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1.
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   

2.
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   

3.
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   

4.
Unsteady laminar free convection flow of a viscous incompressible and electrically conducting fluid past an accelerated vertical infinite porous plate subjected to a suction velocity proportional to (time)–1/2 is studied in presence of a uniform horizontal magnetic field. Results are discussed with the effects of the Grashof number Gr, and the magnetic field parameterM for Pr (the Prandtl number)=0.71 and 7.0 representing air and water respectively at 20 °C.Nomenclature a suction/injection parameter - C p specific heat at constant pressure - B 0 magnetic induction - g acceleration due to gravity - Gr Grashof number (vg(T'w-T')/U 0 3 ) - K thermal conductivity - M magnetic field parameter (B 0 2 e 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 variable - t dimensionless time (t' U 0 2 /v) - u non-dimensional velocity (u'/U 0) - U' velocity of the plate - U dimensionless velocity of the plate (U'/U o) - U 0 reference velocity - v' 0 suction velocity - v 0 nondimensional suction velocity (v' 0/U 0)=at–1/2 - v' normal velocity component - v dimensionless normal velocity - Ec Eckert number ((vU 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 - y dimensionless ordinate (=y' U o/v) - v kinematic viscosity - coefficient of volume expansion - electric conductivity of the fluid - similarity variable (y/2t) - w density of the fluid at the plate - density of the fluid at infinity - ' skin-friction - dimensionless skin-friction - coefficient of viscosity - e magnetic permeability  相似文献   

5.
The Main-Sequence positions as well as the evolutionary behavior of Population III stars up to an evolution age of 2×1010 yr, taking this time as the age of the Universe, have been investigated in the mass range 0.2 and 0.8M . While Population III stars with masses greater than 0.3M develop a radiative core during the approach to the Main Sequence, stars with masses smaller than 0.3M reach the Main Sequence as a wholly convective stars. Population III stars with masses greater than 0.5M show a brightening of at most 2.2 in bolometric magnitude when the evolution is terminated as compared to the value which corresponds to zero-age Main Sequence. The positions of stars with masses smaller than 0.5M remain almost the same in the H-R diagram.If Population III stars have formed over a range of redshifts, 6相似文献   

6.
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.  相似文献   

7.
The distortions of the relict radiation spectrum in the region of the wavelength <120 are considered. These distortions are due to the emission of photons under the formation of molecular hydrogen in the expanding universe in the cosmological epoch 40z200. It is shown that the real intensity of the relict radiation in the region of the wavelength under consideration must significantly exceed Planck's intensity, with a radiation temperature amounting to 2.8 K.  相似文献   

8.
The general conception of the critical inclinations and eccentricities for theN-planet problem is introduced. The connection of this conception with the existence and stability of particular solutions is established. In the restricted circular problem of three bodies the existence of the critical inclinations is proved for any values of the ratio of semiaxes . The asymptotic behaviour of the critical inclinations as 1 is investigated.
. . . 1.
  相似文献   

9.
,   相似文献   

10.
A semi-continuous hierarchy, (i.e., one in which there are galaxies outside clusters, clusters outside superclusters etc.), is examined using an expression of the field equations of general relativity in a form due to Podurets, Misner and Sharp. It is shown (a) that for a sufficiently populous hierarchy, the thinning factor( i+1/ i [r i /r i+1] is approximately equal to the exponentN in a continuous density law (=aR –N) provided (r i /r i+1)3-1; (b) that a hierarchical Universe will not look decidedly asymmetric to an observer like a human being because such salient observers live close to the densest elements of the hierarchy (viz stars), the probability of the Universe looking spherically symmetric (dipole anisotropy0.1 to such an observer being of order unity; (c) the existence of a semi-continuous or continuous hierarchy (Peebles) requires that 2 if galaxies, not presently bound to clusters were once members of such systems; (d) there are now in existence no less than ten arguments for believing 2, though recent number counts by Sandageet al. seem to be in contradiction to such a value; (e) Hubble's law, withH independent of distance, can be proved approximately in a relativistic hierarchy provided (i)N=2, (ii)2GM(R)/c 2 R1; (iii)Rc (iv)M0 in a system of massM, sizeR (f) Hubble's law holds also in a hierarchy with density jumps; (g)H100 km s–1 Mpc–1; (h) objects forming the stellar level of the hierarchy (in a cosmology of the Wilson type) must once have had 2GM/c 2 R1; (i) there is a finite pressurep=2Ga in all astrophysical systems (a=R N ,N2); (j) for the Galaxy, theory predictsp G7×10–12 dyn cm–2, observation givesp G5×10–12 dyn cm–2; (k) if the mass-defect (or excess binding energy) hypothesis is taken as a postulate, all non-collapsed astrophysical systems must be non-static, and any non-static, p0 systems must in any case be losing mass; (1) the predicted mass-loss rate from the Sun is 1012 g s–1, compared to 1011 g s–1 in the observed solar wind; (m) the mass-loss rates known by observation imply timescales of 5×109 years for the Sun and 1010 years for other astrophysical systems; (n) degenerate superdense objects composed of fermions must haveN-2 if they were ever at their Schwarzschild radii and comprised a finite numberN B of baryons; (o)N B1057N for degenerate fermion and boson systems; (p)285-4; (q) the metric coefficients for superdense bodies give equations of motion that imply equal maximum luminosities for all evolving superdense bodies (L max1059 erg s–1); (r) larger bodies have longer time-scales of energy radiation atL max (10–5 s for stars,1 h for QSO's) (s) expansion velocities are c soon after the initial loss of equilibrium in a superdense object; (t) if the density parametera(t) in aR –N isa=a (non-atomic constants of physicsc, G, A), andA, thenN=2; (u) N2 is necessary to giveMM at the stellar level of the hierarchy;(v) systems larger than, and including, galaxies must have formed by clumping of smaller systems and not (as advocated by Wertz and others) in a multiple big bang.  相似文献   

