In this study, we model and theoretically analyze a free convective three-dimensional flow of an incompressible second-grade fluid through a highly porous medium bounded by an infinite vertical porous plate subjected to a constant suction. We assume the permeability of the medium to be periodic and the free stream velocity to be uniform. The assumption of either constant or time-dependent permeability of a porous medium leads to two-dimensional flows; however, the flow becomes three-dimensional due to variable permeability of the porous medium. We obtain analytic solutions for velocity field, pressure, skin friction components, temperature distribution, and discuss and graphically visualize effects of physical parameters emerging in the mathematical model of the physical phenomenon on these physical quantities. We note that the main flow velocity component decreases due to enhancement in non-Newtonian parameter; however, the pressure rises due to thickening of the fluid. MSC: 30E25; 47A52; 76Sxx; 80A20

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Laminar flow control plays a vital role in reducing drag resulting enhancement in the vehicle power by a significant amount. Theoretical and experimental studies have proven that the transition from laminar to turbulent flow (causing the drag coefficient to enhance) may be delayed/prevented by the suction of the fluid from the boundary layer to the wall. The purpose of this work is to study the effects of periodic suction on the unsteady 3-dimensional fluctuating flow of a second grade incompressible fluid flowing laminarly over a horizontal porous infinite plate. The plate is subjected to a sinusoidal transverse suction velocity while the free stream velocity oscillates in time about a constant mean. The flow turns out to be 3-dimensional because of transverse direction of the periodic suction velocity. By the series expansion method, analytic expressions for transient velocity, skin friction components, and pressure are attained. Impact of nondimensional parameters evolving in the mathematical model of the problem on these physical quantities are visualized graphically and discussed analytically. The velocity component u is found to be rising with a growth in suction parameter α. The pressure is noted to be growing with a growth in Reynolds number R e . Further, due to suction at the plate and transient free stream velocity, the pressure increases near the plate and then reaches to a steady value far-off the plate. The skin friction along the main flow is noticed to be decreasing with the rise in α for 0.5 ≤ R e ≤ 1.4 , however, an exponential rise is observed for R e > 1.4. The skin friction along the cross flow is noted to be enhancing for the rising values of suction parameter and elastic parameter. The present results have excellent agreement with previous published results in the limiting sense. This study is beneficial in designing and manufacturing laminar flow control system to enhance the vehicle power requirement.