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1.
An exact similarity solution is presented for developing mixed convection flows of electrically conducting fluids over a semi-infinite horizontal plate with vectored mass transfer at the wall which are subjected to an applied transverse magnetic field. This solution is given for the case of a wall temperature that is inversely proportional to the square root of the distance from the leading edge. By application of appropriate coordinate transformations, the governing momentum and energy boundary-layer equations are expressed as a set of coupled ordinary differential equations that depend on a magnetic parameter, the buoyancy parameter, and the Prandtl number. The shear stress, the total heat transfer, and the displacement thickness are calculated for different values of both buoyancy and magnetic parameters.  相似文献   

2.
Effects of magnetic field and permeability of the porous medium on unsteady forced and free-convection flow past an infinite vertical porous plate in presence of temperature-dependent heat source have been analysed. The Laplace transform method is used to obtain the expression for velocity field, skin friction, and leading edge effects. During the course of discussion, the effects ofM (magnetic parameter),S (heat source parameter), (suction parameter), andK (permeability of porous medium) on velocity field, skin friction, and leading edge effect have been extensively discussed.  相似文献   

3.
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   

4.
The unsteady two-dimensional free convection flow of a viscous incompressible and electrically conducting fluid past an infinite non-conducting and non-magnetic porous limiting surface (e.g. of a star) through which suction with uniform velocity occurs is considered when the free-stream velocity, the temperature of the limiting surface and the induced magnetic field are oscillating in the time about a constant mean value. Expressions, in closed form for the velocity, the skin-friction, the displacement thickness, the induced magnetic field and the electrical current density are obtained by the help of the two-sided Laplace transform technique, when the magnetic Prandtl numberP m, and the Prandtl numberP are equal to one, and the magnetic parameterM is smaller to one. During the course of analysis the effects of magnetic parameterM, Grashof numberG and non-dimensional frequency are discussed.  相似文献   

5.
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   

6.
Effect of Hall current on the hydromagnetic free-convection flow of an electrically-conducting viscous incompressible fluid past an impulsively accelerated vertical porous plate in the presence of a uniform transverse magnetic field subjected to a constant transpiration velocity is analyzed for the case of small magnetic Reynolds number. Numberical solutions are obtained for the axial and transverse components of the velocity as well as the skin-friction by employing the Crank-Nicolson implicit finite-difference method for all probable values of the Prandtl number. The results are discussed with the effects of the Grashof number Gr, the transpiration velocity parameter , the Hall current parameterm, and the magnetic field parameterM for the Prandtl number Pr=0.71 which represents air at 20° C.  相似文献   

7.
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   

8.
Unsteady two-dimensional flow of a viscous incompressible and electrical-conducting fluid through a porous medium bounded by two infinite parallel plates under the action of a transverse magnetic field is presented when there is time-varying suction at the plates. The lower plate is at rest while the upper plate is oscillating in its own plane about a constant mean velocity. Expressions for the velocity, fluctuating parts of the velocity, amplitude, and phase of the skin-friction are obtained. The flow phenomenon has been characterized by the parametersK (permeability of the porous medium),N(magnetic parameter) (frequency parameter), andA(variable suction parameter) and the role of these parameters on the flow characteristics has been studied.  相似文献   

9.
An analytical study is performed to examine the laminar flow of an electrically-conducting elasto-viscous fluid (Walters's liquidB) past an infinite porous flat plate to a step function change in suction velocity in the presence of a transverse magnetic field. The influence of the various parameters, entering in the problem, on the velocity field and shearing stress is extensively discussed.  相似文献   

10.
An analysis of Hall and ion-slip current effects on the MHD free-convection flow of a partiallyionised gas past an infinite vertical porous plate in a rotating frame of reference is carried out. A strong magnetic field is applied perpendicular to the plate and the plate temperature oscillates in time about a constant non-zero mean. The problem has been solved for the velocity and temperature fields and the effects of e (the Hall parameter), i (the ion-slip parameter),E r (rotation parameter), and have been discussed and shown graphically.  相似文献   

