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

M. Matalon, S. Schweitzer

Research output: Contribution to journalArticlepeer-review


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
Issue number4
StatePublished - Apr 1974
Externally publishedYes

ASJC Scopus subject areas

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


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