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     

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     

Free-convection effects on MHD flow past a porous plate with step function change in suction velocity

Free convection effects on MHD flow past a semi infinite porous flat plate is studied when the time dependent suction velocity changes in step function form. The solution of the problem is obtained in closed form for the fluid with unit Prandtl number. It is observed that for both cooling and heating of the plate the suction velocity enhances the velocity field. The heat transfer is higher with increase in suction velocity.Notations B intensity of magnetic field - G Grashof number - H magnetic field parameter,H=(M+1/4) ^1/2–1/2 - M magnetic field parameter - N _u Nusselt number - P Prandtl number of the fluid - r suction parameter - T temperature of the fluid - T _w temperature of the plate - T temperature of the fluid at infinity - t time - t non-dimensional time - u velocity of the fluid parallel to the plate - u non-dimensional velocity - U velocity of the free stream - suction velocity - ₁ suction velocity att0 - ₂ suction velocity att>0 - x,y coordinate axes parallel and normal to the plate, respectively - y non-dimensional distance normal to the plate - coefficient of volume expansion - thermal diffusivity - kinematic viscosity - electric conductivity of the fluid - density of the fluid - non-dimensional temperature of the fluid - shear stress at the plate - non dimensional shear stress - erf error function - erfc complementary error function     

Unsteady free-convective flow and mass transfer in a rotating porous medium with Hall current,I

The Hall effect on the unsteady hydromagnetic free-convection resulting from the combined effects of thermal and mass diffusion of an electrical-conducting liquid through a porous medium past an infinite vertical porous plate in a rotating system have been analysed. The expressions for the mean velocity, mean skin friction, and mean rate of heat transfer on the plate are derived. The effects of magnetic parameterM, Hall parameterm, Ekman numberE, and permeability parameterK ^* on the flow field are discussed with the help of graphs and tables.Nomenclature C _p specific heat at constant pressure - C the species concentration inside the boundary layer - C _w the species concentration at porous plate - C the species concentration of the fluid at infinite - C dimensionless species concentration - D chemical molecular diffusivity - E Ekman number - Ec Eckert number - g acceleration due to gravity - Gr Grashof number - Gm modified Grashof number - H ₀ applied magnetic field - (J _x, J_y, J_z) components of current density - M magnetic parameter - m Hall parameter - P Prandtl number - q _m mean rate of heat transfer - Sc Schmidt number - t time - t dimensionless time - T temperature of fluid - T _w temperature of the plate - T temperature of fluid at infinite - T dimensionless temperature - (u, v, w) components of the velocityq - w ₀ suction velocity - (x, y, z) Cartesian coordinates - z dimensionless coordinate normal to the plate Greek symbols coefficient of volume expansion - * coefficient of thermal expansion with concentration - frequency - dimensionless frequency - k thermal conductivity - K ^* permeability parameter - dinematic viscosity - density of the fluid in the boundary layer - coefficient of viscosity - _e magnetic permeability - angular velocity - electrical conductivity of the fluid - _m mean skin friction - _mn mean skin friction in the direction ofx - _mv mean skin friction in the direction ofy     

Research on sunspot Oscillations – I. The Pulkovo CCD Spectroheliograph-Magnetograph

The CCD spectroheliograph-magnetograph is a focal-plane ancillary instrument for the Pulkovo horizontal solar telescope ACU-5. The instrument is placed at an exit port of an isothermal high-resolution diffraction-grating spectrograph. A modified Leighton optical scheme for registration of sunspot magnetic fields is used. The instrument provides FITS-format digital video maps of radial velocities, magnetic fields, and spectroheliograms in any line of the spectral region 3900–11000 Å. The time to obtain one video map of size 91×154 is equal to 10.24 s. The angular resolution of the instrument is 0.8; spectral resolution is 0.01–0.03 Å. Since 1996 the Pulkovo CCD spectroheliograph-magnetograph has been used to obtain high spatial and temporal resolution observations of oscillations of radial velocities and magnetic fields in the photospheric layers of sunspots.     

The solar minimum temperature determined by the CO (A 1Π-X 1Σ)

The synthetic Voigt profile of the following transitions (v=0,v=0), (v=0,v=1), (v=1,v=1), (v=1,v=0) have been computed for different concentrations and temperatures of CO and compaed to the measured intensities of the UV sunspot spectrum by a high resolution spectrograph. From this comparison the solar minimum temperature has been determined.     

