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Multiscale Analysis of Electromechanical System
Published in Young W. Kwon, Multiphysics and Multiscale Modeling, 2015
By expressing magnetic flux as the curl of magnetic vector potential and electrical intensity as the negative sum of the time derivative of magnetic vector potential and the gradient of electric scalar potential, a set of magnetic diffusion equations can be deduced from quasi-static Maxwell’s equations with constitutive relations as follows: () B→=∇×A→ () E→=−∂A→∂t−∇Φ () σ∂A→∂t+∇×1μ0∇×A→+σ∇Φ=J→s () ∇⋅(−σ∂A→∂t−σ∇Φ)=0
Multiplicity in an optimised kinematic dynamo
Published in Geophysical & Astrophysical Fluid Dynamics, 2022
A kinematic dynamo is the simplest system that allows a self-sustaining magnetic field. In this setup, a seed magnetic field is amplified by an electrically conducting fluid that flows according to a prescribed velocity field and becomes sufficiently strong to overcome Ohmic decay as time ; the backreaction from the generated magnetic field on the flow is ignored (Moffatt 1983). Due to the linearity of the induction equation with respect to the magnetic field , for a given flow, the time evolution of can be treated as a linear eigenvalue problem. The magnetic Reynolds number measures the relative strength of the induction effect to magnetic diffusion. For different flows, the efficiency to generate a dynamo at a specific is ranked by the largest real eigenvalue of , while its imaginary part describes the oscillatory frequency.
Global regularity results for the
Published in Applicable Analysis, 2019
where , and denote the unknown velocity vector field, magnetic field and the scalar temperature, while , , with and are given initial data. denotes the vertical unit vector, and is the pressure of the fluid at the point . The nonnegative constants , and are the coefficients of dissipation, magnetic diffusion and thermal diffusivity. The forcing term in the momentum equation describes the acting of the buoyancy force on fluid motion and models the Rayleigh-Bénard convection in a heated inviscid fluid.
A novel design of electromagnetic side sealing in twin-roll strip cast-rolling process
Published in Mechanics Based Design of Structures and Machines, 2021
Minghan Sun, Chuanxing Zheng, Fengshan Du, Zhiwang Zhu
In Eq. (1), is the magnetic diffusion coefficient. Here, μ is the relative magnetic permeability, σ is the conductivity. The above equation relates the velocity to the magnetic field. The first term in the right of the equation is the diffusion term, which represents the change of magnetic induction intensity caused by diffusion. The second term is the convection term, which represents the change of magnetic induction intensity caused by the conducting fluid medium. For the molten metal in the rolling process, the magnetic Reynolds number Rem ≤ 1, then so that the latter term can be ignored.