Magnetohydrodynamic Three-Dimensional Couette Flow of a Second-Grade Fluid with Sinusoidal Injection/Suction

A mathematical model for magnetohydrodynamic (MHD) three-dimensional Couette flow of an incompressible second-grade fluid is developed and analyzed theoretically. The application of normal sinusoidal injection at the lower fixed plate and its equivalent deduction by suction through the uniformlymoving upper plate leads to three-dimensional flow.Approximate solutions for components of velocity, pressure and skin friction are obtained. The effects of flow parameters such as Hartmann number, Reynolds number, suction/injection parameter, non-Newtonian parameter on velocity components, skin friction factors along main flow direction and transverse direction, and pressure through parallel porous plates are discussed graphically. It is noted that Hartmann number provides a mechanism to stable the skin friction component along the main flow direction.