Hall Current Parameter Research Articles

Transient Rotating Hydromagnetic Partially-Ionized Heat-Generating Gas Dynamic Flow with Hall/Ion-Slip Current Effects: Finite Element Analysis

A mathematical model is presented for the unsteady magnetohydrodynamic heat-generating free convection flow of a partially-ionized gas past an infinite vertical porous plate in a rotating frame of reference. Hall and ion-slip current effects are incorporated in the model. A finite element solution to the coupled non-linear differential equations is presented under physically realistic boundary conditions. The effects of Hall current parameter, ion-slip current parameter, Prandtl number, heat generation parameter, rotational parameter, Grashof (buoyancy) parameter and also time on the velocity and temperature fields are presented graphically. Primary velocity profile (u) decreases due to an increase in the Hall parameter and the ionslip parameter; however it is boosted with time for positive Grashof numbers (cooling of the plate by free convection currents) and decreases with time for negative Grashof numbers (heating of the plate by free convection currents). Secondary velocity profile (v) is also reduced with rising Hall parameter and ionslip parameter but boosted with time and stronger rotation. The temperature profile (θ) is enhanced with a rise in the heat generating parameter and also increases with time. The flow regime has important applications in MHD energy systems, plasma aerodynamics and induction flow meter technologies.

Effects of hall current on MHD Couette flow in a rotating system with arbitrary magnetic field

Author has studied the MHD Couette flow in a rotating environment with non- conducting walls in the presence of an arbitrary magnetic field. The solution in dimensionless form contains four pertinent flow parameters, viz. the Hartmann number, the rotation parameter which is the reciprocal of the Ekman number, the Hall current parameter, and the angle of inclination of the magnetic field to the positive direction of the axis of rotation. An interplay of hydromagnetic force and Coriolis force with an inclusion of Hall current plays a significant role in determining the MHD flow behaviour. The velocity and induced magnetic field distributions are depicted graphically. Also, the numerical results of shear stresses and the rate of mass flows are presented graphically.

Similarity analysis in magnetohydrodynamics: effects of hall and ion-slip currents on free convection flow and mass transfer of a gas past a semi-infinite vertical plate

The effects of Hall and ion-slip currents on a steady free convection flow and mass transfer past a semi-infinite vertical plate in a viscous incompressible electrically conducting fluid are investigated when the fluid is subjected to a strong non-uniform magnetic field. The similarity solutions are obtained using a scaling group of transformations. These are the only symmetry transformations admitted by the field equations. The derived fundamental equations under the assumption of a small magnetic Reynolds number are solved numerically by employing the shooting method. The axial and transverse components of the velocity function profiles are computed for various values of magnetic parameters, Hall and ionslip current parameters.

Effect of Hall current on the stability of an anisotropic plasma

The magneto–gravitational instability of an unbounded tenuous plasma, subject to the influence of a uniform magnetic field which results in a tensorial plasma pressure, is investigated. The Chew, Goldberger, and Low equations for a collisionless plasma and a generalized Ohm's law, which includes the effects due to Hall current and electron inertia, are used. Criteria of instability in terms of plasma pressure, parallel and perpendicular to the magnetic field, and the Hall current parameter are derived for the special cases of parallel and perpendicular propagation vectors. It is found that the Hall effect has a stabilizing influence, although it does not produce stability for all wavelength perturbations. The monotonic instability is replaced by a growing wave instability (overstability). The presence of electron inertia, however, destabilizes a certain range of wavelengths which are stabilized by Hall current.

Unsteady hydromagnetic Couette flow within a porous channel with Hall effects

Unsteady hydromagnetic Couette flow of a viscous, incompressible and electrically conducting fluid between two infinitely long parallel porous plates, taking Hall current into account, in the presence of a transverse magnetic field is studied. Fluid flow within the channel is induced due to impulsive movement of the lower plate of the channel. Magnetic lines of force are assumed to be fixed relative to the moving plate. Solution of the governing equations is obtained by Laplace transform technique. The expression for the shear stress at the moving plate due to primary and secondary flows is also derived. Asymptotic behavior of the solution valid for small and large values of time t is analyzed to gain some physical insight into the flow pattern. Numerical values of the primary and secondary velocities are displayed graphically versus non-dimensional channel width variable η for various values of Hall current parameter m, magnetic parameter M2 , suction/injection parameter S and time t whereas the numerical values of shear stress at the moving plate due to primary and secondary flows are presented in tabular form for different values of m, M2 , S and t.

Hall effects on hydromagnetic Couette flow of Class-II in a rotating system in the presence of an inclined magnetic field with asymmetric heating/cooling of the walls

Hall effects on steady hydromagnetic Couette flow of class-II of a viscous, incompressible and electrically conducting fluid with non-conducting walls in a rotating system in the presence of an inclined magnetic field is investigated. Exact solution of the governing equations is obtained in closed form. Expressions for the shear stress at the moving plate due to primary and secondary flows and mass flow rates in the primary and secondary flow directions are also derived. Asymptotic behavior of the solution for velocity and induced magnetic field is analyzed, for small and large values of rotation parameter K2 and magnetic parameter M2 to gain some physical insight into the flow pattern. Heat transfer characteristics of the fluid are considered taking viscous and Joule dissipations into account when walls of the channel are asymmetrically heated or cooled. Numerical solution of energy equation and numerical values of rate of heat transfer at the stationary and moving plates are computed with the help of MATLAB software. The numerical values of velocity, induced magnetic field and fluid temperature are displayed graphically versus channel width variable η for various values of Hall current parameter m and angle of inclination of magnetic field θ whereas numerical values of shear stress at the moving plate due to primary and secondary flows, mass flow rates in the primary and secondary flow directions and rate of heat transfer at the stationary and moving plates are presented in tabular form for various values of m and θ.