11.
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   

12.
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   

13.
The paper studies the flow of a two-component hot plasma in a porous rotating sphere. Asymptotic solutions are derived for small rotation Reynolds number (Re). The overall analysis of the study shows that the temperature distribution of the gas inside the sphere has a minimum value, for the various values of the radiation parameterN 2 at a point where the radius of the solar sphere is 0.5r (wherer 0 is the dimensional radius of the sphere). The general result of the studies are discussed quantitatively. The problem has a lot of application in the understanding of the interior of astrophysical bodies.  相似文献   

14.
Modified similarity method has been used to study the propagation of spherical-variable energy blast waves through a self-gravitating gas. For an energy inputE =E 0t4/3, whereE is the energy released up to timet andE 0 is a functional constant, the similarity solutions correct up to third approximation have been obtained. It is found that the effects of self-gravitational forces are of third order. An increase in the parameterA 2 (characterising the gravitational field) increases the shock velocity.  相似文献   

15.
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   

16.
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   

17.
In this paper the unsteady flow in the Ekman layer of a visco-elastic non-Newtonian fluid near a flat plate is discussed. Laplace transform technique has been employed to show the basic differential equations. Expressions for velocity profile, the skin friction have been calculated. It is shown that the time to attain the steady state increases with the elastic parameter. It is shown that normally the ultimate steady state is reached through a decay of inertial oscillations whose frequency decreases with increase in the elastic parameter. In the present study we examine the following unsteady problem in non-Newtonian fluid. Consider an infinite plate coinciding with the platez=0 and rotating in unison with elasticoviscous liquid occupying the regionz>0 with a uniform angular velocity about thez-axis for timet<-0. At timet>0, the plate starts moving with a uniform velocityU o along thex-axis relative to the rotating frame of reference. The horizontal homogeneity of the problem demands that conditions depend onz andt only. The equation of continuity together with the no slip condition at the plate then shows that thez-component of the velocity vanishes everywhere.  相似文献   

18.
An exact analysis of Hall current on hydromagnetic free convection with mass transfer in a conducting liquid past an infinite vertical porous plate in a rotating fluid has been presented. Exact solution for the velocity field has been obtained and the effects ofm (Hall parameter),E (Ekman number), andS c (Schmidt number) on the velocity field have been discussed.Nomenclature C species concentration - C w concentration at the porous plate - C species concentration at infinity - C p specific heat at constant pressure - D chemical molecular diffusivity - g acceleration due to gravity - E Ekman number - G Grashof number - H 0 applied magnetic field - j x, jy, jz components of the current densityJ - k thermal conductivity - M Hartman number - m Hall parameter - P Prandtl number - Q heat flux per unit area - S c Sehmidt number - T temperature of the fluid near the plate - T w temperature of the plate - T temperature of the fluid in the free-stream - u, v, w components of the velocity fieldq, - U uniform free stream velocity - w 0 suction velocity - x, y, z Cartesian coordinates - Z dimensionless coordinate normal to the plate. Greek symbols coefficient of volume expansion - * coefficient of expansion with concentration - e cyclotron frequency - dimensionless temperature - * dimensionless concentration - v kinematic viscosity - density of the fluid in the boundary layer - coefficient of viscosity - e magnetic permeability - angular velocity - electrical conductivity of the fluid - e electron collision time - u skin-friction in the direction ofu - v skin-friction in the direction ofv  相似文献   

19.
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   

20.
Eselevich  V.G.  Eselevich  M.V. 《Solar physics》2000,195(2):319-332
It is shown on the basis of analyzing the LASCO/SOHO data that the main quasi-stationary solar wind (SW), with a typical lifetime of up to 10 days, flows in the rays of the streamer belt. Depending on R, its velocity increases gradually from V3 km s–1 at R1.3 R to V170 km s–1 at R15 R . We have detected and investigated the movement of the leading edge of the main solar wind at the stage when it occupied the ray, i.e., at the formative stage of a quasi-stationary plasma flow in the ray. It is shown that the width of the leading edge of the main SW increases almost linearly with its distance from the Sun. It is further shown that the initial velocity of the inhomogeneities (`blobs') that travel in the streamer belt rays increases with the distance from the Sun at which they originate, and is approximately equal to the velocity of the main solar wind which carries them away. The characteristic width of the leading edge of the `blob' R , and remains almost unchanging as it moves away from the Sun. Estimates indicate that the main SW in the brightest rays of the streamer belt to within distances at least of order R3 R represents a flow of collisional magnetized plasma along a radial magnetic field.  相似文献   

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