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1.
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  相似文献   

2.
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  相似文献   

3.
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, Jy, Jz) 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  相似文献   

4.
Many trajectories of the third body are integrated numerically in a modified elliptical restricted three body problem (ERTBP), in which the eccentricity, e, of the orbit of the second primary varies sinusoidally with time. It is found that, in the case of the 2:1 resonance, the introduction of the time variability of e modifies significantly the behaviour of the trajectories of the third body. In particular their osculating eccentricity e, present the following two notable features: (a) In all cases it shows a definite chaotic variation, which appears at significantly shorter time-scales than the one found by Wisdom in the e = constant case. (b) In many cases it shows a significant increase, up and beyond the (critical) value e crit = 0.52. As a result the third body approaches the first primary at distances smaller than 0.29 (where by we denote the semi-major axis of the trajectory of the second primary around the first), which in the actual Sun-Jupiter-asteroid problem corresponds to the semi-major axis of Mars. Our result might be of interest in the context of explaining the Kirkwood gaps at the resonances where the osculating eccentricity of asteroid trajectories calculated in the classical (e = constant) ERTBP does not reach Mars crosser values.  相似文献   

5.
In the present paper, the effects of free convection currents and the viscous dissipation on the unsteady flow of an electrically conducting and viscous incompressible fluid around an uniformly accelerated vertical porous plate subjected to a suction or injection velocity inversely proportional to the square root of time, in presence of a transverse magnetic field, have been investigated. Analytical solutions for the velocity and the temperature distributions, the skin-friction and the rate of heat transfer are obtained for small magnetic parameterM. During the course of discussion the effects of the Grashof number Gr, the Eckert number Ec, the suction/injection parametera have been considered for unit value of the Prandtl number Pr.Nomenclature a suction/injection parameter - C p specific heat at constant pressure - B 0 magnetic induction - g acceleration due to gravity - Gr Grashof number (g(T w –T )/U 0 3 ) - K thermal conductivity - M magnetic field parameter (B 0 2 /U 0 2 ) - Pr Prandtl number (C p/K) - T temperature of the fluid near the plate - T w temperature of the plate - T temperature of the fluid at infinity - t time - t dimensionless time (tU 0 2 /) - u velocity of the fluid - u non-dimensional velocity (u/U 0) - U velocity of the plate - U dimensionless velocity of the plate (U/U 0) - U 0 reference velocity - v 0 suction velocity - v 0 non-dimensional suction velocity (v 0/U 0)=at –1/2 - Ec Eckert number ((U 0)2/3/C p(T w –T )) - T dimensionless temperature of the fluid near the plate ((T–T )/(T w –T )) - x, y coordinates along and normal to the plate - x, y dimensionless coordinates (y=yU 0/) - kinematic viscosity - coefficient of volume expansion - electric conductivity of the fluid - y/2t 1/2 - density of the fluid - skin-friction - dimensionless skin-friction - q rate of heat transfer - q non-dimensional rate of heat transfer - coefficient of viscosity - e magnetic permeability On leave of absence from Department of Mathematics, University of Dhaka, Bangladesh  相似文献   

6.
An analysis of the two-dimensional flow of water at 4°C past an infinite porous plate is presented, when the plate is subjected to a normal suction velocity and the heat flux at the plate is constant. Approximate solutions are derived for the velocity and temperature fields and the skin-friction. The effects ofG (Grashof number) andE (Eckert number) on the velocity and temperature fields are discussed.Nomenclature u, v velocity components of the fluid inx, y direction - g acceleration due to gravity - coefficient of thermal expansion of water at 4°C - v kinematic viscosity - density - T temperature inside thermal boundary layer - T free-stream temperature - k thermal conductivity - C p specific heat at constant pressure  相似文献   

7.
8.
9.
Unsteady two-dimensional hydromagnetic flow of an electrically conducting viscous incompressible fluid past a semi-infinite porous flat plate with step function change in suction velocity is studied allowing a first order velocity slip at the boundary condition. The solution of the problem is obtained in closed form and the results are discussed with the aid of graphs for various parameters entering in the problem.Notations B intensity of magnetic field - H magnetic field parameter,H=(M+1/4)1/2–1/2 - h rarefaction parameter - L 1 slip coefficient; ;I, mean free path of gas molecules;f, Maxwell's reflection coefficient - M magnetic field parameter - r suction parameter - t time - t dimensionless time - u velocity of the fluid - u dimensionless velocity of the fluid - U velocity of the fluid at infinity - v suction velocity - v 1 suction velocity att<=0 - v 2 suction velocity att>0 - x distance parallel to the plate - y distance normal to the plate - y nondimensional distance normal to the plate - v kinematic viscosity - electric conductivity of the fluid - density of the fluid - shear stress at the wall - nondimensional shear stress at the wall - erf error function - erfc complementary error function  相似文献   

10.
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.  相似文献   

11.
. . ,e, , . . e, . , .
Stability of the librational triangular points of the three-dimensional elliptic restricted three-body problem is studied. The problem is solved in the non-linear statement at the small values of eccentricity.For all values ofe, , besides ones which correspond to the resonances of the third and the fourth order the librational points are stable taking into account the terms up to the fourth order in the normal form of the Hamiltonian function of the perturbed motion.At sufficiently smalle and the non-stability in sense of Liapunov has been proved. The approximate equations of the boundary of the stability area in the planee, has been obtained. The cause of the non-stability is an equality of the rotational period of the principal attracting masses in the elliptic orbit and the period of oscillation of indefinitely small mass along the direction perpendicular to the plane of their motion.
  相似文献   

