We investigate the fully developed flow between two parallel plates and the film flow over a plate in an electrically conducting fluid under the action of a parallel Lorentz force. Exact analytical solutions are derived for velocity, flow rate and wall shear stress at the plates. The velocity results are presented in figures. All these flows are new and are presented for the first time in the literature.
Interaction of a magnetic dipole with a slowly moving electrically conducting plate
本文分析研究了一个磁偶极子在运动的导电平板附近所受的力和力矩。该问题与冶金中的非接触式电磁流量测量相关，并且扩展了先前的理论工作（Thess等人，Phys. Rev. Lett. 96（2006），164501; New J.Phys.9（2007），299）的情况，其中磁偶极子相对于板的取向是任意的。结果表明，在低磁雷诺数的情况下，可以严格地导出三维感应电势、涡流和感应磁场的分布。它还表明，力和扭矩的所有组件可以计算没有任何进一步的近似。本工作的结果作为一个基准问题，可用于验证更复杂的磁场分布的数值模拟。
Liquid metal ion sources (LMIS) are widely used in applications ranging from local ion implantation in semiconductors, to focused ion beam systems for milling and nanolithography, to space micropropulsion devices being developed by NASA. Above a critically large field strength, an electrically stressed liquid metal develops one or more cuspidal protrusions which undergo accelerated conic tip sharpening with runaway field self-enhancement. Zubarev (2001) first predicted from an inviscid model that the electric stresses at the liquid apex undergo self-similar divergent growth in finite time. The…
We introduce six families of three-dimensional space-periodic steady solenoidal flows, whose kinetic helicity density is zero at any point. Four families are analytically defined. Flows in four families have zero helicity spectrum. Sample flows from five families are used to demonstrate numerically that neither zero kinetic helicity density, nor zero helicity spectrum prohibit generation of large-scale magnetic field by the two most prominent dynamo mechanisms: the magnetic $α$-effect and negative eddy diffusivity. Our computations also attest that such flows often generate small-scale field f…
In this work, we study the implementation of electrically-driven flow (EDF) models in the finite-volume framework of $\text{OpenFOAM}^\circledR$. The Poisson-Nernst-Planck model is used for the transport of charged species and it is coupled to the Navier-Stokes equations, governing the fluid flow. In addition, the Poisson-Boltzmann and Debye-Hückel models are also implemented. The discretization method and the boundary conditions are carefully handled in order to ensure conservativeness of ionic species in generic meshes and second-order accuracy in space and time. The applicability of the dev…
Despite the increasing sophistication of numerical models of hot Jupiter atmospheres, the large time-scale separation required in simulating the wide range in electrical conductivity between the dayside and nightside has made it difficult to run fully consistent magnetohydrodynamic (MHD) models. This has led to many studies that resort to drag parametrizations of MHD. In this study, we revisit the question of the Lorentz force as an effective drag by running a series of direct numerical simulations of a weakly rotating, poorly conducting flow in the presence of a misaligned, strong background …
The research is devoted to the stability of convective flow in a nonuniformly rotating layer of an electrically conducting fluid in a spiral magnetic field. The stationary and oscillatory modes of magnetic convection are considered depending on the profile of the angular rotation velocity (Rossby number $\textrm{Ro}$) and on the profile of the external azimuthal magnetic field (magnetic Rossby number $\textrm{Rb}$). The nonlinear dynamic system of Lorentz type equations is obtained by using the Galerkin method. Numerical analysis of these equations has shown the presence of chaotic behavior of…
In this paper, the generation of magnetic fields in a nonuniformly rotating layer of finite thickness of an electrically conducting fluid by thermomagnetic (TM) instability. This instability arises due to the temperature gradient $\nabla T_0$ and thermoelectromotive coefficient gradient $\nablaα$. The influence of the generation of a toroidal magnetic field by TM instability on convective instability in a nonuniformly rotating layer of an electrically conductive fluid in the presence of a vertical constant magnetic field ${\bf{B}}_0 \| {\rm OZ}$ is established. As a result of applying the meth…
Thermal convection in an electrically conducting fluid (for example, a liquid metal) in the presence of a static magnetic field is considered in this chapter. The focus is on the extreme states of the flow, in which both buoyancy and Lorentz forces are very strong. It is argued that the instabilities occurring in such flows are often of unique and counter-intuitive nature due to the action of the magnetic field, which suppresses conventional turbulence and gives preference to two-dimensional instability modes not appearing in more conventional convection systems. Tools of numerical analysis su…
Comments on An implicit-Chebyshev pseudospectral method for the effect of radiation on power-law fluid past a vertical plate immersed in a porous medium, by N.S. Elgazery,CNSNS,2008
