A three-dimensional (3-D) Hall MHD simulation is carried out to study the roles of initial current carrier in the topology of magnetic field, the generation and distribu- tion of field aligned currents (FACs), and the...A three-dimensional (3-D) Hall MHD simulation is carried out to study the roles of initial current carrier in the topology of magnetic field, the generation and distribu- tion of field aligned currents (FACs), and the appearance of Alfvén waves. Consid- ering the contribution of ions to the initial current, the topology of the obtained magnetic field turns to be more complex. In some cases, it is found that not only the traditional By quadrupole structure but also a reversal By quadrupole structure appears in the simulation box. This can explain the observational features near the diffusion region, which are inconsistent with the Hall MHD theory with the total ini- tial current carried by electrons. Several other interesting features are also emerged. First, motions of electrons and ions are decoupled from each other in the small plasma region (Hall effect region) with a scale less than or comparable with the ion inertial length or ion skin depth di=c/ωp. In the non-Hall effect region, the global magnetic structure is shifted in +y direction under the influence of ions with initial y directional motion. However, in the Hall effect region, magnetic field lines are bent in ?y direction, mainly controlled by the motion of electrons, then By is generated. Second, FACs emerge as a result of the appearance of By. Compared with the prior Hall MHD simulation results, the generated FACs shift in +y direction, and hence the dawn-dusk symmetry is broken. Third, the Walén relation in our simulations is consistent with the Walén relation in Hall plasma, thus the presence of Alfvén wave is confirmed.展开更多
The inhomogeneity is introduced by a nonzero density gradient which separates the plasma into two different regions where plasma density are constant.The Alfvén waves,the phase mixing and the fast magnetosonic wa...The inhomogeneity is introduced by a nonzero density gradient which separates the plasma into two different regions where plasma density are constant.The Alfvén waves,the phase mixing and the fast magnetosonic wave are excited by the boundary condition in inhomogeneous magnetized plasma.By using the Hall–magnetohydrodynamics(MHD)model,it is found that there are Alfvén waves in the homogeneous regions,while the phase mixing appears in the inhomogeneous region.The interesting result is that a fast magnetosonic wave is excited in a different direction which has a nonzero angle between the wave propagation direction and the direction of the background magnetic field.The dependence of the propagation direction of the excited fast magnetosonic wave and its strength of the magnetic field on the plasma parameters are given numerically.The results show that increasing both the driving frequency and the ratio of magnetic pressure to thermal pressure will increase the acceleration of the electrons.The electron acceleration also depends on the inhomogeneity parameters.展开更多
In this paper, we consider the global existence and decay rates of strong solutions to the three-dimensional compressible quantum Hall-magneto-hydrodynamics equations. By combing the Lp-Lq estimates for the linearized...In this paper, we consider the global existence and decay rates of strong solutions to the three-dimensional compressible quantum Hall-magneto-hydrodynamics equations. By combing the Lp-Lq estimates for the linearized equations and a standard energy method, the global existence and its convergence rates are obtained in various norms for the solution to the equilibrium state in the whole space when the initial perturbation of the stationary solution is small in some Sobolev norms. More precisely, the decay rates in time of the solution and its first order derivatives in L2-norm are obtained when the L1-norm of the perturbation is bounded.展开更多
This paper investigates the effects of Hall currents and radiation on free-convective steady laminar boundary-layer flow past a semi-infinite vertical plate for large temperature differences. A uniform magnetic field ...This paper investigates the effects of Hall currents and radiation on free-convective steady laminar boundary-layer flow past a semi-infinite vertical plate for large temperature differences. A uniform magnetic field is applied perpendicular to the plate. The fluid density is assumed to vary exponentially and the thermal conducting linearly with temperature. The fluid viscosity is assumed to vary as a reciprocal of a linear function of temperature. The usual Boussinesq approximation is neglected. The nonlinear boundary layer equations governing the problem under consideration are solved numerically by applying an efficient numerical technique based on the shooting method. The effects of the magnetic parameter , the Hall parameter m, the density/temperature parameter n, the radiation parameter N , the thermal conductivity parameter S, the viscosity temperature , and the temperature ratio parameter are examined on the velocity and temperature distribution as well as the coefficient of heat flux and shearing stress at the plate.展开更多
