Unsteady hydromagnetic laminar flow of a conducting dusty fluid between two parallel plates started impulsively from rest

TLDR: In this article, the Hartmann number has been used to measure the acceleration of the particles in the laminar motion of an electrically conducting, viscous and incompressible dusty fluid between two infinitely extended nonconducting parallel plates.

Abstract: The unsteady laminar motion of an electrically conducting, viscous and incompressible dusty fluid between two infinitely extended non-conducting parallel plates under a uniform transverse magnetic field, fixed relative to the fluid has been considered. The lower and the upper plate are started impulsively from rest and thereafter move with different but uniform velocities. The velocity fields for the conducting dusty fluid and non-conducting dust particle have been obtained in terms of three non-dimensional parametersl (concentration), σ (relaxation time parameter) andM (Hartmann number). The expressions for the discharge per unit breadth of the plate and the skin-friction at the lower plate are calculated. It is observed, from numerical calculations, that as the Hartmann number increases velocities of the dusty gas and dust particle increase when both the plates are in motion (velocity of the upper plate being equal to, greater than and less than that of the lower plate in the same direction) and decrease in case of Couette motion.