The flow of an unsteady incompressible fluid with uniform distribution of dust particles through a narrowing system has been investigated analytically. In the proposed problem, Laplace transform techniques reduce the governing equations to zeroth order Bessel differential equation. The solutions thus obtained are in the form of Bessel functions and yield the velocity distributions of the fluid and dust particles. Expressions for shear stress are obtained for various cases and the solutions are plotted graphically to appreciate the effect of different parameters like Reynolds number, number density and the permeability of the porous medium on the velocity of dust and fluid phase.

narrowing channel, dusty fluid, pressure gradient, porous media.