Flow of a Conducting Fluid with Suspension of Particles in Cylinders with Arbitrary Time Varying Pressure Gradient

Abstract

The problem of unsteady flow of a viscous incompressible conducting fluid containing a dilute suspension of small inert shperical particles in cylinders with circular and sectorial cross-sections, in the presence of a radial magnetic field, have been discussed. The analysis applies to flows with pressure gradients which are arbitrary functions on time. Explicit expressions for the exact velocities of the fluid and that of the particles are obtained by using the methods of operational calculus-the Laplace transform, the finite Hankel transforms etc. Numerical results have been obtained for the developing flow due to a constant pressure gradient, when the flow is taking place in a coaxial circular cylinder. The effects of mass concentration and relaxation time of particles and the magnetic field on the velocities have also been discussed.