International Journal of Mathematics and Mathematical Sciences
Volume 12 (1989), Issue 3, Pages 559-578
doi:10.1155/S0161171289000694
Flow of a dusty fluid due to Wavy motion of a wall for moderately large Reynolds numbers
Department of Mathematics, Indian Institute of Technology, Kharagpur 721302, India
Received 22 January 1987
Copyright © 1989 V. Ramamurthy and U. S. Rao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.