Unsteady Three–Dimensional Oscillatory Jeffrey Fluid Flow Over an Infinite Horizontal Plate with Periodic Suction

Suction is a well-established technique for boundary-layer control, yet the effects of periodic transverse suction on three-dimensional oscillatory flows of viscoelastic fluids remain unexplored. This study investigates the unsteady 3D oscillatory flow of a Jeffery fluid over an infinite horizontal porous plate, driven by an oscillating free-stream velocity and transverse sinusoidal suction. Using a regular perturbation expansion technique, analytical solutions for velocity, shear stresses, and pressure distribution are obtained. The results provide three key insights: increasing the Reynolds number enhances primary flow and reduces boundary-layer thickness, improving flow stability; higher fluid elasticity (Deborah number) thickens the boundary layer and modifies the pressure distribution, revealing the interplay between suction and viscoelasticity; and transverse suction generates three-dimensional secondary flows and complex shear stress patterns, which have not been reported previously. These findings offer important guidance for designing advanced laminar flow-control systems and recover classical Newtonian results as special cases.