We discussed the unsteady flow of an incompressible viscous fluid in a rotating parallel plate channel bounded on one side by a porous bed under the influence of a uniform transverse magnetic field taking hall current...We discussed the unsteady flow of an incompressible viscous fluid in a rotating parallel plate channel bounded on one side by a porous bed under the influence of a uniform transverse magnetic field taking hall current into account. The perturbations are created by a constant pressure gradient along the plates in addition to the non-torsional oscillations of the upper plate. The flow in the clean fluid region is governed by Navier-Stoke’s equations while in the porous bed the equations are based on Darcy-Lapwood model. The exact solutions of velocity in the clean fluid and the porous medium consist of steady state and transient state. The time required for the transient state to decay is evaluated in detail and ultimate quasi-steady state solution has been derived analytically and also its behaviour is computationally discussed with reference to different flow parameters. The shear stresses on the boundaries and the mass flux are also obtained analytically and their behaviour is computationally discussed.展开更多
The combined effects of Hall current and radiation on an unsteady MHD free convective flow of a viscous incompressible electrically conducting fluid in a vertical channel with an oscillatory wall temperature have been...The combined effects of Hall current and radiation on an unsteady MHD free convective flow of a viscous incompressible electrically conducting fluid in a vertical channel with an oscillatory wall temperature have been studied. We have considered two different cases 1) flow due to the impulsive motion of one of the channel walls and 2) flow due to the accelerated motion of one of the channel walls. The governing equations are solved analytically using the Laplace transform technique. It is found that the primary velocity and the magnitude of the secondary velocity increase with an increase in Hall parameter for both the impulsive as well as the accelerated motions of one of the channel walls. An increase in either radiation parameter or frequency parameter leads to decrease in the primary velocity and the magnitude of the secondary velocity for both the impulsive as well as accelerated motions of one of the channel walls. The fluid temperature decreases with an increase in radiation parameter. Further, the shear stresses at the left wall reduce with an increase in either radiation parameter or frequency parameter for both the impulsive as well as the accelerated motions of one of the channel wall.展开更多
The effect of the Hall current on the magnetohydrodynamic （MHD） natural convection flow from a vertical permeable flat plate with a uniform heat flux is analyzed in the presence of a transverse magnetic field.It is ...The effect of the Hall current on the magnetohydrodynamic （MHD） natural convection flow from a vertical permeable flat plate with a uniform heat flux is analyzed in the presence of a transverse magnetic field.It is assumed that the induced magnetic field is negligible compared with the imposed magnetic field.The boundary layer equations are reduced to a suitable form by employing the free variable formulation （FVF） and the stream function formulation （SFF）.The parabolic equations obtained from FVF are numerically integrated with the help of a straightforward finite difference method.Moreover,the nonsimilar system of equations obtained from SFF is solved by using a local nonsimilarity method,for the whole range of the local transpiration parameter ζ.Consideration is also given to the regions where the local transpiration parameter ζ is small or large enough.However,in these particular regions,solutions are acquired with the aid of a regular perturbation method.The effects of the magnetic field M and the Hall parameter m on the local skin friction coefficient and the local Nusselt number coefficient are graphically shown for smaller values of the Prandtl number P r （= 0.005,0.01,0.05）.Furthermore,the velocity and temperature profiles are also drawn from various values of the local transpiration parameter ζ.展开更多
An electrically conducting fluid is driven by a stretching sheet, in the presence of a magnetic field that is strong enough to produce significant Hall current. The sheet is porous, allowing mass transfer through suct...An electrically conducting fluid is driven by a stretching sheet, in the presence of a magnetic field that is strong enough to produce significant Hall current. The sheet is porous, allowing mass transfer through suction or injection. The limiting behavior of the flow is studied, as the magnetic field strength grows indefinitely. The flow variables are properly scaled, and uniformly valid asymptotic expansions of the velocity components are obtained through parameter straining. The leading order approximations show sinusoidal behavior that is decaying exponentially, as we move away from the surface. The two-term expansions of the surface shear stress components, as well as the far field inflow speed, compare well with the corresponding finite difference solutions;even at moderate magnetic fields.展开更多
