Unsteady flow of a dusty conducting non-Newtonian fluid through a pipe

In this paper, the unsteady flow of a dusty viscous incompressible electrically conducting non-Newtonian power-law fluid through a circular pipe is investigated. A constant pressure gradient in the axial direction and a uniform magnetic field directed perpendicular to the flow direction are applied. The particle phase is assumed to behave as a viscous fluid. A numerical solution is obtained for the governing nonlinear momentum equations using finite differences. The effects of the magnetic-field parameter Ha, the non-Newtonian fluid characteristics (the flow index n), and the particle-phase viscosity beta on the transient behavior of the velocity, volumetric flow rates, and skin friction coefficients of both fluid and particle phases are studied. It is found that all the flow parameters for both phases decrease as the magnetic field increases or the flow index decreases. On the other hand, increasing the particle-phase viscosity increases the skin friction of the particle phase, but decreases the other flow parameters.