Flow of a dusty fluid due to Wavy motion of a wall for moderately large Reynolds numbers

Abstract

The two-dimensional flow of a dusty fluid induced by sinusoidal wavy motion of an infinite wavy wall is considered for Reynolds numbers which are of magnitude greater than unity. While the velocity components of the fluid and the dust particles along the axial direction consist of a mean steady flow and a periodic flow, the transverse components of both the fluid and the dust consist only of a periodic flow. This is true both for the outer flow (the flow beyond the boundary layer) and the inner flow (boundary layer flow). It is found that the mean steady flow is proportional to the ratio 4π2a2/L2(a/L<<1) , where a and L are the amplitude and the wavelength of the wavy wall, respectively. Graphs of the velocity components, both for the outer flow and the inner flow for various values of mass - concentration of the dust particles are drawn. It is found that the steady flow velocities of the fluid and the dust particles approach to a constant value. Certain interesting results regarding the axial and the transverse velocity components are also discussed.