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1.
A study is made of the free convection in hydromagnetic flows through a porous medium of a heat generating fluid past an infinite vertical porous plate. A strong magnetic field is imposed in a direction which is perpendicular to the free stream and makes an alge to the vertical direction. The governing equations for the hydromagnetic fluid flow and the heat transfer are solved analytically. The influence of Hall currents, the permeabilityK and the inclination upon the velocity field are shown in figures.  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.
Infinite series expansions are obtained for the doubly averaged effects of the Moon and Sun on a high altitude Earth satellite, and the results used to interpret numerically integrated examples. New in this paper are: (1) both sublunar and translunar satellites are considered; (2) analytic expansions include all powers in the satellite and perturbing body semi-major axes; (3) the fact that retrograde orbits have more benign eccentricity behavior than direct orbits should be exploited for high altitude satellite systems; and (4) near circular orbits can be maintained with small expenditures of fuel in the face of an exponential driving force one forI ab, whereI b=180°–I a andI a is somewhat less than 39.2° for sublunar orbits and somewhat greater than 39.2° for translunar orbits.Nomenclature a semi-major axis - A lk coefficient defined in Equation (11) - B lk coefficient defined in Equation (24) - C km coefficient defined in Equation (25) - D, E, F coefficients in Equations (38), (39) - e eccentricity - H k expression defined in Equation (34) - expression defined in Equation (35) - I inclination of satellite orbit on lunar (or solar) ring plane - J 2 coefficient of second harmonic of Earth's gravitational potential (1082.637×10–6 R E 2 ) - K k, Lk, Mk expressions in Section 4 - expressions in Section 4 - p=a(1–e 2) semi-latus rectum - P l Legendre polynomial of degreel - q argument of Legendre polynomial - radial distance of satellite - R E Earth equatorial radius (6378.16 km) - R, S, W perturbing accelerations in the radial, tangential and orbit normal directions - syn synchronous orbit radius (42 164.2 km=6.6107R E) - t time - T satellite orbital period - T orbital period of perturbing body (Moon) - T e period of long periodic oscillations ine for |I|<I a - T s synodic period - U gravitational potential of lunar (or solar) ring - x, y, z Cartesian coordinates of a satellite with (x, y) being the ring plane - coefficient defined in Equation (20) - average change in orbital element over one orbit (=a, e, I, , ) - 1,23 unit vectors in thex, y, z coordinate directions - r , s , w unit vectors in the radial, tangential and orbit normal directions - =+ angle along the orbital plane from the ascending node on the ring plane to the true position of the satellite - angle around the ring - gravitational constant times mass of Earth (3.986 013×105 km s–2) - gravitational constant times mass of Moon (or Sun) - m gravitational constant times mass of Moon (/81.301) - s gravitational constant time mass of Sun (332 946 ) - ratio of the circumference of a circle to its diameter - radius of lunar (or solar) ring - m radius of lunar ring (60.2665R E) - s radius of solar ring (23455R E) - true anomaly - argument of perigee - 0 initial value of - i critical value of in quadranti(i=1, 2, 3, 4) - longitude of ascending node on ring plane This work was sponsored by the Department of the Air Force.  相似文献   

4.
An analysis of the effects of free convection currents on the flow field of an incompressible viscous fluid past an infinite porous plate, which is uniformly accelerated upwards in its own plane, is presented, when the fluid is subjected to a variable suction (or injection) velocity. It is assumed that this normal velocity at the porous plate varies att–1/2, wheret denotes time. The equations governing the flow are solved numerically, using two-point boundary value shooting techniques.  相似文献   

5.
An analysis of Hall effects on the hydromagnetic free convection resulting from the combined effects of thermal and mass diffusion of an electrically-conducting liquid passed an infinite vertical porous plate in a rotating frame of reference is carried out when a strong magnetic field is imposed in a plane which makes an angle with the normal to the plate. The expressions for the mean velocity, mean temperature in the boundary layer, and the mean skin-friction, the mean rate of heat transfer on the plate are derived. The influence of Hall currents on the flow is studied for various values of .  相似文献   

6.
The velocity field has been mapped for 42 min in an area 80 by 85 containing a unipolar sunspot. Apparent shifts of Fe i 5233 were measured photoelectrically using a rectangular scanning aperture 1.6 × 4.0. The sunspot did not exert a marked influence on the generally random pattern of oscillations at a period of 300 s. Discrete periods of oscillation both longer and shorter than 300 s were excited within the enhanced magnetic field boundaries of this spot. Umbral oscillations at periods near 180 s were detected in agreement with independent observations of the same spot during the previous solar rotation.NRC Postdoctoral Fellow, 1969–71.  相似文献   

7.
An explicit finite-difference method is employed to study the MHD free convection heat generating fluid past an impulsively started vertical infinite plate when a strong magnetic field is applied perpendicular to the plate. The velocity and temperature profiles are shown on graphs and the results are discussed in terms of the non-dimensional parameters e (Hall parameter), i (ionslip parameter), (heat source parameter), and Gr (Grashof number).  相似文献   