An exact solution to the problem of an MHD transient flow with Hall current past a uniformly accelerated horizontal porous plate in a rotating system has been presented. The dimensionless governing equations of the fl...An exact solution to the problem of an MHD transient flow with Hall current past a uniformly accelerated horizontal porous plate in a rotating system has been presented. The dimensionless governing equations of the flow problem are solved by Laplacetransform technique in closed form. A uniform magnetic field is assumed to be applied transversely to the direction of the flow. The expressions for velocity fields and skin-frictions are obtained in non-dimensional form. The primary and secondary velocity distributions and skin-frictions at the plate due to primary and secondary velocity field are demonstrated graphically and the effects of the different parameters namely, rotational parameter, Hartmann number, Hall parameter and acceleration parameter are discussed and the results are physically interpreted.展开更多
The unsteady magnehydrodynamics （MHD） Couette flow of an electrically conducting fluid in a rotating system is investigated by taking the Hall and ion-slip currents into consideration. The derived fundamental equati...The unsteady magnehydrodynamics （MHD） Couette flow of an electrically conducting fluid in a rotating system is investigated by taking the Hall and ion-slip currents into consideration. The derived fundamental equations on the assumption of a small magnetic Reynolds number are solved analytically with the well-known Laplace transform technique. The unified closed-form expressions axe obtained for the velocity and the skin friction in the two different cases of the magnetic field being fixed to either the fluid or the moving plate. The effects of various parameters on the velocity and the skin friction axe discussed by graphs. The results reveal that the primary and secondary velocities increase with the Hall current. An increase in the ion-slip paxameter also leads to an increase in the primary velocity but a decrease in the secondary velocity. It is also shown that the combined effect of the rotation, Hall, and ion-slip parameters determines the contribution of the secondary motion in the fluid flow.展开更多
The present numerically study investigates the influence of the Hall current and constant heat flux on the Magneto hydrodynamic (MHD) natural convection boundary layer viscous incompressible fluid flow in the manifest...The present numerically study investigates the influence of the Hall current and constant heat flux on the Magneto hydrodynamic (MHD) natural convection boundary layer viscous incompressible fluid flow in the manifestation of transverse magnetic field near an inclined vertical permeable flat plate. It is assumed that the induced magnetic field is negligible compared with the imposed magnetic field. The governing boundary layer equations have been transferred into non-similar model by implementing similarity approaches. The physical dimensionless parameter has been set up into the model as Prandtl number, Eckert number, Magnetic parameter, Schmidt number, local Grashof number and local modified Grashof number. The numerical method of Nactsheim-Swigert shooting iteration technique together with Runge-Kutta six order iteration scheme has been used to solve the system of governing non-similar equations. The physical effects of the various parameters on dimensionless primary velocity profile, secondary velocity profile, and temperature and concentration profile are discussed graphically. Moreover, the local skin friction coefficient, the local Nusselt number and Sherwood number are shown in tabular form for various values of the parameters.展开更多
The unsteady MHD Couette flow of an incompressible viscous electrically conducting fluid between two infinite non- conducting horizontal porous plates under the boundary layer approximations has been studied with the ...The unsteady MHD Couette flow of an incompressible viscous electrically conducting fluid between two infinite non- conducting horizontal porous plates under the boundary layer approximations has been studied with the consideration of both Hall currents and ion-slip. An analytical solution of the governing equations describing the flow is obtained by the Laplace transform method. It is seen that the primary velocity decreases while the magnitude of secondary velocity increases with increase in Hall parameter. It is also seen that both the primary velocity and the magnitude of secondary velocity decrease with increase in ion-slip parameter. It is observed that a thin boundary layer is formed near the stationary plate for large values of squared Hartmann number and Reynolds number. The thickness of this boundary layer increases with increase in either Hall parameter or ion-slip parameter.展开更多