Effect of perturbations in Coriolis and centrifugal forces on the stability of libration points in the restricted problem

The location and the stability of the libration points in the restricted problem have been studied when small perturbation and are given to the Coriolis and the centrifugal forces respectively. It is seen that the pointsL ₄ andL ₅ form nearly equilateral triangles with the primaries and the pointsL ₁,L ₂,L ₃ remain collinear. It is further observed that for the pointsL ₄ andL ₅, the range of stability increases or decreases depending upon whether the point (, ) lies in one or the other of the two parts in which the (, ) plane is divided by the line 36-19=0 and the stability of the collinear points is not influenced by the perturbations and they remain unstable.     

Spectroscopic Studies of the Solar Corona – V. Physical Properties of Coronal Structures

Spectra around the 6374 Å [Fex] and 7892 Å [Fexi] emission lines were obtained simultaneously with the 25-cm coronagraph at Norikura Observatory covering an area of 200 ×500 of the solar corona. The line width, peak intensity and line-of-sight velocity for both the lines were computed using Gaussian fits to the observed line profiles at each location (4 ×4 ) of the observed coronal region. The line-width measurements show that in steady coronal structures the FWHM of the 6374 Å emission line increases with height above the limb with an average value of 1.02 mÅ arc sec^–1. The FWHM of the 7892 Å line also increases with height but at a smaller average value of 0.55 mÅ arc sec^–1. These observations agree well with our earlier results obtained from observations of the red, green, and infrared emission lines that variation of the FWHM of the coronal emission lines with height in steady coronal structures depends on plasma temperatures they represent. The FWHM gradient is negative for high-temperature emission lines, positive for relatively low-temperature lines and smaller for emission lines in the intermediate temperature range. Such a behaviour in the variation of the FWHM of coronal emission lines with height above the limb suggests that it may not always be possible to interpret an increase in the FWHM of emission line with height as an increase in the nonthermal velocity, and hence rules out the existence of waves in steady coronal structures.     

Structure and evolution of solar radio bursts at 26.4 MHz

Two dimensional source brightness distributions at 26.4 MHz for solar bursts of spectral type II, III, IV, and V are derived from observations with a multiple-baseline, time-sharing interferometer system. It was designed explicitly to study the large angle (40 halo) component of low frequency solar bursts first reported by Weiss and Sheridan (1962). Thirty-two bursts occurring in the interval of June–August, 1975, were fit with a circular gaussian core and an elliptical gaussian halo component. Half-power halo diameters (E-W×N-S) averaged 30×28 for type III bursts and 42×27, 28×37, 30×25 for type V, II and IV bursts respectively. Typical core sizes fell in the range of 10±4 giving 31 halo to core size ratio. All burst types were found to have some large angle structure: the specific intensity was 10% compared to the core but the total power in each component was comparable. Two processes for producing the core-halo structure of type III bursts are compared: scattering and refraction of a point source and refraction from many sources over an extended region. It is concluded that the core can be explained by either model but the halo is more consistent with emission from an extended source region of 40° in longitude.     

Fine structure of the Solar Chromosphere: Arch-Shaped Mottles

We analyze a time series of high resolution observations near the solar limb, obtained in H and the Mg b1 line. We identified arch-shaped dark mottles, which are thin, faint H structures observable under very good seeing conditions, best seen in H +0.75 Å. Their mean length is about 15, their mean height about 6 and indicative lifetimes is of the order of 5 min. They show negative (away from the observer) line-of-sight velocities. A possible interpretation is that material flows from the apex towards the feet of the arches.     

Magnetic absorption lines in stellar spectra

We analyze the process of absorption which is produced under conditions of strong magnetic fields in the magnetosphere of a compact stellar source. The magnitude of the magnetic field lies in the range 10¹²-10¹³ Gauss, which are common values in modelling pulsars.Analyzing the first absorption lines (N = 0 toN 3) we arrive to the conclusions that the orientation of electron's spin does not change if it absorbs a photon. It means it maintains its orientation opposite to the external magnetic field after the absorption. For the fundamental line (N = 0 toN = 1) the dominant polarization of the photon is. For the next two transition lines (N = 0 toN = 2 andN = 0 toN = 3), the polarization is. In the case that the absorption lines belong to one of the first three transition lines, then the mean photon energy can be approached with the relation =AN B and thus we get an error of 13.6% with respect to values obtained by the theoretical expression. Also we applied our absorption transition probabilities some known pulsar spectra and we determine which transition feature corresponds in their spectra.Presented at the 2nd UN/ESA Workshop, held in Bogotá, Colombia, 9-13 November, 1992.     