12.
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 lnlml. In helium forbidden lines are excited, which may develop strengths larger than those of the allowed lines.  相似文献   

13.
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.  相似文献   

14.
The aim of the present paper will be to present a new approach to the light changes of eclipsing binary systems. The light changes have been expanded into the Fourier-Bessel and Dini series. The coefficients of these expansions which are the Hankel transforms of the order of the loss of light (1–l) have been expressed in terms of the eclipse elements. These discrete Hankel transformsH (j m ) andH ( m ) valid for only the positive real zerosj m and m of the functionsJ and [xJ(x)+J (x)] have been generalized for any positive value of andy. Thus, these general expressions for the Hankel transforms of the light curves which are valid for all types of eclipses, for any arbitrary degree of the adopted limb-darkening law and, moreover, for any positive value of the free parameters andy, may be used for the solution of the elements of eclipsing binary systems.  相似文献   

15.
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.  相似文献   

16.
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  相似文献   

17.
Two-dimensional unsteady free convection and mass transfer, flow of an incompressible viscous dissipative and electrically conducting fluid, past an infinite, vertical porous plate, is considered, when the flow, is subjected in the action of uniform transverse magnetic field. The magnetic Reynolds number is taken to be small enough so that the induced magnetic field is negligible. The solution of the problem is obtained in the form of power series of Eckert numberE, which is very small for incompressible fluids. Analytical expressions for the velocity field and temperature field are given, as well as for the skin friction and the rate of heat transfer for the case of the mean steady flow and for the unsteady one. The influence of the magnetic parameter,M, modified Grashof numberG c , Schmidt numberS c and frequency , on the flow field, is discussed with the help of graphs, when the plate is being cooled, by the free convection currents (G r ,E>0), or heated (G r ,E<0). A comparative study with hydrodynamic case (M=0) and the hydromagnetic one (M0) is also made whenever necessary.List of symbols B0 applied magnetic field - |B| amplitude of the skin friction - C concentration inside the boundary layer - C concentration in the free stream - C w concentration at the porous plate - C p specific heat at constant pressure - D diffusion coefficient - E Eckert number - g x acceleration due to gravity - G c modified Grashof number - G r Grashof number - M magnetic parameter - N u Nusselt number - P Prandtl number - |Q| amplitude of the rate of heat transfer - S c Schmidt number - T temperature of the fluid - T w temperature of the plate - T temperature of the fluid in the free stream - T r ,T i fluctuating parts of the temperature profile - u, v velocity components in thex, y directions - u dimensionless velocity in thex direction - u 0 mean steady velocity - u 1 unsteady part of the velocity - u r ,u i fluctuating parts of the velocity profile - U dimensionless free stream volocity - U 0 mean free stream velocity - v 0 suction velocity - x, y co-rodinate system Greek Symbols phase angle of the skin-friction - coefficient of volume expansion - * coefficient of expansion with concentration - phase angle of the rate of heat transfer - dimensionless co-ordinate normal to the plate - dimensionless temperature - 0 mean steady temperature - 1 unsteady part of temperature - k thermal conductivity - v kinematic viscocity - density of fluid in the boundary layer - density of fluid in the free stream - electrical conductivity of the fluid - skin friction - 0 mean skin friction - frequency - dimensionless frequency  相似文献   

18.
The electro-optic deflector as an analyzer of circular polarization in the photoelectric magnetograph is described. The electro-optic deflector consists of an electro-optic crystal and a polarizing beamsplitter. The plane bifurcation of this beamsplitter coincides with the spectrograph dispersion direction. The beamsplitter bifurcates a spectral line in two components. The distance between them is 0. The photometer slit is situated between these components. Both components of Zeeman splitting fall on the photometer slit but the distance between them varies from 0 + 2 H to 0 – 2 H (where H is the Zeeman splitting) with the electric voltage frequency applied to the electro-optic crystal. The intensity variations at the photometer slit are proportional to 4 H .  相似文献   

19.
In the quasi-linear theory of pitch angle scattering the power spectrum of magnetic field fluctuations is related to the shape of the pitch angle diffusion coefficient D(), the absolute value of the mean free path , and the rigidity dependence of the mean free path (R). We discuss these relations in detail during the solar particle event of 11 April, 1978 which was observed on HELIOS-2 at a distance of 0.49 AU from the Sun. Magnetic field measurements obtained during the time of the event are used as a basis for the layer model in which the method of particle trajectories in an actually measured field is used to simulate pitch angle diffusion. The values of D() and based on the trajectory simulation for 100 MeV protons (field approach) are compared with results obtained from solar proton data (particle approach) and with predictions from quasi-linear theory based on the additional assumption of the slab model for magnetic field fluctuations (QLT approach). The time of the event is characterized by a high level of field fluctuations, the observed mean free path of about 0.03 AU for 100 MeV protons is smaller than the average value near 1 AU. Results from the field and particle approaches agree surprisingly well. The remaining difference in the mean free path of about a factor of 2 could be due to tangential discontinuities which are measured by the magnetometer, but not seen by the real particles traveling along the average field. The results from the field and QLT approaches based on the same set of magnetic field measurements differ by about a factor of 4. One of the reasons for this discrepancy is that the conditions for resonance scattering are only marginally valid. In addition, the wave vectors representing Alfvén-type fluctuations may not be totally field aligned. This deviation from the slab model would cause an increase of the theoretically predicted mean free path and lead to better agreement with the other two approaches.  相似文献   

20.
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  相似文献   

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