8.
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   

9.
As a consequence of the Taylor–Proudman balance, a balance between the pressure, Coriolis and buoyancy forces in the radial and latitudinal momentum equations (that is expected to be amply satisfied in the lower solar convection zone), the superadiabatic gradient is determined by the rotation law and by an unspecified function of r, say, S(r), where r is the radial coordinate. If the rotation law and S(r) are known, then the solution of the energy equation, performed in this paper in the framework of the ML formalism, leads to a knowledge of the Reynolds stresses, convective fluxes, and meridional motions. The ML-formalism is an extension of the mixing length theory to rotating convection zones, and the calculations also involve the azimuthal momentum equation, from which an expression for the meridional motions in terms of the Reynolds stresses can be derived. The meridional motions are expanded as U r(r,)=P 2(cos)2(r)/r 2+P 4(cos)4(r)/r 2 +..., and a corresponding equation for U (r,). Here is the polar angle, is the density, and P 2(cos), P 4(cos) are Legendre polynomials. A good approximation to the meridional motion is obtained by setting 4(r)=–H2(r) with H–1.6, a constant. The value of 2(r) is negative, i.e., the P 2 flow rises at the equator and sinks at the poles. For the value of H obtained in the numerical calculations, the meridional motions have a narrow countercell at the poles, and the convective flux has a relative maximum at the poles, a minimum at mid latitudes and a larger maximum at the equator. Both results are in agreement with the observations.  相似文献   

10.
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   

11.
An exact analysis of Stokes' problem for an infinite vertical plate, whose temperature varies linearly with time, has been presented. It is observed that the velocity near the plate increases with the timet, and the Grashof numberGr. The skin-friction has been found to vary ast 7/2 and the Nusselt number varies as or whereP is the Prandtl number.  相似文献   

12.
Hall effects on the flow of electrically conducting rarefied gas due to combined buoyant effects of thermal and mass diffusion past an infinite porous plate with constant suction in the presence of strong transverse magnetic field have been investigated. The equations governing the flow poblem have been solved for primary, secondary velocities and temperature. The effects of Hall current, magnetic field and the effect of rarefication have been discussed graphically followed by a discussion.Nomenclature x,y coordinate system - u velocity inx direction - v 0 suction velocity - w velocity inz direction - E Eckert number - G, G* Grashof numbers - h 1 velocity slip coefficient - h 2 temperature jump coefficient - h 3 concentration jump coefficient - M, m magnetic field parameter, Hall parameter - Pr Prandtl number - Sc Schmidt number - T, T w, T temperature in flow regime, plate temperature, temperature outside the boundary layer very away from the plate - C, C w, C concentration of the gas in flow, concentration at the plate, concentration far away from the plate - thermal conductivity - D coefficient of chemical molecular diffusion - coefficient of kinematic viscosity - coefficient of viscosity - electrical conductivity - C p specific heat of gas at constant pressure density  相似文献   

13.
Thermal instability of a finitely conducting hydromagnetic composite medium is considered including the effects of Hall currents and the collisions with neutrals. The equilibrium magnetic field is assumed to be uniform and vertical. For stationary convection, the collissions have no effect, while the Hall currents are found to have a destabilizing effect on the thermal instability. It is further shown that whenM is finite andQ the asymptotic behaviours of the critical Rayleigh number, the critical wave number and the critical temperature gradient remain the same as those obtained by Chandrasekhar whereM is a nondimensional number which includes the Hall current effects andQ stands for the Chandrasekhar number.  相似文献   

14.
We observed the large post-flare loop system, which developed after the X 3.9 flare of 25 June 1992 at 2011 UT, in H with the Multichannel Subtractive Double Pass Spectrograph at Pic-du-Midi and in X-rays with the it Yohkoh/SXT instrument. Following the long-term development of cool and hot plasmas, we have determined the emission measure of the cool plasma and, for the first time, the temporal evolution of the hot-loop emission measure and temperature during the entire gradual phase. Thus, it was possible to infer the temporal variation of electron densities, leading to estimates of cooling times. A gradual decrease of the hot-loop emission measure was observed, from 4 × 1030 cm–5 at 2300 UT on 25 June 1992 to 3 × 1028 cm–5 at 1310 UT on 26 June 1992. During the same period, the temperature decreased only slowly from 7.2 to 6.0 × 106 K. Using recent results of NLTE modeling of prominence-like plasmas, we also derive the emission measure of cool H loops and discuss their temperature and ionisation degree. During two hours of H observations (11–13 hours after the flare) the averaged emission measure does not show any significant change, though the amount of visible cool material decreases and the volume of the loops increases. The emission measure in H, after correction for the Doppler-brightening effect, is slightly lower than in soft X-rays. Since the hot plasma seems to be more spatially extended, we arrive at electron densities in the range n infe supho n infe supcool 2 × 1010 cm–3 at the time of the H observations.These results are consistent with the post-flare loop model proposed by Forbes, Malherbe, and Priest (1989). The observed slow decrease of the emission measure could be due to an increase of the volume of the loops and a gradual decrease of the chromospheric ablation driven by the reconnection, which seems to remain effective continuously for more than 16 hours. The cooling time for hot loops to cool down to 104 K and to appear in H would be only a few minutes at the beginning of the gradual phase but could be as long as 2 hours at the end, several hours later.  相似文献   

