scholarly journals MHD Equations with Regularity in One Direction

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Zujin Zhang
Keyword(s):  
Fluid Velocity ◽  
Directional Derivative ◽  
Mhd Equations

We consider the 3D MHD equations and prove that if one directional derivative of the fluid velocity, say, ∂3u∈Lp0, T;LqR3, with 2/p + 3/q = γ ∈ [1,3/2), 3/γ ≤ q ≤ 1/(γ - 1), then the solution is in fact smooth.  This improves previous results greatly.

scholarly journals Generalized analytic functions in magnetohydrodynamics

2011 ◽  
Vol 467 (2136) ◽  
pp. 3343-3370 ◽  
Author(s):  
Michael Zabarankin
Keyword(s):  
Analytic Functions ◽  
Boundary Integral Equations ◽  
Integral Formula ◽  
Fluid Velocity ◽  
Boundary Integral ◽  
Mhd Equations ◽  
Generalized Analytic Functions ◽  
Electrically Conducting ◽  
Minimum Drag ◽  
Sphere Drag

An approach of generalized analytic functions to the magnetohydrodynamic (MHD) problem of an electrically conducting viscous incompressible flow past a solid non-magnetic body of revolution is presented. In this problem, the magnetic field and the body’s axis of revolution are aligned with the flow at infinity, and the fluid and body are assumed to have the same magnetic permeability. For the linearized MHD equations with non-zero Hartmann, Reynolds and magnetic Reynolds numbers ( M , Re and Re m , respectively), the fluid velocity, pressure and magnetic fields in the fluid and body are represented by four generalized analytic functions from two classes: r -analytic and H -analytic. The number of the involved functions from each class depends on whether the Cowling number S= M 2 /( Re m   Re ) is 1 or is not 1. This corresponds to the well-known peculiarity of the case S=1. The MHD problem is proved to have a unique solution and is reduced to boundary integral equations based on the Cauchy integral formula for generalized analytic functions. The approach is tested in the MHD problem for a sphere and is demonstrated in finding the minimum-drag spheroids subject to a volume constraint for S<1, S=1 and S>1. The analysis shows that as a function of S, the drag of the minimum-drag spheroids has a minimum at S=1, but with respect to the equal-volume sphere, drag reduction is smallest for S=1 and becomes more significant for S≫1.

scholarly journals Resistive accretion flows around a Kerr black hole

2020 ◽  
Vol 37 ◽  
Author(s):  
M. Shaghaghian
Keyword(s):  
Magnetic Field ◽  
Black Hole ◽  
Accretion Rate ◽  
Fluid Velocity ◽  
Boundary Surface ◽  
Kerr Black Hole ◽  
Accretion Disc ◽  
Mhd Equations ◽  
Poloidal Magnetic Field ◽  
Mass Accretion Rate

Abstract In this paper, we present the stationary axisymmetric configuration of a resistive magnetised thick accretion disc in the vicinity of external gravity and intrinsic dipolar magnetic field of a slowly rotating black hole. The plasma is described by the equations of fully general relativistic magnetohydrodynamics (MHD) along with the Ohm’s law and in the absence of the effects of radiation fields. We try to solve these two-dimensional MHD equations analytically as much as possible. However, we sometimes inevitably refer to numerical methods as well. To fully understand the relativistic geometrically thick accretion disc structure, we consider all three components of the fluid velocity to be non-zero. This implies that the magnetofluid can flow in all three directions surrounding the central black hole. As we get radially closer to the hole, the fluid flows faster in all those directions. However, as we move towards the equator along the meridional direction, the radial inflow becomes stronger from both the speed and the mass accretion rate points of view. Nonetheless, the vertical (meridional) speed and the rotation of the plasma disc become slower in that direction. Due to the presence of pressure gradient forces, a sub-Keplerian angular momentum distribution throughout the thick disc is expected as well. To get a concise analytical form of the rate of accretion, we assume that the radial dependency of radial and meridional fluid velocities is the same. This simplifying assumption leads to radial independency of mass accretion rate. The motion of the accreting plasma produces an azimuthal current whose strength is specified based on the strength of the external dipolar magnetic field. This current generates a poloidal magnetic field in the disc which is continuous across the disc boundary surface due to the presence of the finite resistivity for the plasma. The gas in the disc is vertically supported not only by the gas pressure but also by the magnetic pressure.

Numerical study of the flow of a mixture of reacting gases in an inhomogeneous catalyst layer

2003 ◽  
Vol 3 ◽  
pp. 246-254
Author(s):  
C.I. Mikhaylenko ◽  
S.F. Urmancheev
Keyword(s):  
Velocity Field ◽  
Chemical Reactions ◽  
Porous Layer ◽  
Computational Experiment ◽  
Numerical Study ◽  
Fluid Velocity ◽  
Catalyst Layer ◽  
Granular Catalyst ◽  
Fluid Velocity Field

The behavior of a liquid flowing through a fixed bulk porous layer of a granular catalyst is considered. The effects of the nonuniformity of the fluid velocity field, which arise when the surface of the layer is curved, and the effect of the resulting inhomogeneity on the speed and nature of the course of chemical reactions are investigated by the methods of a computational experiment.

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