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1.
With viscous dissipation and Joule heating taking into account a numerical solution of magnetohydrodynamic free convection flow, in the Stokes's problem, is obtained for different values of Prandtl numberP. The fluid is viscous, incompressible, and electrically conducting and the magnetic lines of force are assumed to be fixed relative to the plate which is started moving impulsively in its own plane (ISP) or it is uniformly accelerated (UAP). The solution is obtained with an implicit second-order method, forP=0.71 (air) andP=7 (water) and the obtained results are shown on figures and tables.  相似文献   

2.
A similarity analysis for the free and forced convection hydromagnetic flow over a horizontal semi-infinite flat plate through a non-homogeneous porous medium is presented, taking into account the hydrostatic pressure variation normal to the flat plate. The similarity solution of the problem under consideration is obtained under certain valid simplifying assumptions when, (i) the plate temperature is inversely proportional to the square root of the distance from the leading edge, (ii) the intensity of the applied magnetic field, normal to the plate, changes with the inverse square root of the distance from the leading edge, and (iii) the permeability of the porous medium, occupying a semi-infinite region of the space bounded by the flat plate, is proportional to the distance measured in the direction of the flow. A numerical solution of the resulting system of ordinary differential equations of motion and energy is obtained, depending on the Prandtl number Pr, the magnetic parameterM n ,the bouyancy parameter , and the permeability parameterP m .The variations of the fundamental quantities of the problem are shown graphically followed by a quantitative discussion.  相似文献   

3.
It is well known from Helioseismology that the Sun exhibits oscillations on a global scale, most of which are non-radial in nature. These oscillations help us to get a clear picture of the internal structure of the Sun as has been demonstrated by the theoretical and observational (such as GONG) studies. In this study we formulate the linearised equations of motion for non-radial oscillations by perturbing the MHD equilibrium solution for an axisymmetric incompressible fluid. The fluid motion and the magnetic field are expressed as scalarsU, V, P andT, respectively. In deriving the exact solution for the equilibrium state, we neglect the contribution due to meridional circulation. The perturbed quantitiesU *, V *, P *, T * are written in terms of orthogonal polynomials. A special case of the above formulation and its stability is discussed.  相似文献   

4.
In the plate collection of the Harvard College Observatory, we have obtained 528 photographic magnitude estimates for the recently discovered long-period classical Cepheid ASAS 101538-5933.1 (P = 51.4 days). Together with the published photoelectric and CCD observations, our data have allowed us to construct an O-C diagram spanning a time interval of 120 years. The O-C diagram has the shape of a parabola, which has made it possible to determine for the first time the quadratic light elements and to calculate the rate of evolutionary increase in the period, dP/dt = 51.8 (±4.8) s yr−1 or $ \dot P $ \dot P /P = 7.3 (±0.7) s, in agreement with the results of theoretical calculations for the third crossing of the instability strip. The available data reduced by the method of Eddington and Plakidis reveal small random period fluctuations that do not distort the evolutionary trend in the O-C residuals.  相似文献   

5.
The Soret effect on MHD free-convective and mass-transfer flow of an incompressible, viscous, and electrically-conducting fluid, past a moving vertical infinite plate is studied. The flow is assumed to be at small Reynolds numbers so that the induced magnetic field is neglected. The problem is solved with the help of the Laplace transform method for two different values of the dimensionless functionf(t) signifying two different cases, e.g., (i) when the boundary surface, the flat plate, is impulsively started, moving in its own plane (I.S.P.) and (ii) when it is uniformly accelerated (U.A.P.). The effects on the velocity field as well as on the skin-friction of the various dimensionless parameters occurring into the problem, especially the magnetic parameterM and Soret number So, are discussed with the help of graphs.  相似文献   

6.
The stellar equilibrium equations for given surface pressureP * and temperatureT *, and in the absence of convection, are translated into a nonlinear integral equation, in which the radiusR of the star enters as an eigenvalue. We show that under broad mathematical assumptions on the constitutive equations (equation of state, opacity and energy generation) a global existence and uniqueness property can be formulated. If a valueP M is selected, which restricts the allowed pressure and temperature range |P(r)–P *|+E|T(r)–T *P M (E, arbitrary constant of dimensions of a pressure over temperature), thenat least one solutionP(r),T(r) exists in the pressure-temperature range chosen, for anyR<R E . This solution isunique forR<R c .R E andR c are expressed in terms of the constitutive equations, and of the pressure-temperature range adopted. A physical argument in favour of the stability of this solution is presented.  相似文献   

