The influence of dissipative effects on dynamic processes in a rotating electrically conductive liquid medium

Abstract

The present study is concerned with dynamical processes in a rotating layer of electrically conducting incompressible liquid located in a magnetic field which is parallel to the normal vector to the boundary surfaces. We take into account not only the convective terms, but also the diffusion terms in the magnetic field induction equations. This problem, as well as the geophysical hydrodynamics problem, calls for the construction of approximate variants of the principal hydromagnetic equations and rigorous mathematical analysis of these approximate equations. Moreover, advancements in the above problems depend on the approximations to be introduced. To this end, by introducing characteristic scales of variation of the variables in the original equations and estimating the magnitude orders of the terms involved in the equations, one can single out the principal and secondary terms, simplify the equations, and build a model of the process under consideration. By introduction of auxiliary functions, the system of partial differential equations is reduced to one scalar equation. This suggests the conclusion about the analytical structure of magnetohydrodynamic characteristics. From the results obtained it follows that the magnetic field generation in an electrically conducting liquid stems from the instability characterized by the corresponding relations between the gravitation force, the Coriolis force, the magnetic force, and the peculiarities of the relief topography.

Research on Dynamic and Mechanical Properties of Magnetoactive Elastomers with High Permeability Magnetic Filling Agent at Complex Magneto-Temperature Exposure

“…The frequency of such agglomerations significantly increases with the increase in concentration of the filling agent, it also increases their linear size. A more detailed consideration of such structures reveals an arbitrarily shaped core consisting of large particles of the filling agent [ 31 ]. Furthermore, the smaller particles are organized in an orderly manner around the larger ones forming a spatial layered structure.…”

Research on Dynamic and Mechanical Properties of Magnetoactive Elastomers with High Permeability Magnetic Filling Agent at Complex Magneto-Temperature Exposure

“…The frequency of such agglomerations significantly increases with the increase in concentration of the filling agent, it also increases their linear size. A more detailed con-sideration of such structures reveals an arbitrarily shaped core consisting of large particles of the filling agent [25]. Further, the smaller particles are organized in an orderly manner around the larger ones forming a spatial layered structure.…”