Forward and inverse problems in fundamental and applied magnetohydrodynamics

Giesecke, A.; Stefani, Frank; Wondrak, Thomas; Xu, Mingtian

doi:10.1140/epjst/e2013-01793-3

Cited by 1 publication

(2 citation statements)

References 66 publications

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“…The first contribution from Giesecke et al [9] reviews SFB 609 activities devoted to high Rm-problems. First, the two basic mathematical formulations, the differential equation approach, based on the induction equation and the integral equation approach that relies on Biot-Savart's law are discussed.…”

Section: Fundamentalsmentioning

confidence: 99%

“…One of these new techniques, the Contactless Inductive Flow Tomography (CIFT), uses the magnetic field, measured in the exterior of the fluid, to infer the velocity field in the interior [9]. The state-of-the-art of two other prominent measuring techniques is reviewed in Cramer, Eckert and Gerbeth [10], namely electric potential difference measurements and ultrasound Doppler velocimetry.…”

Section: Fundamentalsmentioning

confidence: 99%

See 1 more Smart Citation

Electromagnetic flow control in metallurgy, crystal growth and electrochemistry

Gerbeth

Eckert

Odenbach

2013

Eur. Phys. J. Spec. Top.

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Electromagnetic fields, produced either by alternating (AC) or constant (DC) electric currents, or by simple permanent magnets, strongly influence the flow of liquid metals or electrolytes. This is caused by the Lorentz force (density) f L = j × B, resulting from the interaction between the magnetic induction B and the electric current density j, either induced by Faraday's law in liquid metals, or injected in the case of weakly conducting liquids, e.g. in electrochemical systems. The study of the feedback between B and the velocity field u, driven by f L is called magnetohydrodynamics (MHD), a discipline dating back to the discovery of the induction law in 1831 by Faraday. For the basics of MHD we refer to excellent textbooks [1][2][3] or a recent review [4]. Important early milestones in the development of MHD were the first liquid metal experiments in channels performed by Hartmann in 1937 [5] and the Nobel prize decorated discovery of incompressible waves in 1942 [6], now called Alfvén waves, that play an important role in solar physics. More recent developments consist in the rapid emergence of a new discipline, the electromagnetic processing of materials with own conferences [7], or the experimental proofs of the dynamo action, i.e. the self-excitation of B solely caused by the flowing liquid metal in specifically designed laboratory experiments [8].This remarkable diversity of phenomena is sorted in MHD by the magnetic Reynolds number Rm = μ 0 σul, where μ 0 , σ, u and l refer to vacuum permeability, electric conductivity and to the characteristic scales of velocity and length, respectively. The dynamo problem as well as other important astrophysical problems, such as phenomena in the solar atmosphere, fall into the class of high-Rm problems due to the large length scales involved. Here, the magnetic fields induced by the flow of electrically conducting liquids via the induction equation have to be taken into account, making the calculation of f L a formidable task. By contrast, nearly all laboratory and industrial problems of MHD belong to the low-Rm range in which the acting B is the applied one, which drastically simplifies the determination of f L . This richness in topics on various length scales, including geo-and astrophysical problems as well a

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Section: Fundamentalsmentioning

confidence: 99%

Section: Fundamentalsmentioning

confidence: 99%