is severely limited by the gas pressure of the plasma. Using the family of solutions obtained previously by Priest and Forbes, we show that the Alfvén Mach number of the plasma flowing towards the reconnection site cannot exceed _e/(8 ln R _me), where _e and R _me are the plasma and magnetic Reynolds numbers at large distance. This limit corresponds to a very weak flux-pile-up, and it is a factor of _e slower than the maximum Petschek rate. Thus the maximum flux-pile-up reconnection rate in the corona is at least two orders of magnitude smaller than the rate implied by flare observations.     

Effect of cavitation on spherical blast waves

For spherical blast waves propagating through a self-gravitating gas with an energy inputE =E ₀ t , whereE is the energy released up to timet,E ₀ is a functional constant, and is a constant, kinetic, internal heat, and gravitational potential energies have been computed. Taking the parameterA ², which characterises the gravitational field, equal to 2, variations of the percentages of these energies for =0, 1/2, 4/3, and 3 with shock strength have been presented. For =3, the effect of cavitation on the percentages of kinetic energy and internal heat energies has been explored.     

Global photometric observations and physical properties ofHii regions in the small magellanic cloud

Integrated photoelectric measurements of the equivalent widthW _H, the [Oiii]/H ratio and the H emission line flux were obtained for 30Hii regions in the SMC. Physical properties of theHii regions and their ionizing stellar associations were derived. Some aspects of the recent star formation in the SMC and the evolution ofHii regions are discussed.     

Convective instability of thin flux tubes

The stability of magnetic flux tubes embedded vertically in a convection zone is investigated. For thin tubes, the dominant instability is of the convective type, i.e. it is driven by buoyancy forces associated with displacements along the tube. The stability is determined by = 8P/B ²; if _c the tube is convectively stable, otherwise it is unstable, where the critical value _c depends on the stratification of the convection zone. For a solar convection zone model, _c = 1.83, corresponding to a magnetic field strength of 1350 G at the surface of the Sun. It is concluded that the flux tubes making up the small scale field of the Sun are probably hydrodynamically stable.In tubes with > _c, the instability is expected to transform the tube either into a state of vanishing surface field strength (in the case of an upward flow), or one with a field strength higher than the original value (if the instability sets in as a downward flow). Following Parker, we suggest that this effect is related to the concentrated nature of the observed solar fields.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Effects of Hall current on hydromagnetic free-convective flow through a porous medium

An analysis of the effects of Hall current on hydromagnetic free-convective flow through a porous medium bounded by a vertical plate is theoretically investigated 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. The influence of Hall currents on the flow is studied for various values of .Nomenclature c _p specific heat at constant pressure - e electrical charge - E Eckert number - E electrical field intensity - g acceleration due to gravity - G Grashof number - H ₀ applied magnetic field - H magnetic field intensity - (j _x , j _y , j _z ) components of current densityJ - J current density - K permeability of porous medium - M magnetic parameter - m Hall parameter - n _e electron number density - P Prandtl number - q velocity vector - (T, T _w , T ) temperature - t time - (u, v, w) components of the velocity vectorq - U ₀ uniform velocity - v ₀ suction velocity - (x, y, z) Cartesian coordinates Greek Symbols angle - coefficient of volume expansion - _e cyclotron frequency - frequency - dimensionless temperature - thermal conductivity - coefficient of viscosity - magnetic permeability - kinematic viscosity - mass density of fluid - _e charge density - electrical conductivity - _e electron collision time     

Hydromagnetic Ekman layer on free convection past an infinite porous flat plate

Free convection in a conducting liquid past an infinite porous vertical flat plate in a rotating frame of reference when the Hall current is present is considered. Exact solutions for the velocity and temperature fields have been derived. The effects ofM (Hartmann number),m (Hall parameter), andE (Ekman number) on the velocity field are discussed.Nomenclature C _p specific heat at constant pressure - g acceleration due to gravity - E Ekman number - G Grashof number - H ₀ applied magnetic field - j _x ,j _y ,j _z components of the current densityJ - k thermal conductivity - M Hartmann number - m Hall parameter - P Prandtl number - Q heat flux per unit area - T temperature of the fluid near the plate - T _w temperature of the plate - T temperature of the fluid in the free-stream - u, v, w components of the velocity fieldq - U uniform free-stream velocity - w ₀ suction velocity - x, y, z Cartesian coordinates - z dimensionless coordinate normal to the plate Greek symbols coefficient of volume expansion - _e cyclotron frequency - _e electron collision time - _u skin friction in the direction ofu - _v skin friction in the direction ofv - dimensionless temperature - density of the fluid - kinematic viscosity - _e magnetic permeability - electrical conductivity of the fluid - angular velocity     

Čerenkov radiation in anisotropic plasmas

Following our series of works on anisotropic radiation, we analyze the erenkov condition in magnetized plasmas in this paper. We have discovered that the usual erenkov condition cos =1/n isnot satisfied at a far field point in anisotropic media, implying that when a charge is moving in a magnetized plasma, a linear shock wave front does not form. Thus we can calculate the power received at a far field per unit time in such a medium — this quantity could not be evaluated according to previous theory. Numerical examples are presented to show various relevant characteristics of erenkov radiation in model plasmas.     