A Hall magnetohydrodynamics （MHD） simulation is carried out to study the dynamic process of double tearing mode. The results indicated that the growth rates in the earlier nonlinear and transition phases agree with ...A Hall magnetohydrodynamics （MHD） simulation is carried out to study the dynamic process of double tearing mode. The results indicated that the growth rates in the earlier nonlinear and transition phases agree with the previous results. With further development of reconnection, the current sheet thickness is much smaller than the ion inertia length, which leads to a strong influence of the Hall effects. As a result, the reconnection in the late nonlinear phase exhibits an explosive nature with a time scale nearly independent of resistivity. A localized and severely intensified current density is observed and the maximum kinetic energy is over one order of magnitude higher in Hall MHD than that in resistive MHD.展开更多
基金Supported by the National Natural Science Foundation of China (Grant Nos. 40474058 and 40536030)the Key Project of the National Natural Science Foundation of China (Grant No. 40390152)+2 种基金Chinese Fundamental Research Project (Grant No. G200000784)Chinese Key Research Project (Grant No. 2006CB805305)the Key Displine Project of Beijing
文摘A three-dimensional (3-D) Hall MHD simulation is carried out to study the roles of initial current carrier in the topology of magnetic field, the generation and distribu- tion of field aligned currents (FACs), and the appearance of Alfvén waves. Consid- ering the contribution of ions to the initial current, the topology of the obtained magnetic field turns to be more complex. In some cases, it is found that not only the traditional By quadrupole structure but also a reversal By quadrupole structure appears in the simulation box. This can explain the observational features near the diffusion region, which are inconsistent with the Hall MHD theory with the total ini- tial current carried by electrons. Several other interesting features are also emerged. First, motions of electrons and ions are decoupled from each other in the small plasma region (Hall effect region) with a scale less than or comparable with the ion inertial length or ion skin depth di=c/ωp. In the non-Hall effect region, the global magnetic structure is shifted in +y direction under the influence of ions with initial y directional motion. However, in the Hall effect region, magnetic field lines are bent in ?y direction, mainly controlled by the motion of electrons, then By is generated. Second, FACs emerge as a result of the appearance of By. Compared with the prior Hall MHD simulation results, the generated FACs shift in +y direction, and hence the dawn-dusk symmetry is broken. Third, the Walén relation in our simulations is consistent with the Walén relation in Hall plasma, thus the presence of Alfvén wave is confirmed.
基金supported by National Natural Science Foundation of China(Nos.11965019,42004131 and 61863032)。
文摘The inhomogeneity is introduced by a nonzero density gradient which separates the plasma into two different regions where plasma density are constant.The Alfvén waves,the phase mixing and the fast magnetosonic wave are excited by the boundary condition in inhomogeneous magnetized plasma.By using the Hall–magnetohydrodynamics(MHD)model,it is found that there are Alfvén waves in the homogeneous regions,while the phase mixing appears in the inhomogeneous region.The interesting result is that a fast magnetosonic wave is excited in a different direction which has a nonzero angle between the wave propagation direction and the direction of the background magnetic field.The dependence of the propagation direction of the excited fast magnetosonic wave and its strength of the magnetic field on the plasma parameters are given numerically.The results show that increasing both the driving frequency and the ratio of magnetic pressure to thermal pressure will increase the acceleration of the electrons.The electron acceleration also depends on the inhomogeneity parameters.
文摘In this paper, we consider the global existence and decay rates of strong solutions to the three-dimensional compressible quantum Hall-magneto-hydrodynamics equations. By combing the Lp-Lq estimates for the linearized equations and a standard energy method, the global existence and its convergence rates are obtained in various norms for the solution to the equilibrium state in the whole space when the initial perturbation of the stationary solution is small in some Sobolev norms. More precisely, the decay rates in time of the solution and its first order derivatives in L2-norm are obtained when the L1-norm of the perturbation is bounded.
