Viscous MFD low Hartmann flow in an annular gap-a magnetic prandtl number expansion

Moshe Matalon, S. Schweitzer

Research output: Contribution to journalArticle

Abstract

The problem of a liquid conductor confined between two concentric cylindrical electrodes and driven electromagnetically is considered. The steady, three-dimensional viscous case is treated asymptotically in the limit of small magnetic Prandtl numbers. The zeroth-order solution to the coupled hydrodynamic and Maxwell equations yields the trivial solution of no motion in the limit of vanishing conductivity. Results for the first-order solution indicate two-dimensional effects in the electromagnetic field quantities while the first-order velocity is one dimensional in the circumferential direction. Due to secular effects the solution is limited to values of small Hartmann numbers. The formulation of the second order and a limited solution for the velocity distribution indicates that the velocity field is three-dimensional having a cell-type structure.

Original languageEnglish (US)
Pages (from-to)259-285
Number of pages27
JournalJournal of the Franklin Institute
Volume297
Issue number4
DOIs
StatePublished - Apr 1974
Externally publishedYes

Fingerprint

Prandtl number
First-order
Three-dimensional
Hydrodynamic Equations
Zeroth
Concentric
Velocity Distribution
Conductor
Maxwell's equations
Velocity Field
Electromagnetic Fields
Conductivity
Electrode
Trivial
Maxwell equations
Liquid
Velocity distribution
Electromagnetic fields
Motion
Formulation

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Signal Processing
  • Computer Networks and Communications
  • Applied Mathematics

Cite this

Viscous MFD low Hartmann flow in an annular gap-a magnetic prandtl number expansion. / Matalon, Moshe; Schweitzer, S.

In: Journal of the Franklin Institute, Vol. 297, No. 4, 04.1974, p. 259-285.

Research output: Contribution to journalArticle

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