An approximate analytical solution of the self-similar flow with frozen-in magnetic field, I

1983 ◽  
Vol 95 (2) ◽  
pp. 291-298 ◽  
Author(s):  
J. B. Singh
Keyword(s):  
Magnetic Field ◽  
Analytical Solution ◽  
Approximate Analytical Solution ◽  
The Self ◽  
Self Similar

Dominant Diffusing Mode in the Self-Similar Phase Separation of a Magnetic Suspension in a Magnetic Field

Langmuir ◽  
1998 ◽  
Vol 14 (3) ◽  
pp. 578-581 ◽  
Author(s):  
Adriana S. Silva ◽  
Denis Wirtz
Keyword(s):  
Magnetic Field ◽  
Phase Separation ◽  
Magnetic Suspension ◽  
The Self ◽  
Self Similar ◽  
Similar Phase

Hydromagnetic effects on non-Newtonian Hiemenz flow

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Suman Sarkar ◽  
Bikash Sahoo
Keyword(s):  
Magnetic Field ◽  
Free Boundary ◽  
Existence And Uniqueness ◽  
Uniform Magnetic Field ◽  
Magnetic Parameter ◽  
Similarity Transformation ◽  
The Self ◽  
Free Boundary Value Problem ◽  
Uniqueness Of The Solution ◽  
Self Similar

Abstract The stagnation point flow of a non-Newtonian Reiner–Rivlin fluid has been studied in the presence of a uniform magnetic field. The technique of similarity transformation has been used to obtain the self-similar ordinary differential equations. In this paper, an attempt has been made to prove the existence and uniqueness of the solution of the resulting free boundary value problem. Monotonic behavior of the solution is discussed. The numerical results, shown through a table and graphs, elucidate that the flow is significantly affected by the non-Newtonian cross-viscous parameter L and the magnetic parameter M.

A self-similar solution of dissipative MHD for a jet in the boundary-layer approximation

1995 ◽  
Vol 53 (1) ◽  
pp. 49-62
Author(s):  
Alejandro G. Gonález ◽  
Martin Heyn
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Analytical Solution ◽  
Exact Analytical Solution ◽  
Viscous Drag ◽  
Integrals Of Motion ◽  
Boundary Layer Approximation ◽  
Initial Stage ◽  
Self Similar Solution ◽  
Self Similar

A solution of dissipative nonlinear MHD taking account of the balance between viscous drag, the Lorentz force, resistive diffusion and inertia in a boundary- layer approximation is presented. It is a steady solution corresponding to a jet in a conducting fluid with viscosity. The problem is solved using a self-similar variable. An exact analytical solution is possible. The integrals of motion are obtained and their physical meaning is explained. The behaviour of the solutions is described. The entrainment of the jet is observed in some examples after an initial stage dominated by magnetic fields. These solutions are an extension of Bickley's jet for a case with magnetic field and resistivity.

scholarly journals NAKED SINGULARITIES IN THREE-DIMENSIONS

2003 ◽  
Vol 12 (05) ◽  
pp. 791-799
Author(s):  
G. OLIVEIRA-NETO
Keyword(s):  
Scalar Field ◽  
Analytical Solution ◽  
Cosmic Censorship ◽  
The Self ◽  
Three Dimensions ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Naked Singularities ◽  
Asymptotically Flat ◽  
Self Similar

We study an analytical solution to the Einstein's equations in (2+1)-dimensions, representing the self-similar collapse of a circularly symmetric, minimally coupled, massless, scalar field. Depending on the value of certain parameters, this solution represents the formation of naked singularities. Since our solution is asymptotically flat, these naked singularities may be relevant for the weak cosmic censorship conjecture in (2+1)-dimensions.

scholarly journals ON THE SELF-SIMILAR HEAT BOUNDARY LAYER PROBLEMS IN MAGNETOHYDRODYNAMICS

