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 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.

Circulation control in magnetohydrodynamic rotating flows

2017 ◽  
Vol 829 ◽  
pp. 328-344 ◽  
Author(s):  
V. D. Borisevich ◽  
E. P. Potanin ◽  
J. Whichello
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Exact Analytical Solution ◽  
External Rotation ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Rotating Cylinder ◽  
Rotating Disc ◽  
Angular Velocities ◽  
Energy Equations

A model of a laminar viscous conducting flow, near a dielectric disc in a uniform magnetic field and in the presence of external rotation, is considered, where there is a uniform suction and an axial temperature gradient between the flow and the disc’s surface. It is assumed that the parameters of the suction or the magnetohydrodynamic (MHD) interaction are such that the nonlinear inertial terms, related to the circulation flow, are negligible in the differential equations of the MHD boundary layer on a rotating disc. Analysis of the motion and energy equations, taking the dependence of density on temperature into account, is carried out using the Dorodnitsyn transformation. The exact analytical solution for the boundary layer and heat transfer equations is obtained and analysed, neglecting the viscous and Joule dissipation. The dependence of the flow characteristics in the boundary layer on the rate of suction and the magnetic field induction is studied. It is shown that the direction of the radial flow in the boundary layer on a disc can be changed, not only by variation of the ratio between the angular velocities in the external flow and the boundary layer, but also by changing the ratio of the temperatures in these two flows, as well as by varying the hydrodynamic Prandtl number. The approximate calculation of a three-dimensional flow in a rotating cylinder with a braking disc (or lid) is carried out, demonstrating that a magnetic field slows the circulation velocity in a rotating cylinder.

New Self Similar Solution of Spherical Radiative Gasdynamic Shock Wave With Increasing Density Under The Effect Of Axial And Azimuthal Magnetic Field

2015 ◽  
Vol 4 (2) ◽  
Author(s):  
Ajay Singh Yadav ◽  
Pravin Kumar Srivastava ◽  
Kishor Kumar Srivastava
Keyword(s):  
Magnetic Field ◽  
Shock Wave ◽  
Magnetic Fields ◽  
Initial Density ◽  
Radiation Energy ◽  
Azimuthal Magnetic Field ◽  
Self Similar Solution ◽  
Complete Study ◽  
Self Similar ◽  
Spherical Shock

In the present chapter we investigated the self similar flow behind a spherical shock wave propagating in a medium with increasing density, in the presence of magnetic fields. The medium is assumed to be non gravitational due to the heavy nucleus at origin. The medium ahead and behind the shock front are assumed to be inviscid. The initial density of gas is assumed to vary as some power of distance. It is assumed that gas is grey and opaque. The assumption of optically thick grey gas is physically consistant with the neglect of radiation pressure and radiation energy. Total energy of the flow field behind the spherical shock is assumed to be increasing with time, where the gas ahead of the shock is assumed to be at rest. The results of numerical calculations were shown in the form of graphs. A complete study was made for axial and azimuthal magnetic field. Also the effect of variation of initial density behind the shock, shock velocity and respective magnetic fields were investigated.

Experimental Investigation of the Laminar Boundary Layer Flow on a Rotating Wavy Disk

2016 ◽  
Author(s):  
Christian Helcig ◽  
Christian Teigeler ◽  
Stefan aus der Wiesche
Keyword(s):  
Boundary Layer ◽  
Exact Solution ◽  
Laminar Flow ◽  
Laminar Boundary Layer ◽  
Boundary Layer Flow ◽  
Similar Solution ◽  
Surface Shape ◽  
Self Similar Solution ◽  
Self Similar ◽  
Layer Flow

Since nearly one century, the flow on a flat rotating disk has provided the paradigm for studying rotating flows. For the laminar flow regime, a self-similar solution was obtained by von Kármán [6] in 1921, and a rather special feature of his exact solution of the Navier-Stokes equation is a constant boundary layer thickness not depending on the radial coordinate. A substantial modification of this canonical configuration is given by a wavy disk with a sinusoidal surface shape. Although axis-symmetric, no exact solution for the laminar flow on a wavy disk is known so far. In this study, detailed measurements of the velocity profiles were performed within the laminar boundary layer flow on a wavy disk. Based upon the experimental data, the potential of a self-similar solution approach for describing the resulting flow field was assessed. It was found that such an approach is useful for approximating the far-field solution but systematic deviations were observed in the vicinity of the disk origin.

scholarly journals An Exact Analytical Solution of the Strong Shock Wave Problem in Nonideal Magnetogasdynamics

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
S. D. Ram ◽  
R. Singh ◽  
L. P. Singh
Keyword(s):  
Magnetic Field ◽  
Shock Wave ◽  
Analytical Solution ◽  
Shock Front ◽  
Total Energy ◽  
Wave Motion ◽  
Exact Analytical Solution ◽  
Strong Shock ◽  
Strong Shock Wave ◽  
Wave Problem

We construct the solutions to the strong shock wave problem with generalized geometries in nonideal magnetogasdynamics. Here, it is assumed that the density ahead of the shock front varies according to a power of distance from the source of the disturbance. Also, an analytical expression for the total energy carried by the wave motion in nonideal medium under the influence of magnetic field is derived.

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