文摘This paper investigates the effects of Hall currents and radiation on free-convective steady laminar boundary-layer flow past a semi-infinite vertical plate for large temperature differences. A uniform magnetic field is applied perpendicular to the plate. The fluid density is assumed to vary exponentially and the thermal conducting linearly with temperature. The fluid viscosity is assumed to vary as a reciprocal of a linear function of temperature. The usual Boussinesq approximation is neglected. The nonlinear boundary layer equations governing the problem under consideration are solved numerically by applying an efficient numerical technique based on the shooting method. The effects of the magnetic parameter , the Hall parameter m, the density/temperature parameter n, the radiation parameter N , the thermal conductivity parameter S, the viscosity temperature , and the temperature ratio parameter are examined on the velocity and temperature distribution as well as the coefficient of heat flux and shearing stress at the plate.
文摘We discussed the unsteady flow of an incompressible viscous fluid in a rotating parallel plate channel bounded on one side by a porous bed under the influence of a uniform transverse magnetic field taking hall current into account. The perturbations are created by a constant pressure gradient along the plates in addition to the non-torsional oscillations of the upper plate. The flow in the clean fluid region is governed by Navier-Stoke’s equations while in the porous bed the equations are based on Darcy-Lapwood model. The exact solutions of velocity in the clean fluid and the porous medium consist of steady state and transient state. The time required for the transient state to decay is evaluated in detail and ultimate quasi-steady state solution has been derived analytically and also its behaviour is computationally discussed with reference to different flow parameters. The shear stresses on the boundaries and the mass flux are also obtained analytically and their behaviour is computationally discussed.
文摘The combined effects of Hall current and radiation on an unsteady MHD free convective flow of a viscous incompressible electrically conducting fluid in a vertical channel with an oscillatory wall temperature have been studied. We have considered two different cases 1) flow due to the impulsive motion of one of the channel walls and 2) flow due to the accelerated motion of one of the channel walls. The governing equations are solved analytically using the Laplace transform technique. It is found that the primary velocity and the magnitude of the secondary velocity increase with an increase in Hall parameter for both the impulsive as well as the accelerated motions of one of the channel walls. An increase in either radiation parameter or frequency parameter leads to decrease in the primary velocity and the magnitude of the secondary velocity for both the impulsive as well as accelerated motions of one of the channel walls. The fluid temperature decreases with an increase in radiation parameter. Further, the shear stresses at the left wall reduce with an increase in either radiation parameter or frequency parameter for both the impulsive as well as the accelerated motions of one of the channel wall.
文摘The effect of the Hall current on the magnetohydrodynamic （MHD） natural convection flow from a vertical permeable flat plate with a uniform heat flux is analyzed in the presence of a transverse magnetic field.It is assumed that the induced magnetic field is negligible compared with the imposed magnetic field.The boundary layer equations are reduced to a suitable form by employing the free variable formulation （FVF） and the stream function formulation （SFF）.The parabolic equations obtained from FVF are numerically integrated with the help of a straightforward finite difference method.Moreover,the nonsimilar system of equations obtained from SFF is solved by using a local nonsimilarity method,for the whole range of the local transpiration parameter ζ.Consideration is also given to the regions where the local transpiration parameter ζ is small or large enough.However,in these particular regions,solutions are acquired with the aid of a regular perturbation method.The effects of the magnetic field M and the Hall parameter m on the local skin friction coefficient and the local Nusselt number coefficient are graphically shown for smaller values of the Prandtl number P r （= 0.005,0.01,0.05）.Furthermore,the velocity and temperature profiles are also drawn from various values of the local transpiration parameter ζ.
文摘An electrically conducting fluid is driven by a stretching sheet, in the presence of a magnetic field that is strong enough to produce significant Hall current. The sheet is porous, allowing mass transfer through suction or injection. The limiting behavior of the flow is studied, as the magnetic field strength grows indefinitely. The flow variables are properly scaled, and uniformly valid asymptotic expansions of the velocity components are obtained through parameter straining. The leading order approximations show sinusoidal behavior that is decaying exponentially, as we move away from the surface. The two-term expansions of the surface shear stress components, as well as the far field inflow speed, compare well with the corresponding finite difference solutions;even at moderate magnetic fields.