2002 ◽  
Vol 7 (1) ◽  
pp. 93-102
Author(s):  
V. Kremenetsky
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Temperature Field ◽  
Joule Heat ◽  
The Self ◽  
Horizontal Flows ◽  
Self Similar Solution ◽  
Steady Magnetic Field ◽  
Self Similar ◽  
Boundary Layer Problems

Usually all self‐similar heat boundary layer problems in presence of magnetic field are solved neglecting the Joule heat, created by current, induced in fluid by interaction of velocity and magnetic field. But the analysis of this heat shows that its influence to the temperature field is very important. For vertical flows it is impossible to find self‐similar solution of boundary layer problems due to the Joule heat influence in temperature field. For horizontal flows only two self‐similar boundary layer problems can be formulated: flow near the critical point in magnetic field with the neutral point and in the transverse steady magnetic field.

Dynamical effects of the ambipolar diffusion in a protoplanetary disc

2020 ◽  
Vol 497 (2) ◽  
pp. 1634-1653 ◽  
Author(s):  
Mahmoud Gholipour
Keyword(s):  
Magnetic Field ◽  
Angular Momentum ◽  
Numerical Solutions ◽  
Turbulent Viscosity ◽  
Outer Region ◽  
Ambipolar Diffusion ◽  
The Self ◽  
Mhd Equations ◽  
Solution Technique ◽  
Self Similar

ABSTRACT Several recent simulation works in the non-ideal magnetohydrodynamic (MHD) formalism have shown the importance of ambipolar diffusion (AD) within the protoplanetary discs (PPDs) at large radii. In this study, we model the time evolution of a polytropic PPD in the presence of the AD. In this regard, the non-ideal MHD equations are investigated in the outer region of a PPD where the magnetic field evolution is dominated by the AD. The self-similar solution technique is used for a polytropic fluid including the self-gravity and viscosity. The ambipolar diffusivity and its derivative are crucial for the formulation of this study. Hence, this variable is scaled by an important factor, that is the Elsasser number. The self-similar equations are derived, and the semi-analytical and numerical solutions are presented for the isothermal and polytropic cases. The analytical approach enables us to know the asymptotic behaviour of the physical variables in a PPD, such as the angular momentum and magnetic field. Furthermore, the coupling/decoupling of magnetic field with the angular momentum was discussed analytically to find a corresponding model for the angular momentum loss at large radii of a PPD. Regarding this approach, we found that the magnetic braking induced by the AD at large radii has a high potential to loss the angular momentum even if the turbulent viscosity is not efficient. Also, the sign and values of vertical velocity strongly depends on the sign and values of radial field in the polytropic case.

scholarly journals The self-similar structure of advection-dominated discs with outflow and radial viscosity

2020 ◽  
Vol 493 (4) ◽  
pp. 5107-5119
Author(s):  
S M Ghoreyshi ◽  
M Shadmehri
Keyword(s):  
Magnetic Field ◽  
Similarity Solutions ◽  
Observational Evidence ◽  
The Self ◽  
Accretion Discs ◽  
Gas Velocity ◽  
State Structure ◽  
Self Similar ◽  
Strong Winds ◽  
The Magnetic Field

ABSTRACT Observational evidence and theoretical arguments postulate that outflows may play a significant role in the advection-dominated accretion discs (ADAFs). While the azimuthal viscosity is the main focus of most previous studies in this context, recent studies indicated that disc structure can also be affected by the radial viscosity. In this work, we incorporate these physical ingredients and the toroidal component of the magnetic field to explore their roles in the steady-state structure of ADAFs. We thereby present a set of similarity solutions where outflows contribute to the mass loss, angular momentum removal, and the energy extraction. Our solutions indicate that the radial viscosity causes the disc to rotate with a slower rate, whereas the radial gas velocity increases. For strong winds, the infall velocity may be of order the Keplerian speed if the radial viscosity is considered and the saturated conduction parameter is high enough. We show that the strength of magnetic field and of wind can affect the effectiveness of radial viscosity.

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