Analytical solution for flow of a dusty fluid in a circular pipe with hall and ion slip effects

Unsteady flow of a dusty electrically conducting incompressible viscous fluid in a circular pipe is studied considering ion slip. 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 nonconducting fluid. A series solution for the governing equations of both fluid and particle phases is obtained for the whole range of physical parameters.