Light Deflection Near the Sun's Limb: Refraction by the Solar Atmosphere

Light refraction by the Sun's atmosphere is calculated.As detected from the Earth, the refraction can deflect a light ray emitted from the Sun's limb by 13 or a starlight ray grazing the solar limb by 26, an effect 15 times larger than the gravitational deflection.     

Zonal comparison of modern selenodetic reference systems

An account is given of the results of a comparison of existing basic selenodetic systems in the equatorial zone of the Moon together with plan and altitude data, which have been provided by means of a specially worked out method, based on the use of the LAC charts of the Moon (scale 1:1000000), and which does not require the presence of common catalogued reference points. It is shown that systematic differences of the form () for different catalogues are, on the whole, relatively small and do not exceed 2. Systematic differences of the form () have a minimum in the region = ± 20° and significantly increase towards the edges of the visible disk, where they may attain a value of 6 between catalogues. Random errors in latitude have on the whole, a similar behaviour in different catalogues, being practically independent of longitude and not exceeding 3. Random errors in longitude significantly increase towards the limb regions in all the studied catalogues, and may reach values of 6 to 8. Author's estimates of the accuracy of absolute heights in selenodetic catalogues is not always sufficiently precise; in certain cases it was found that the accuracy was underestimated by a factor of one and a half. The data on relative heights in the LAC charts are expressed with a vertical step of 300 m, errors in these values are of the order of 250 m for each step in height. As a result of the comparison a set of better points has been obtained forming a catalogue which may be referred to as LPL. The selection was made on the basis of magnitude and character of both the systematic and random errors.     

Hydrogen and helium spectra in large magnetic fields

The energy levels and wave functions of hydrogen and helium atoms in the presence of large (10⁷G) magnetic fields are found by assuming that the eigenvalues and eigenvectors may be approximated by those of a truncated Hamiltonian matrix. In these atoms, fields of this size produce, in addition to the usual Paschen-Back effect, a quadratic Zeeman effect. This contributes an upward shift to the energy of all levels, which at sufficiently high fields dominates the Paschen-Back splitting.The behavior of a number of eigenvalues and wave functions as a function of magnetic field is presented. The effects of the field on the wavelengths and strengths of the components of H and the helium lines 4471, 4026 and 4120 as well as the forbidden 4025 are examined. In hydrogen the lines are split into components attributed to the now nondegenerate transitionsnlm _lnlm_l. In helium forbidden lines are excited, which may develop strengths larger than those of the allowed lines.     

On a transformation of the differential equations of the lunar theory

This work contains a transformation of Hill-Brown differential equations for the coordinates of the satellite to a type which can be integrated in a literal form using an analytical programming language. The differential equation for the parallax of the satellite is also established. Its use facilitates the computation of Hill's periodic intermediary orbit of the satellite and provides a good check for the expansion of the coordinates and frequencies. The knowledge of the expansion of the parallax facilitates the formation of differential equations for terms with a given characteristic. These differential equations are put into a form which favors the solution by means of iteration on the computer. As in the classical theory we obtain the expansions of the coordinates and of the parallax in the form of trigonometric series in four arguments and in powers of the constants of integration. We expand the differential operators into series in squares of the constants of integration. Only the terms of order zero in these expansions are employed in the integration of the differential equations. The remaining terms are responsible for producing the cross-effects between the perturbations of different order. By applying the averaging operator to the right sides of the differential equations we deduce the expansion of the frequencies in powers of squares of the constants of integration.Basic Notations f the gravitational constant - E the mass of the planet - M the mass of the satellite - t dynamical time - x, y, z planetocentric coordinates of the satellite - u x+y–1 - s x–y–1 - the planetocentric distance of the satellite - w 1/ - ₀ the variational part of - w ₀ the variational part ofw, - n the mean daily sidereal motion of the satellite - a the mean semi-major axis of the satellite defined by means of the Kepler relation:a ³ n ²=f(E+M) - a the mean semi-major axis defined as the constant factor attached to the variational solution - e the constant of the eccentricity of the satellite - the sine of one half the orbital inclination of the satellite relative to the orbit of the sun - c(n–n) the anomalistic frequency of the satellite - c ₀ the part ofc independent frome,e, and - g(n–n) the draconitic frequency of the satellite, - g ₀ the part ofg independent frome,e, and - exp (n–n)t–1 - D d/d - e the eccentricity of the solar planetocentric orbit - a the semi-major axis of the solar orbit - n the mean daily motion of the sun in its orbit around the planet - m n/(n–n) - a/a-the parallactic factor - the disturbing function     

