Two-dimensional stagnation point flow of a dusty fluid near an oscillating plate

Abstract

The laminar boundary layer flow of a dusty fluid on an infinite flat plate normal to an oncoming stream, the plate making transverse oscillations in its own plane, has been studied. The fluid velocity and the velocity of the pseudofluid of dust particles has been shown to depend on a pair of coupled ordinary differential equations which have been solved by Karman-Pohlhausen method. It is found that the dimensionless boundary layer thickness increases either with the increase of α, the parameter representing the concentration of dust particles, or with increase in β, the parameter which increases with decrease in diameter of the dust particles. The steady part of the dimensionless skin friction at the plate decreases with increase in either α or β. The amplitude and the phase lead of the unsteady part of the dimensionless skin friction decreases with increase in β. The steady part of the dimensionless slip velocity of the particles does not depend upon α, but increases with increase in β. The amplitude and the phase lag of the unsteady part of the dimensionless slip velocity of the particles at the plate increases with increase in α and decreases with increase in β.