Magnetohydrodynamic flow of continuous dusty particles and non-Newtonian Darcy fluids between parallel plates

The coupled unsteady power-law conducting fluid flow and continuous dusty viscous fluid flow under the influence of magnetic field are solved using the finite difference method. The resistive forces of Darcy porous medium and the external uniform magnetic field are applied on the flow. The second-order accurate finite difference schemes are applied on the coupled governing equations to transform the non-linear partial differential equations to linearized system of algebraic equations. This system is solved iteratively using the generalized Thomas algorithm. Some results are introduced to study the convergence and stability of the present works. The effects of non-Newtonian fluid, continuous dusty particles, Darcy model on the velocity field, and friction factor of both the fluid and dust particles phases are demonstrated.