Mathematical Problems in Engineering
Volume 2008 (2008), Article ID 754262, 18 pages
Complete Solutions to Extended Stokes' Problems
General Education Center, Chienkuo Technology University, Changhua City 500, Taiwan
Received 20 January 2008; Revised 30 May 2008; Accepted 4 September 2008
Academic Editor: Francesco Pellicano
Copyright © 2008 Chi-Min Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.