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     

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.     

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.     

Fine structure in a metric type IV burst: Multi-site spectrographic,polarimetric, and heliographic observations

The spectral fine structure of solar radio continua is thought to reveal wave-particle and wave-wave interactions in magnetic traps in the solar corona. We present observations of spectra, polarization, and spatial characteristics of combined emission/extinction features (zebra patterns) during a decimetric/metric type IV event on 5 June, 1990. Very high modulation depths are observed. The size and location of the sources during emission and extinction are determined for the first time. Two remarkable features are found: (1) The sources of emission stripes have finite size, up to nearly 2; during extinction stripes the brightness is reduced across the whole extent of the unperturbed continuum, which is slightly larger than 2. (2) During emission stripes the sources drift over distances up to several × 10⁴ km, with apparent velocities up to 10⁵ km s^–1. The observed features are briefly discussed with respect to interpretations based on wave-particle interactions and on the scattering of electromagnetic waves.     

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.     

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.     

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.     

Eclipse Observations of Compact Sources in the Outer Solar Corona

We report here on high angular resolution observations of solar noise storm sources at a frequency of 75 MHz. The data for the study were obtained at the Gauribidanur Radio Observatory (long.: 77°2612 E, lat.: 13°3612 N) about 100 km north of Bangalore, India, during the solar eclipse of 24 October 1995. Our main conclusion is that there are structures of angular size 2.5 arc min in the outer solar corona.     

Parameter values for stable low-inclination periodic motion in the restricted three-body problem with oblateness

The known intervals of possible stability, on the mgr-axis, of basicfamilies of 3D periodic orbits in the restricted three-body problem areextended into -A₁ regions for oblate larger primary, A ₁ beingthe oblateness coefficient. Eight regions, corresponding to the basicstable bifurcation orbits l1v, l1v, l2v, l3v, m1v, m1v,m2v, i1v are determined and related branching 3D periodic orbits arecomputed systematically and tested for stability. The regions for l1v,m1v and m2v survive the test emerging as the regions allowing thesimplest types of stable low inclination 3D motion. For l1v, l2v,l3v, m1v and m2v oblateness seems to have a stabilising effect,while stability of i1v survives only for a very small range of A ₁values.     

Observations of the Rosette Nebula using the Decameter Wave Radio Telescope at Gauribidanur

A map of Rosette Nebula in continuum absorption is made at 34.5 MHz using the Decameter Wave Radio Telescoe at Gauribidanur, India, with a resolution of 26×40, is presented. These observations are combined with the 2700 MHz measurements of Grahamet al. (1982) to derive the electron temperature distribution across the nebula. It is found that the temperatures in the southeastern parts of the nebula are around 5000 K and increase up to 8000 K towards the northwestern regions. It is suggested that the lower electron temperatures in the southeastern regions are due to the presence of more dust there compared to other regions in the nebula.     

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.     

Sources of the Slowly-Varying Component of Solar Microwave Emission and their Relationship with their Host Active Regions

Daily surveys of the solar disc made at 2.8 cm wavelength over the period 1–13 November 1981, complemented by magnetograms and H filtergrams, are used to examine the relationship between sources of the slowly varying component of solar radio emission and properties of their host regions. Two classes of source are noted: diffuse and compact. Sources are designated compact when smaller than 40. The diffuse sources may be explained in terms of free–free thermal emission from trapped plasma in loops overlying the active region. The great majority of compact sources can be accounted for in terms of gyroresonance from thermal electrons in the strong magnetic fields overlying sunspots. A small minority are less amenable to this explanation. They are associated with magnetic complexity and dynamism, lie close to magnetic polarity reversals, and could be non-thermal. Microwave sources are an evolutionary feature common to all but the smallest active regions.     

Observations and interpretation of the slowly varying component of solar radio emission at decameter wavelengths

We have observed the slowly varying component of solar radio emission at a frequency of 34.5 MHz with half power beam widths of 26/40 in the east-west and north-south directions, respectively. It is found that the observed brightness temperatures vary within the limits of 0.3×10⁶K to 1.5×10⁶K, and the average half power widths of the brightness distribution on the Sun is about 3R . Thermal emission from coronal regions of various electron densities and temperatures with and without the magnetic field has been computed and compared with the observed results.     

