Viscous Flows Driven by Uniform Shear over a Porous Stretching Sheet in the Presence of Suction/Blowing

An analysis is carried out to study the steady two-dimensional flow of an incompressible viscous fluid past a porous deformable sheet, which is stretched in its own plane with a velocity proportional to the distance from the fixed point subject to uniform suction or blowing. A uniform shear flow of strain rate β is considered over the stretching sheet. The analysis of the result obtained shows that the magnitude of the wall shear stress increases with the increase of suction velocity and decreases with the increase of blowing velocity and this effect is more pronounced for suction than blowing. It is seen that the horizontal velocity component (at a fixed streamwise position along the plate) increases with the increase in the ratio of shear rate β and stretching rate (c) (i.e., β/c) and there is an indication of flow reversal. It is also observed that this flow reversal region increases with the increase in β/c. 1. Introduction Suction or injection (blowing) of a fluid through the bounding surface can significantly change the flow field and consequently affects the heat transfer rate from the surface. Injection or withdrawal of fluid through a porous bounding heated/cooled wall is of great general interest in practical problems such as cooling of films, cooling of wires, and coating of polymer fiber. The process of suction or blowing has its importance in many engineering and industrial activities such as in the design of thrust bearing and radial diffusers and thermal oil recovery. Suction is also applied to chemical processes to remove reactants whereas blowing is used to add reactants, prevent corrosion or scaling, and reduce the drag. During the last decades, the study of flow over a stretching surface has attracted much more interest of the researchers due to its various industrial applications such as extrusion of polymer sheets, continuous stretching, manufacturing plastic films, and artificial fibers. In a melt-spinning process, the extrudate from the die is generally drawn and simultaneously stretched into a sheet which is then solidified through quenching or gradual cooling by direct contact with the water. The mechanical properties of the final product depend crucially on the rate of cooling/heating along the surface while being stretched. Sakiadas [1] was the first to study boundary layer flow due to a rigid flat continuous surface moving in its own plane. Erickson et al. [2] analyzed the boundary layer flow due to the motion of a porous flat plate when the transverse velocity at the surface is nonzero. A detailed analysis of the boundary