### 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 language | English (US) |
---|---|

Pages (from-to) | 259-285 |

Number of pages | 27 |

Journal | Journal of the Franklin Institute |

Volume | 297 |

Issue number | 4 |

DOIs | |

State | Published - Apr 1974 |

Externally published | Yes |

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### ASJC Scopus subject areas

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

### Cite this

*Journal of the Franklin Institute*,

*297*(4), 259-285. https://doi.org/10.1016/0016-0032(74)90025-8

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

Research output: Contribution to journal › Article

*Journal of the Franklin Institute*, vol. 297, no. 4, pp. 259-285. https://doi.org/10.1016/0016-0032(74)90025-8

}

TY - JOUR

T1 - Viscous MFD low Hartmann flow in an annular gap-a magnetic prandtl number expansion

AU - Matalon, Moshe

AU - Schweitzer, S.

PY - 1974/4

Y1 - 1974/4

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0016050523&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0016050523&partnerID=8YFLogxK

U2 - 10.1016/0016-0032(74)90025-8

DO - 10.1016/0016-0032(74)90025-8

M3 - Article

AN - SCOPUS:0016050523

VL - 297

SP - 259

EP - 285

JO - Journal of the Franklin Institute

JF - Journal of the Franklin Institute

SN - 0016-0032

IS - 4

ER -