Ultraviolet spectra of the Cygnus loop-depletion of the heavy elements

A comparison between the observed UV spectra and detailed consistent calculations of the Cygnus Loop is presented. The results demonstrate that the spectra can be explained by supposing that the Cygnus Loop (C.L.) moves into a fully ionized gas. The [O III]/H ratio is shown to be an indicator to the fraction of He⁺⁺ in the gas entering the shock.Further results are:(a) Observed shocks of higher velocity propagation move into regions of lower density; (b) the optical and UV spectra are emitted by very close and almost overlapping shocks (c) fast shocks (v240 km s^–1) propagation in the intercloud medium produce the X-ray emission, however, they can also produce faint H on impinging interstellar clouds.We find that carbon (C_I, C_II, C_III, and C_IV) depletion relative to other heavy elements is not more than a factor 3; whereas, we confirm that all heavy elements, relative to their solar abundance, are depleted by a factor 10. Heavy elemental depletion is likely to result formation of grains, sputtering and molecules in ISM.     

Formation of coronal MHD shock waves – II. The Pressure Pulse Mechanism

The ignition of coronal shock waves by flares is investigated. It is assumed that an explosive expansion of the source region caused by impulsive heating generates a fast-mode MHD blast wave which subsequently transforms into a shock wave. The solutions of 1-D MHD equations for the flaring region and for the external region are matched at their boundary. The obtained results show under what conditions flares can ignite shock waves that excite the metric type II bursts. The heat input rate per unit mass has to be sufficiently high and the preflare value of the plasma parameter in the flaring region has to be larger than ₀ ^crit. The critical values depend on the flare dimensions and impulsiveness. Larger and more impulsive flares are more effective in generating type II bursts. Shock waves of a higher Mach number require a higher preflare value of and a more powerful heating per unit mass. The results demonstrate why only a small fraction of flares is associated with type II bursts and why the association rate increases with the flare importance.     

Dynamics of the physical state during two-current-loop collisions

A model of two-current-loop collisions is presented to explain the impulsive nature of solar flares. From MHD equations considering the gravity and resistivity effects we find self-consistent expressions and a set of equations governing the behavior of all physical quantities just after magnetic reconnection has taken place. Numerical simulations have revealed that the most important parameters of the problem are the plasma and the ratio of initial values of pressure gradient in the longitudinal and radial directions. Thus, the low plasma case during aY-type interaction (initial longitudinal pressure gradient is comparable with initial radial pressure gradient) shows a rapid pinch and simultaneous enhancement of all physical quantities, including the electric field components, which are important for high-energy particle acceleration. However, an increase of the plasma causes a weakening of the pinch effect and a decrease of extreme values of all physical quantities. On the other hand, for anX-type collision (initial longitudinal pressure gradient is much greater than initial radial pressure gradient), which is able to provide a jet, the increase of the plasma causes a high velocity jet. As for aI-type collision (initial longitudinal pressure gradient is much less than initial radial pressure gradient) it shows neither jet production nor very strong enhancement of physical quantities. We also consider direct and oblique collisions, taking into account both cases of partial and complete reconnection.     

Comparison of large-scale structures and velocities in the local universe

Comparison of the large-scale density and velocity fields in the local universe shows detailed agreement, strengthening the standard paradigm of the gravitational origin of these structures. Quantitative analysis can determine the cosmological density parameter, , and biasing factor,b; there is virtually no sensitivity in any local analyses to the cosmological constant,. Comparison of the dipole anisotropy of the cosmic microwave background with the acceleration due to theIRAS galaxies puts the linear growth factor in the range ^0.6 /b = 0.6 _–0.3 ^+0.7 (95% confidence). A direct comparison of the density and velocity fields of nearby galaxies gives = 1.3 _–0.6 ^+0.7 , and from nonlinear analysis the weaker limit > 0.45 forb > 0.5 (again 95% confidence). A tighter limit, > 0.3 (4–6), is obtained by a reconstruction of the probability distribution function of the initial fluctuations from which the structures observed today arose. The last two methods depend critically on the smooth velocity field determined from the observed velocities of nearby galaxies by thePOTENT method. A new analysis of these velocities, with more than three times the data used to obtain the above quoted results, is now underway and promises to tighten the uncertainties considerably, as well as reduce systematic bias.     

Similarities between chromospheric and photospheric quiet-Sun magnetograms

Simultaneous observations of chromospheric (H) and photospheric (Fei 5324.19 Å) magnetograms in quiet solar regions enable us to study the spatial configuration of the magnetic field in the solar atmosphere. With the typical spatial resolution of the Huairou magnetograph, the photospheric and chromospheric magnetic structures of the quiet Sun maintain a very similar pattern. Moreover, the vertical magnetic flux is almost the same from the photosphere to the chromosphere. As an intermediate step, we analyze the formation of the working lines used by the Huairou video magnetograph of the Beijing Astronomical Observatory. The Stokes V contribution function of H and Fei 5324.19 Å are calculated. It is found that our H magnetograms provide the distribution of the chromospheric magnetic field at a height some 1000–1500 km above the photosphere.     

Rediscussion of balmer decrement of broad-line radio-galaxies

On the basis of the erenkov line emission theory in the optically thick case, a new interpretation of intensity ratios H/H and H/H in broad-line radio-galaxies (BLRGs) is reported. Calculation shows that if the theoretical ratio H/H is just taken to be the mean observed value 0.21, equivalently, the parameterX(H)=3.0, then the expected ratio H/H=6.70 is almost the same as the observations. By comparing these values with the previous investigations of QSOs (X(H)=20.9), we conclude that the number density of neutral hydrogen gas in BLRGs is almost one order-of-magnitude smaller than that in the QSOs.Preliminary verification of the erenkov line emission has been obtained by Xuet al. (1981) in the laboratory.