In the present study, the transient hydromagnetic flow between parallel porous plates of a dusty viscous, incompressible, electrically conducting fluid under the influence of a constant pressure gradient is studied, considering the ion slip. The parallel plates are assumed to be porous and subjected to uniform suction from above and injection from below, while the fluid is acted upon by an external uniform magnetic field applied perpendicular to the plates. The equations of motion are solved analytically to yield the velocity distributions for both the fluid and dust particles as functions of time and space.
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