Numerical solutions of a time-dependent hydromagnetic micropolar dusty fluid between parallel plates through an inclined channel

Numerical simulation of an incompressible micropolar dusty fluid (fluid–particle suspension) is proposed for three types of flows in the inclined channel, i.e., Poiseuille flow, Couette flow and the generalised Couette flow. Although the fluid flow is time-dependent, hydromagnetic and channel walls are parallel to each other. The governing coupled partial differential equations for the flow of non-Newtonian micropolar dusty fluid are formulated in a Cartesian coordinate system and simulated approximately using a modified cubic B-spline differential quadrature method. The effects of ion slip, Hall current, Reynolds number, micropolar material and other important hydrodynamic fluid parameters have been examined on unsteady flow velocity and microrotation characteristics. It is observed that the linear velocity of the fluid and particle rises from the horizontal to the vertical channel, fluids and particle velocities are reduced with increasing Hartmann numbers, whereas they are elevated with increment in the Hall parameter. Findings of the present model can be helpful in various industrial fluid flow applications, particularly in petroleum industries.