Complete solutions to extended Stokes' problems

Abstract

The main object of the present study is to theoretically solve the viscous flow of either a finite or infinite depth, which is driven by moving plane(s). Such a viscous flow is usually named as Stokes first or second problems, which indicates the fluid motion driven by the impulsive or oscillating motion of the boundary, respectively. Traditional Stokes problems are firstly revisited, and three extended problems are subsequently examined. Using some mathematical techniques and integral transforms, complete solutions which can exactly capture the flow characteristics at any time are derived. The corresponding steady-state and transient solutions are readily determined on the basis of complete solutions. Current results have wide applications in academic researches and are of significance for future studies taking more boundary conditions and non-Newtonian fluids into account.