AG Pegasi: The episode of minimum 1985

The profiles of the emission lines of H HeI 5876 and HeII 5411 in the spectrum of AG Peg obtained in the minimum of 1985 are described. The light curves in UBVRI system are presented. No indication for the presence of a magnetic field exceeding the error of observations (200 gauss) has been found.Paper presented at the IAU Colloquium No. 93 on Cataclysmic Variables. Recent Multi-Frequency Observations and Theoretical Developments, held at Dr. Remeis-Sternwarte Bamberg, F.R.G., 16–19 June, 1986.     

The Hard X-ray Imaging Spectrometer (HXIS)

The HXIS, a joint instrument of the Space Research Laboratory at Utrecht, The Netherlands, and the Department of Space Research of the University of Birmingham, U.K., images the Sun in hard X-rays: Six energy bands in energy range 3.5–30 keV, spatial resolution 8 over Ø 240 and 32 over Ø 624 field of view, and time resolution of 0.5–7 s depending on the mode of operation. By means of a flare flag it alerts all the other SMM instruments when a flare sets in and informs them about the location of the X-ray emission. The experiment should yield information about the position, extension and spectrum of the hard X-ray bursts in flares, their relation to the magnetic field structure and to the quasi-thermal soft X-rays, and about the characteristics and development of type IV electron clouds above flare regions.     

Перенос резонансного излучения И случайные ълуждания Фотонов

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Transfer of resonance radiation in infinite medium is considered as a process of random walks of photons. Close relation is shown to exist between the problems of transfer of line radiation and the stable distributions of the probability theory. This relation is used as a basis of a new method for the investigation of the asymptotic properties of the radiation field far from the sources.

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Investigation of He I 10 830 Å `Dark Points' at the Sayan Solar Observatory and the Baikal Astrophysical Observatory

A new two-bandpass birefringent filter has been produced at ISTP, Irkutsk for the investigation of the fine structure of the chromosphere. One filter passband is centered on the Hei 10830 Å line, the second one is centered on H. The FWHM of the Hei 10830 Å passband is 0.46 Å and of the H passband is 0.3 Å. A large number of filtergrams were obtained with the filter at the Sayan observatory. At the same time, spectral observations with high spatial and spectral resolution were carried out by the large solar vacuum telescope at the Baikal Observatory. We selected 29 `dark point' spectra with sizes from 2 to 13, as well as `dark points' on the filtergrams. Comparison of spectrograms and filtergrams has shown a good agreement of their size and intensity in relation with the surrounding chromosphere as well as the absence of primary line-of-sight velocities in both observation types. From spectral observations, the depth of 10830 Å is over 30% for some `dark points', and the FWHM is more than 1 Å. Hei 10830 Å line profiles in `dark points' are more deep and wide than in quiet regions. The optical depth of the chromosphere in `dark points' is estimated. Comparison with the unperturbed chromosphere showed that `dark points' in Hei 10830 Å are more optically thin than the nearby chromosphere.     

Spectro-Polarimetry of Polar Faculae

This contribution deals with the properties of small-scale magnetic elements at the polar caps of the Sun. Spectro-polarimetric observations, obtained with high spatial resolution with the Gregory Coudé Telescope at the Observatorio del Teide on Tenerife, were analysed. We find, though with limited data sets, that polar faculae differ in two aspects from faculae of the network in non-active regions near the equator (equatorial faculae): (1) Polar faculae appear to have the same magnetic polarity as the general polar magnetic field. Presumably, the latter is rooted in the small-scale faculae. The equatorial faculae show both magnetic polarities. (2) Polar faculae, with a size of 3.5 ± 1.3, are larger than equatorial faculae with 2.1 ± 0.4. Yet as for equatorial faculae, polar faculae possess kilogauss magnetic fields.