B,V surface photometry of the UV continuum galaxy NGC 838

Surface photometry of the UV continuum galaxy NGC 838 has been carried out in theB, V system using photographic plates obtained with the 74 Kottamia telescope, Egypt. Isophotes, luminosity profiles, integrated photographic magnitudes, effective diameters and other photometric parameters are derived.The photoelectrically calibrated total apparent magnitudes areB _T =13.57 with maximum diameters 1.57×1.34 (at threshold _m =27.7 mag.//) andV _T =12.91 with maximum diameters 1.54×1.32 (at threshold _m =27.7 mag./). The integrated colour index(B–V) _T =0.66 and the effective surface brightness _e (B=19.0 mag./) and _e (V=19.7 mag./. The major axis is at position angle =85°±1°.The nucleus of NGC 838 is quite blue (integrated colour(B–V)=0.41 forr ^*<0.1) compared to normal galaxies while the colour becomes redder from the nucleus outwards. The UV excess, H emission and radio continuum emission previously observed from this galaxy by other investigators may be attributed to a recent burst of star formation in the nucleus of the galaxy of duration slightly greater than 2×10⁷ yr.     

Observations of prominences at 3.5 millimeter wavelength

At 3.5 mm wavelength absorption features are observed in correspondence with H dark filaments on the disk; beyond the limb the prominences correspond to emissive regions. The absorption features are larger (2–3 arc) than the corresponding H dark filaments; the emissive regions at the limb have similar angular sizes. The emissive regions at the limb have electron temperatures of 5500±500 K; the amount of absorption observed on the disk leads to mean electron densities of about 5 × 10¹⁰ per cm³.     

Structure of magnetic fields on the quiet sun

To obtain quantitative temporal and spatial information on the network magnetic fields, we applied auto- and cross-correlation techniques to the Big Bear videomagnetogram (VMG) data. The average size of the network magnetic elements derived from the auto-correlation curve is about 5700 km. The distance between the primary and secondary peak in the auto-correlation curve is about 17000 km, which is half of the size of the supergranule as determined from the velocity map. The correlation time is about 10 to 20 hours. The diffusion constant derived from the cross-correlation curve is 150 km² s^-1. We also found that in the quiet regions the total magnetic flux in a window 3 × 4 changes very little in nearly 10 hours. That means the emergence and the disappearance of magnetic flux are in balance. The cancelling features and the emergence of ephemeral regions are the major sources for the loss and replenishment of magnetic flux on the quiet Sun.     

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.     

Almost stable regions for an area-preserving mapping

The area preserving mapping x = x + a(y – y ³), y = y – a(x – x³), for 0.3 a 2.0 has been studied to locate approximately the x-axis points bounding almost stable regions. For each value of a, these are fixed points with variational trace just greater than 2.0. Transition to chaos can occur rapidly as a increases (with n/k fixed).     

Ubiquitous chromospheric structures observed in the quiet Sun at millimeter and centimeter wavelengths

Unique long-term visibility variations are detected when the quiet Sun is observed with interferometers operating at 8 mm and 11 cm wavelength with angular resolutions of 0.5. Quasiperiodic fluctuations in fringe amplitude are observed with periods between 20 and 30 min, and with amplitude nulls which are correlated with 180° phase changes. These variations are interpreted in terms of a changing projected baseline while viewing a few sources with angular sizes of 0.5 which are distributed within the main interferometer beam with typical angular separations of 7. The observed variations cannot be due to expanding or contracting sources of the type envisaged by Bocchia and Poumeyrol (1976) when explaining similar variations observed at 8 mm wavelength. A comparison of the flux observed at 8 mm and 11 cm indicates that the individual sources are optically thick thermal radiators with a flux which decreases with increasing wavelength, but with a temperature which increases with increasing wavelength where higher, hotter levels of the chromosphere are observed. For a source whose angular size is 0.5, the observed flux values correspond to respective temperatures of 5000 K and 19 000 K at 8 mm and 11cm - suggesting that elements of the chromospheric network are being observed. A thermal origin for the individual sources is consistent with the lack of any detectable circular or linear polarization (< 10%) in the interferometer signal.     

Rayleigh-Cabannes scattering in planetary atmospheres III. The Milne problem in conservative atmospheres

The discrete ordinale method by Chandrasekhar is used to solve the conservative Milne problem in a homogeneous plane-parallel atmosphere which scatters the radiation according to the Rayleigh-Cabannes law.The approximate solution which is supposed to converge uniformly to an exact one when increasing the order of approximation is obtained explicitly. In addition to a tabulation of the Hopf vector for different factors of depolarization, the extrapolation distance, the values of c, q and the Rubenson degrees of polarization at the limb are given.