On Hydromagnetic Channel Flow of a Dusty Fluid Induced by Tooth Pulses

Abstract

This paper deals with the problem of unsteady motion of an incompressible electrically conducting dusty fluid in a channel bounded by two rigid, non-conducting, infinite parallel plates subject to the conditions that an external magnetic field is acting transversely to the plates and the flow is generated from rest due to velocity tooth pulses applied on the upper plate with the lower plate held fixed. It is assumed that no external electric field is imposed on the fluid-particle system and the magnetic Reynolds number is very small. the problem is solved by the method of Fourier Analysis instead of applying the method of Laplace transforms which involves complicated inversions. The exact expressions for the velocities of the fluid and of the dust particles and the skin-friction at the walls are obtained. The results are analyzed quantitatively with a view to find the effects of the magnetic field and the dust particles on the flow as well as on the wall shear stresses. Finally, the exact solution of the problem is obtained by the method of Laplace transforms and this result has been compared with that of the present one. It is found that both the methods provide the same exact solution although the method of Fourier analysis is much simpler than the method of Laplace transforms.