UNSTEADY-FLOW OF A DUSTY VISCOELASTIC FLUID THROUGH A COAXIAL PIPE

The flow of a dusty visco-elastic fluid through a coaxial pipe has been studied taking into consideration the volume fraction-phi of dust particles, when the axial pressure gradient is an arbitrary function of time. Making use of finite Hankel transform and Laplace transform, we have obtained the exact solutions of the velocities of the fluid and dust particles. The fluid flows in the direction of z-axis and the upper limit of phi has been taken as 0.1 in order to maintain the Saffman model. The maxima for both the velocities increase with the increase in the value of phi. Similarly maxima in both cases increase with the increase of lambda-1, the relaxation parameter. With the increase of b/a, the ratio of the radius of the outer cylinder to that of the inner cylinder, it is observed that the number of oscillations for both the velocities increase before reaching the steady state as also the time for reaching the maxima. The maxima increase with the increase of b/a in case of particle velocity but decrease in case of fluid velocity.