15.
We have observed 10 solar bursts during the thermal phase using the Haystack radio telescope at 22 GHz. We show that these high frequency flux observations, when compared with soft X-ray band fluxes, give useful information about the temperature profile in the flare loops. The microwave and X-ray band fluxes provide determinations of the maximum loop temperature, the total emission measure, and the index of the differential emission measure (q(T)/T = cT–1). The special case of an isothermal loop ( = ) has been considered previously by Thomas et al. (1985), and we confirm their diagnostic calculations for the GOES X-ray bands, but find that the flare loops we observed departed significantly from the isothermal regime. Our results ( = 1–3.5) imply that, during the late phases of flares, condensation cooling ( 3.5) competes with radiative cooling ( 1.5). Further, our results appear to be in good agreement with previous deductions from XUV rocket spectra ( 2–3).  相似文献   

16.
On the basis of observational data for the absolute R and relative R/R amplitudes of variations in radius of galactic classical cepheids (55 stars from Balona and Stobie (1979) and 30 stars from Sollazzoet al. (1981)), four kinds of empirical linear relations are obtained: log(P V)–logR, logP–logR, log(P V)–log(R/R), and logP–log(R/R);P, R, and V are the pulsation periods, the mean stellar radii, and the amplitudes of light variations, respectively. Three groups of stars are considered: short-period cepheids (SPC)-with logP1.1; long-period cepheids (LPC)-with logP>1.1; and s-cepheids (sC). Both the R values and the R/R values increase withP andP V, for a given group of variables. A comparison is performed with our results obtained from data in other sources (Kurochkin, 1966; Gieren, 1982; etc.). The investigated relations can be applied for determining R and R/R of galactic classical cepheids, by using their observedP and V. All studied galactic classical cepheids have R/R<0.35, R<10R for SPC and 10R <R60R for LPC. The sC have smaller R and R/R values than other classical cepheids, at the same periods (the difference is about 2 times for R and 1.4–2.8 times for R/R); the studied sC have R/R in the range 0.025–0.075 and R in the range 1–3R (only Y Oph has R8R ).  相似文献   

17.
An exact analysis of the unsteady free and forced convection flow of an incompressible viscous fluid past a porous plate has been presented in presence of a constant heat source. A solution has been derived by Laplace-transform technique. Velocity profiles, skin-friction and leading edge effects have been obtained. During the course of the discussion, the effects ofS (heat source parameter), (suction parameter) on velocity, skin-friction and leading edge effect have been extensively discussed with the help of graphs and the table.  相似文献   

18.
A study of the combined buoyancy effects of thermal and mass diffusion on MHD convection flow in the presence of Hall currents with variable suction and heat generation has been carried out. Analytical expressions for the velocity and the temperature of the fluid are given. The effects of Hall currents, parameterm, and heat source parameter on the velocity are discussed.  相似文献   

19.
The stability of magnetic flux tubes embedded vertically in a convection zone is investigated. For thin tubes, the dominant instability is of the convective type, i.e. it is driven by buoyancy forces associated with displacements along the tube. The stability is determined by = 8P/B 2; if c the tube is convectively stable, otherwise it is unstable, where the critical value c depends on the stratification of the convection zone. For a solar convection zone model, c = 1.83, corresponding to a magnetic field strength of 1350 G at the surface of the Sun. It is concluded that the flux tubes making up the small scale field of the Sun are probably hydrodynamically stable.In tubes with > c, the instability is expected to transform the tube either into a state of vanishing surface field strength (in the case of an upward flow), or one with a field strength higher than the original value (if the instability sets in as a downward flow). Following Parker, we suggest that this effect is related to the concentrated nature of the observed solar fields.The National Center for Atmospheric Research is sponsored by the National Science Foundation.  相似文献   

20.
The24MgH+ (A 1+ –X 1+) molecular lines have been identified in the photospheric spectrum. The rotational excitation temperature determined from the analysis of molecular line intensities of24MgH+ is found to be of the order of 4850 K which corresponds to the photospheric temperature of the Sun. The CNDO/2 dipole moments of24MgH+ for internuclear distance range: (1.3–2.1) Å in theX 1+ state can be approximated byM(R)=4.92+1.33R. Estimations for the spontaneous emission Einstein coefficients (A v v ) and the absorption oscillator strengths (f v v ) for the (1, 0), (2, 0), and (2, 1) transitions in theX 1+ state of the24MgH+ ion are also made.Work partially supported by the CNPq, Brasilia under contract number 30.4076/77.  相似文献   

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