## A variational principle for magnetohydrodynamic channel flowNorman C. Wenger, Lewis Research Center, United States. National Aeronautics and Space Administration Variational principle for calculating velocity profile and electric potential distribution in magnetohydrodynamic channel flow. |

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### Contents

SUMMARY | 1 |

VARIATIONAL EXPRESSION | 7 |

SQUARE CHANNEL WITH CONDUCTING WALLS | 14 |

1 other sections not shown

### Common terms and phrases

6V and 6W adjustable parameters admissible functions average fluid velocity average velocity basic equations boundary condition equations channel cross section channel flow problems channel power dissipated channel walls channel with conducting class of admissible condition equations 6d conducting walls current density dimensionless coordinates dimensionless fluid velocity dimensionless pressure gradient dX dY electric current normal electrical conductivity electromagnetic flowmeter equa equations 15a expression for F F given formulation is presented Fourier expansion given by equations governing equations Hartmann number identically zero induced electric potential induced magnetic field insulated walls length of channel Lewis Research Center magnetic flux density magnetic permeability matrix see eq maximum for F MHD channel flow obtained ohmic loss pump applications quantities in brackets rectangular shown in figure square channel static magnetic field stationary point thin wall tion 8b trial functions unit length VARIATIONAL EXPRESSION variational formulation VARIATIONAL PRINCIPLE variational solution vector velocity and potential velocity profile viscous force z-component