11.
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   

12.
-- () ., , , , , . , , . , .  相似文献   

13.
Infrared continuum observations of the Sun at wavelengths between 10 and 30 show a nonisothermal response of the upper photosphere to compression waves associated with the five-minute oscillations. Observations were made with four broad-band filters with effective transmission wavelengths between 10 and 26 and with a 10 aperture. Further observations at submillimeter wavelengths with a 2 aperture did not resolve oscillatory fluctuations of five-minute period.Comparisons with velocity field data of Howard (1976) suggest that the relaxation time of the photosphere exceeds (300/2) seconds at the height of formation of the 26 continuum (5000Å 10-2). The photosphere reponds to 3 mHz oscillatory motion with considerably less compression than expected for simple acoustic modes in an adiabatically responsive atmosphere, confirming the evanescent character of the five-minute oscillations.  相似文献   

14.
, , , , , . , , . - . — , , .  相似文献   

15.
In this paper, a technique of recursive analysis is developed for the integral transform A of the exponential integral functionsE n which is denoted as n (). The main result of this analysis enables us to establish a two-term recurrence formula for n (0) and a three-term recurrence formula for n (); 0. A computational algorithm based on these formulae is also constructed and its numerical results forn=2(1)25 are presented to 15-digit accuracy.  相似文献   

16.
In this paper we introduce a new parameter, the shear angle of vector magnetic fields, , to describe the non-potentiality of magnetic fields in active regions, which is defined as the angle between the observed vector magnetic field and its corresponding current-free field. In the case of highly inclined field configurations, this angle is approximately equal to the angular shear, , defined by Hagyardet al. (1984). The angular shear, , can be considered as the projection of the shear angle, , on the photosphere. For the active region studied, the shear angle, , seems to have a better and neater correspondence with flare activity than does . The shear angle, , gives a clearer explanation of the non-potentiality of magnetic fields. It is a better measure of the deviation of the observed magnetic field from a potential field, and is directly related to the magnetic free energy stored in non-potential fields.  相似文献   

17.
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   

18.
We emphasize the sharp distinctions between different one-body gravitational trajectories made by the ratio of time averagesR(t)–E kin/E pot.R is calculated as a function of the eccentricity (e) and of the energy (E). Whent, independently ofe andE, R1/2 for closed orbits (this clearly illustrates the fulfillment of the virial theorem in classical mechanics); whereasR1, at any time, for open orbits.  相似文献   

19.
, . () . , , , . ( ), , , . . (2.7). ( 1 k 1 ,V — , — .) (k 1) (k) §2 ( (2.14)). , (3.6) (3.4), (3.8) . (3.9)–(3.13) ( (3.9), (3.10) (3.11) , (3.12)–(3.13) ). (3.14), (3.16)–(3.19). - . (3.15). ( (4.14)–(4.15)). (4.23)–(4.25). (4.26)–(4.28). §5. , . ((5.5)–(5.6)). , . (5.10) .  相似文献   

20.
The stars in the Main Sequence are seen as a hierarchy of objects with different massesM and effective dynamical radiiR eff=R/ given by the stellar radii and the coefficients for the inner structure of the stars.As seen in a previous work (Paper I), during the lifetime in the Main SequenceR eff(t) remains a near invariant when compared to the variation in the time ofR(t) and (t).With such an effectiveR eff one obtains the amounts of actionA c(M), the effective densities eff(M)=(M)3(M), the densities of action and of energy (or mean presures in the stellar interior)a c(M),e c(M), and the potential energiesE p(M).The amounts of action areA cM k withk1.87 for the M stars,k5/3 for the KGF stars, andk1.83 for the A and earlier stars, representing very simples conditions for the other dynamical parameters. For instancek5/3 means a near invariant effective density eff for the KGF stars, while for such stars the mean densities and coefficients present the strongest variations with masses (M)M –1.81, (M)M0.6.The cases for the M stars (e c(M)M –1) and for the A and earlier stars (betweena c(M)=constant and eff(M)M –1) and also discussed. These conditions for the earlier stars also represent reasonable mean values for the whole stellar hierarchy in the range of masses 0.2M M25M .With all this, one can build dynamical HR diagrams withA c(M), Ep(M), eff M –p , etc., whose characteristics are analogous to these in the photometrical HR diagram. A comparison is made betweenA c(M) from the models here and the HR diagram with the best known stars of luminosity classes IV, V, and white dwarfs.The comparison of the potential energiesE p(M)M –p according to the stellar models used here and the observed frequency function (MM –q (number of stars in a given interval of masses) from different authors suggests the possibility that the productE p(M)(M) is a constant, but this must be confirmed with further studies of the function (M) and its fine structure.There are analogies between the formulation used here for the stellar hierarchy and other physical processes, for instance, in modified forms of the Kolmogorov law of turbulence and in the formulation used for the hierarchy of molecular clouds in gravitational equilibrium. Besides, the function of actionA c(M) for the stars has analogous properties to the relations of angular momenta and massesJ(M) for different types of objects. The cosmological implications of all this are discussed.  相似文献   

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