山形大学紀要（工学） 第11巻 第1号（1970）75-104
The Oscillating Flow of Conducting Fluids in Pipes
under Uniform Transverse Magnetic Fields III
Plane-Parallel Walls With Finite Electrical Conductivity
A theoretical analysis is developed for the oscillatory Hartmann flow the periodically oscillatory flow of an incompressible conducting viscous fluid through a channel with finite electrical conductivity in a uniform transverse magnetic field on the assumption of magnetohydrodynamic approximations.
The flow is assumed to be induced by a harmonically oscillating pressure gradient. The velocity and induced fields are provided to have the same forms of time dependencies as pressure gradient.
The exact solutions are the generailzed ones containing the limiting cases through the ideal channels with insulators and perfect conductors.
It is found that magnetohydrodynamic effects -- which decrease and flatten the amplitude of velocity, and shift the oscillatory phase -- are more remarkable for the walls with the larger electrical conductivity.