Boundary layer flow of a dusty fluid over a semi-infinite flat plate

Summary

Both the drag force due to slip and the transverse force due to slip-shear have been considered in boundary layer equations. The solution has been found in a power series of non-dimensionalx, x being the distance in the down-stream direction. Solutions for high slip region and small slip region characterised byx≪1 andx≫1 respectively, have been found separately. In the high slip region the effect of increase in concentration parameter α of the dust particles is to increase the magnitude of the longitudinal fluid phase velocityu. Also the magnitude of the longitudinal particle slip velocityu _p -u is becoming maximum on the plate and decreasing along the plate withx. The transverse particle velocityv _p is independent of α but it is directly proportional to β, the transverse force coefficient. An interesting result is thatv _p is assuming small positive value on the plate. The transverse force has taken an important role in migration of particles away from the plate. In the small slip region the flow of dust particles is mainly governed by the fluid-phase. The effect of α on the flow field in this region is to decrease the boundary layer thickness. In this region the particles are having some tendency to accumulate near the plate. Lastly, it has been found that the shearing stress, skinfriction and the dimensionless drag-coefficient on the plate increase with increase of α.