7.
A new analytic approach to the solution of the Sitnikov Problem is introduced. It is valid for bounded small amplitude solutions (z max = 0.20) (in dimensionless variables) and eccentricities of the primary bodies in the interval (–0.4 < e < 0.4). First solutions are searched for the limiting case of very small amplitudes for which it is possible to linearize the problem. The solution for this linear equation with a time dependent periodic coefficient is written up to the third order in the primaries eccentricity. After that the lowest order nonlinear amplitude contribution (being of order z 3) is dealt with as perturbation to the linear solution. We first introduce a transformation which reduces the linear part to a harmonic oscillator type equation. Then two near integrals for the nonlinear problem are derived in action angle notation and an analytic expression for the solution z(t) is derived from them. The so found analytic solution is compared to results obtained from numeric integration of the exact equation of motion and is found to be in very good agreement. CERN SL/AP  相似文献   

8.
It is proved that monoparametric families of periodic orbits of theN-body problem in the plane, for fixed values of all masses, exist in a rotating frame of reference whosex axis contains always two of the bodiesP 1 andP 2. A periodic motion of theN-body problem is obtained as a continuation ofN–2 symmetric periodic orbits of the circular restricted three-body problem whose periods are in integer dependence, by increasing the masses of the originallyN–2 massless bodiesP 3, ...,P k. The analytic continuation, for sufficiently small values of theN–2 bodiesP 3 ...P k and finite values for the masses ofP 1 andP 2 has been proved by the continuation method and the solution itself has been found explicitly to a linear approximation in the small masses. Also, the possible application of the above periodic orbits to the study of the Solar system and of stellar systems is mentioned.  相似文献   

9.
This paper presents a suitable numerical method for the treatment of the unsteady hydromagnetic thermal boundary layer problem for flows past an infinite porous flat plate, the motion of which is governed by a general time-dependent law, under the influence of a transverse externally set magnetic field. The normal velocity of suction/injection at the plate is also assumed to be time-dependent. The results obtained on the basis of numerical approximations seem to compare favourably with earlier results (Pandeet al., 1976; Tokis, 1978). Analytical approximations are given for the cases of a plate (i) generally accelerated and (ii) harmonically oscillating. The direct numerical treatment is obviously advantageous since it allows, handling of cases where the known methods for analytical approximations are not applicable. This problem is closely related to the motions and heat transfer occurring locally on the surfaces of stars.  相似文献   

10.
On the basis of the results by Huang et al. (1990), this paper further discusses and analyses the four post-Newtonian effects in a near-Earth satellite orbit: the Schwarzschild solution, the post-Newtonian effects of the geodesic precession, the Lense-Thirring precession and the oblateness of the Earth. A full analytical solution to the effects including their direct perturbations and mixed perturbations due to the Newtonian oblateness (J 2) perturbation and the Schwarzschild solution is obtained using the quasi-mean orbital element method analogous to the Kozai's mean orbital element one. Some perturbation properties of the post-Newtonian effects are revealed. The results obtained not only can provide a sound scientific basis for the precise determination of a man-made satellite orbit but also is suitable for similar mechanics systems, such as the motions of planets, asteroids and natural satellites.  相似文献   

11.
For a special choice of the initial conditions a solution of the plane restricted problem of four bodies i.e. the problem of the motion of a passively gravitating material pointP attracted according to Newton's law by three fixed point massesP 1,P 2 andP 3 has been obtained.  相似文献   

12.
The motion of a semi-infinite incompressible viscous fluid, caused by the oscillation of a plane vertical plate, has been studied, taking into account the presence of free convection currents. Closed form solutions to the velocity, temperature and the penetration distance through which the leading edge effect propagates have been derived on neglecting the transient part. Velocity profiles are shown forGr>0 (Grashof number) (cooling of the plate by the free convection currents),Gr<0 (heating of the plate) on graph. Also the penetration distance has been shown on graphs for different values ofP, the Prandtl number. It has been observed that for t=3/2, greater cooling of the plate may cause the flow to become unstable. Also, the penetration distance is not found to be affected by the frequency of the oscillating vertical plate.  相似文献   

13.
Relativistic stellar structures can be obtained both analytically and by computation, but all these models do not stand the tests of physical reality. It is shown that for a physically reasonable solution d/dr -r and d(e v /dr r near the centre, d(P/)/dr<-0 and (dP/d)>-(P/). If we change the variabler tox=Cr 2, whereC is a constant, the field equations are reduced to a form which is easier to solve. A new set of exact solutions is obtained by consideringe v (1-x) n . Also, a method has been given to obtain generalized solution.It is shown that the solution discussed by Durgapal and Rawat (1980) is the only exact solution which in its most generalized form for a given density distribution stands all the tests of physical reality and for which both (P/) and (dP/d) decrase with increasing value ofr.Neutron star model is proposed by assuming >-2×1014g cm–3. Two specific cases are considered, viz.,P<-1/3 and dP/d<-1, respectively. The structures are found to be bound and stable under radial perturbations. The models have been studied for slow rotation and the mass of the Crab pulsar has been estimated for different mechanisms.  相似文献   

