Abstract
A study is made of the unsteady motion of an incompressible
viscous conducting fluid with embedded small spherical particles
bounded by two infinite rigid non-conducting plates. The operational
method derives exact solutions for the fluid and the particle velocities
and the wall shear stress. The quantitative evaluation of these results is
considered when the two plates oscillate in phase but with different
frequencies. The results are shown graphically for different values of
the time period of oscillations of the plates which represent the cases:
(i) the lower plate oscillates with time period less than the upper, (ii)
both the plates oscillate with the same time period, (iii) the lower plate
oscillates with time period greater than the upper. The magnetic field
damps the fluid motion for all values of the time period of oscillations
of the plates. When the time periods are small, i.e., when the plates
oscillate with high frequency, the fluid motion is retarded by the
particles. However, when the plates oscillate with larger time periods
(smaller frequencies), the fluid velocity is increased by the presence of
the particles at the early stage of the motion, and this effect persists
until the equilibrium is reached when the particles exert their influence
to resist the flow. The drag on the plate, which is evaluated
numerically for the lower plate oscillating with large time period,
depends on the ratio of the time periods of the oscillating plates. If the
ratio of the time periods is not equal to unity, the drag on the plate,
irrespective of the values of the magnetic field, oscillates with larger
amplitude compared to its value when the ratio of the time periods is
equal to unity. Further, for the ratio of the time periods less than or
equal to unity and for any fixed values of the magnetic field, the drag
increases by the presence of the particles after a time