ON HYDROMAGNETIC CHANNEL FLOW OF A DUSTY FLUID INDUCED BY TOOTH PULSES

This paper deals with the problem of unsteady motion of an incompressi ble electrically conducting dusty fluid in a channel bounded by two ri gid, non-conducting, infinite parallel plates subject to the condition s that an external magnetic field is acting transversely to the plates and the flow is generated from rest due to velocity tooth pulses appl ied on the upper plate with the lower plate held fixed. It is assumed that no external electric field is imposed on the fluid-particle syste m and the magnetic Reynolds number is very small. the problem is solve d by the method of Fourier Analysis instead of applying the method of Laplace transforms which involves complicated inversions. The exact ex pressions for the velocities of the fluid and of the dust particles an d the skin-friction at the walls are obtained. The results are analyze d 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 stres ses. Finally, the exact solution of the problem is obtained by the met hod 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 simple r than the method of Laplace transforms.