14.
A linear analysis of axial sheared flow in magnetohydrodynamic (MHD) jets with helical magnetic fields is presented. A linearized set of ideal MHD equations allows the investigation of plasmas with both magnetic shear and flow shear included in the equilibrium profile. These equations are integrated numerically by following the linear development in time of an initial seed perturbation. Global instability growth rates are obtained after the numerical solution converges to the fastest growing mode. It is shown that axial sheared flow reduces the growth of current-driven instabilities in plasma jets with constant magnetic pitch P = rB z /B θ.  相似文献   

15.
Theory of the motion of an artificial Earth satellite   总被引：1，自引：0，他引：1  
An improved analytical solution is obtained for the motion of an artificial Earth satellite under the combined influences of gravity and atmospheric drag. The gravitational model includes zonal harmonics throughJ 4, and the atmospheric model assumes a nonrotating spherical power density function. The differential equations are developed through second order under the assumption that the second zonal harmonic and the drag coefficient are both first-order terms, while the remaining zonal harmonics are of second order.Canonical transformations and the method of averaging are used to obtain transformations of variables which significantly simplify the transformed differential equations. A solution for these transformed equations is found; and this solution, in conjunction with the transformations cited above, gives equations for computing the six osculating orbital elements which describe the orbital motion of the satellite. The solution is valid for all eccentricities greater than 0 and less than 0.1 and all inclinations not near 0o or the critical inclination. Approximately ninety percent of the satellites currently in orbit satisfy all these restrictions.  相似文献   

16.
A total of 321 observations of the Delta Scuti star BD –6°4932, obtained in 1968 by Hall and Mallama (1970), are analyzed. We find four frequencies which represent the light curves satisfactorily.The three periods:P 1=0 . d 240,P 3=0 . d 182 andP 4=0 . d 114 seem to correspond to the radial modes of pulsation withK=0, 1, and 3, respectively. The last periodP 2=0 . d 220 can be related to a non-radial mode.  相似文献   

17.
The unsteady flow of an incompressible electrically-conducting and elasto-viscous fluid (Walter's liquidB), filling the semi-infinite space, in contact with an infinite non-conducting plate, in a rotating medium and in the presence of a transverse magnetic field is investigated. An arbitrary time-dependent forcing effect on the motion of the plate is considered and the plate and fluid rotate uniformly as a rigid body. The solution of the problem is obtained with the help of the Laplace transform technique and the analytical expressions for the velocity field as well as for the skin-friction are given.  相似文献   

18.
A method is proposed for constructing a map of the electron density distribution in the galactic plane. Data on the dispersion measures DM of more than 1500 pulsars and their distances, found by an independent method, are used. The independent distances of the pulsars are estimated using an empirical relation of the form L=γP α Ṗ β W δ between the radio luminosity L of the pulsars and their periods P, the rate of change Ṗ. of their periods, and the half width W of their pulses. A map of the electron density distribution in the galactic plane within a ±400 pc layer is provided. __________ Translated from Astrofizika, Vol. 49, No. 2, pp. 277–287 (May 2006).  相似文献   

19.
The effects of heat and mass transfer on the flow field of a laminar boundary layer is considered. The flow is that of an incompressible viscous fluid past an impulsively started permeable vertical limiting surface with constant heat flux. The solution of the problem was obtained numerically, using an implicit finite difference scheme. The solution is given in a number of diagrams, which depict the influence ofG on velocity,P on temperature and Sc on concentration. The influence ofG on skin friction is also given.  相似文献   

20.
Sixty-two spectrograms of the supergiant P Cyg, obtained with the Coudé spectrograph of the 2 m RCC telescope at NAO (National Astronomical Observatory, Bulgaria) were used in order to study the behaviour (we mean the displacements of the absorption components only) of the Hei spectrum of this star. Twelve lines from four series (23 P 0–n3S, 23P0 –n 3 D, 2 1 P 0 –n 1 D, and 21 S–n 1 P 0) were examined. It was established that all observed cases can be reduced to a few (three or four) which are typical. These cases are stated in the form of the comparison between the hydrogen and helium lines. All profiles were rectified and their complex structure was taken into consideration. The fixed peculiarities were explained by an optical depth effect.  相似文献   

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