The effect of tensor conductivity on continuum magnetogasdynamic flows

Abstract

Introduction.In recent years much work, both theoretical and experimental, has been done in the exploration of magnetogasdynamic or plasmadynamic phenomena, their engineering applications and their astrophysical implications. A good deal of this work, however, has included the approximation that the electric current always flows in the direction of the electric field vector. In reality, charged particles in a magnetic field do not move in straight lines, but rather tend to drift in a direction perpendicular to both the electric and magnetic fields, giving rise to the so-called Hall current or Hall effect. Because of the Hall effect, Ohm's law is modified in such a way that the electrical conductivity becomes a tensor quantity. The usual approximation of scalar conductivity is valid only when the collision frequency of the particles is so large that the particles have negligible time to drift across the magnetic field lines between collisions, i.e. when the cyclotron frequency of the particles is much less than their collision frequency. For cases where this condition is not met, the Hall effect must be taken into consideration. This paper extends our earlier results [1] to account for this phenomenon. We consider a dense plasma with a plasma frequency much greater than the cyclotron frequency of the particles present which, in turn, is much larger than the inverse of the characteristic flow time (i.e. the ratio of the free stream velocity to the characteristic length of the obstacle). In addition, the cyclotron frequency for the electrons is assumed to be of the same order of magnitude as the collision frequency between electrons and ions. We begin Sec. 2 by stating the equations pertinent to this problem. After linearization

On the motion past thin airfoils of incompressible fluids with conductivity tensor

“…The aligned-fields case has been considered by Sears and Resler [1] and Tang and Seebass [3]. In [1] a qualitative study was made and in [3] a quantitative description of the solution in symmetrical flow was given.…”

“…The aligned-fields case has been considered by Sears and Resler [1] and Tang and Seebass [3]. In [1] a qualitative study was made and in [3] a quantitative description of the solution in symmetrical flow was given. Working independently, we examined the general problem in [2] and [4], In these papers, however, the solution is expressed with the aid of generalized functions.…”