On hydromagnetic rotating flow of a dusty fluid near a pulsating plate

TLDR: In this paper, an initial value problem is solved for the motion of an incompressible viscous conducting fluid with embedded small inert spherical particles bounded by an infinite rigid nonconducting plate.

Abstract: An initial value problem is solved for the motion of an incompressible viscous conducting fluid with embedded small inert spherical particles bounded by an infinite rigid non-conducting plate. Both the plate and the fluid are in a state of solid-body rotation with constant angular velocity about an axis normal to the plate. The unsteady flow is generated in the fluid-particle system due to velocity tooth pulses subjected on the plate in presence of a transverse magnetic field. It is assumed that no external electric field is imposed on the system and the magnetic Prandtl number is very small. The operational method is used to derive exact solutions for the fluid and the particle velocities and the shear stress at the wall. Some limiting cases of these solutions including the steady-state results are discussed. The general solutions for the fluid velocity and the wall shear stress are examined numerically and the simultaneous effects of rotation, the magnetic field and the particles on them are determined. Finally, the present result for the fluid velocity has been compared numerically with that generated by an impulsively moved plate in a particular case when time is large.