Analysis of Shear Stress on Flow around Sudden Accelerated Plate (Stokes’ First Problem)

Abstract

Stokes' First Problem, often referred to as the "sudden accelerated plate," was studied using similarity method to obtain velocity and shear stress profile by analyzing the flow of an infinite body of fluid near a wall that experiences sudden motion. The flow is assumed to be Newtonian, viscous, and incompressible, while at initial condition the velocity considered as zero and the condition of the flow were at rest. The obtained results are then numerically solved employing Simpson's approximation. Furthermore, this study explores variations in velocity and shear stress at the wall across different time intervals. The study of the velocity profile within this scenario demonstrates its consistency with the non-slip condition and the specified boundary conditions. Specifically, for t > 0, the velocity of the flow at the surface (y = 0) aligns with the plate's speed, while at y = ∞, the velocity decreases to zero, mirroring the initial condition. The findings reveal that at the moment the plate initiates its motion (t = 0), the shear stress reaches its maximum value. As time progresses, the shear stress at the wall gradually decreases.