文摘An exact solution to the problem of an MHD transient flow with Hall current past a uniformly accelerated horizontal porous plate in a rotating system has been presented. The dimensionless governing equations of the flow problem are solved by Laplacetransform technique in closed form. A uniform magnetic field is assumed to be applied transversely to the direction of the flow. The expressions for velocity fields and skin-frictions are obtained in non-dimensional form. The primary and secondary velocity distributions and skin-frictions at the plate due to primary and secondary velocity field are demonstrated graphically and the effects of the different parameters namely, rotational parameter, Hartmann number, Hall parameter and acceleration parameter are discussed and the results are physically interpreted.
文摘The unsteady magnehydrodynamics （MHD） Couette flow of an electrically conducting fluid in a rotating system is investigated by taking the Hall and ion-slip currents into consideration. The derived fundamental equations on the assumption of a small magnetic Reynolds number are solved analytically with the well-known Laplace transform technique. The unified closed-form expressions axe obtained for the velocity and the skin friction in the two different cases of the magnetic field being fixed to either the fluid or the moving plate. The effects of various parameters on the velocity and the skin friction axe discussed by graphs. The results reveal that the primary and secondary velocities increase with the Hall current. An increase in the ion-slip paxameter also leads to an increase in the primary velocity but a decrease in the secondary velocity. It is also shown that the combined effect of the rotation, Hall, and ion-slip parameters determines the contribution of the secondary motion in the fluid flow.
文摘The present numerically study investigates the influence of the Hall current and constant heat flux on the Magneto hydrodynamic (MHD) natural convection boundary layer viscous incompressible fluid flow in the manifestation of transverse magnetic field near an inclined vertical permeable flat plate. It is assumed that the induced magnetic field is negligible compared with the imposed magnetic field. The governing boundary layer equations have been transferred into non-similar model by implementing similarity approaches. The physical dimensionless parameter has been set up into the model as Prandtl number, Eckert number, Magnetic parameter, Schmidt number, local Grashof number and local modified Grashof number. The numerical method of Nactsheim-Swigert shooting iteration technique together with Runge-Kutta six order iteration scheme has been used to solve the system of governing non-similar equations. The physical effects of the various parameters on dimensionless primary velocity profile, secondary velocity profile, and temperature and concentration profile are discussed graphically. Moreover, the local skin friction coefficient, the local Nusselt number and Sherwood number are shown in tabular form for various values of the parameters.
文摘The unsteady MHD Couette flow of an incompressible viscous electrically conducting fluid between two infinite non- conducting horizontal porous plates under the boundary layer approximations has been studied with the consideration of both Hall currents and ion-slip. An analytical solution of the governing equations describing the flow is obtained by the Laplace transform method. It is seen that the primary velocity decreases while the magnitude of secondary velocity increases with increase in Hall parameter. It is also seen that both the primary velocity and the magnitude of secondary velocity decrease with increase in ion-slip parameter. It is observed that a thin boundary layer is formed near the stationary plate for large values of squared Hartmann number and Reynolds number. The thickness of this boundary layer increases with increase in either Hall parameter or ion-slip parameter.
基金National Science Foundation of China(Nos.40474058,40536030 and 10575031)
文摘A Hall magnetohydrodynamics （MHD） simulation is carried out to study the dynamic process of double tearing mode. The results indicated that the growth rates in the earlier nonlinear and transition phases agree with the previous results. With further development of reconnection, the current sheet thickness is much smaller than the ion inertia length, which leads to a strong influence of the Hall effects. As a result, the reconnection in the late nonlinear phase exhibits an explosive nature with a time scale nearly independent of resistivity. A localized and severely intensified current density is observed and the maximum kinetic energy is over one order of magnitude higher in Hall MHD than that in resistive MHD.
