On the Berman Slip-Flow in a Parallel-Sided Channel with Porous Boundaries

The title problem which has recently been addressed in this journal is revisited in the present paper under a new point of view. It is shown that the joint effect of the Berman suction or injection normal to the boundaries and the velocity slip along the boundaries is equivalent to the sole effect of an oblique suction or injection of the fluid. The solution of the corresponding boundary value problem is given by a Maclaurin series expansion of the similar stream function to powers of the scaled transverse coordinate y/h. Compared to the classical Berman problem, the existence of several new solution branches of the oblique suction/injection problem is reported. Subsequently, the physical and mathematical aspects of the mentioned equivalence are discussed in the paper in some detail. It is pointed out that the vanishing midplane velocity represents the crossover from the physically feasible unidirectional flows to the unfeasible bidirectional flow configurations, where in the neighborhood of the midplane of the channel reverse flows occur.