Unsteady Flow of Dusty Fluid along the Vertical Plate in a Porous Medium with Rotation

This study investigates the unsteady flow behavior of a dusty fluid past a vertical plate embedded in a porous medium within a rotating system. The fluid is assumed to be viscous, incompressible, and free from external electromagnetic forces, while the dust particles are assumed to be uniformly distributed. The governing equations incorporating the effects of rotation, permeability, and dust-fluid interaction are formulated and solved under appropriate boundary conditions. The finite explicit numerical techniques are employed to obtain expressions for the velocity profiles of both the fluid and dust phases. The influence of various physical parameters, such as the rotational parameter, permeability parameter, fluid concentration parameter, and particle mass parameter, is thoroughly analyzed and graphically presented. The results reveal that the rotation significantly affects the velocity distribution and induces a phase difference between the fluid and dust particles. Additionally, the presence of a porous medium introduces resistance to flow, which slows down the fluid motion over time. These findings are relevant to several engineering and geophysical applications, such as pollutant transport, oil recovery, and astrophysical fluid dynamics.