ISRN Applied Mathematics
Volume 2012, Article ID 274914, 12 pages
http://dx.doi.org/10.5402/2012/274914
Another Approach to the Extended Stokes’ Problems for the Oldroyd-B Fluid
Division of Mathematics, General Education Center, Chienkuo Technology University, Changhua City 500, Taiwan
Received 15 March 2012; Accepted 8 May 2012
Academic Editors: Y. Dimakopoulos, S. W. Gong, S. Prudhomme, and X.-S. Yang
Copyright © 2012 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.
Abstract
The extended Stokes problems, which study the flow suddenly driven by relatively moving half-planes, are reexamined for the Oldroyd-B fluid. This topic has been studied (Liu, 2011) by applying the series expansion to calculate the inverse Laplace transform. The derived solution was correct but tough to perform the calculation due to the series expansion of infinite terms. Herein another approach, the contour integration, is applied to calculate the inversion. Moreover, the Heaviside unit step function is included into the boundary condition to ensure the consistence between boundary and initial conditions. Mathematical methods used herein can be applied to other fluids for the extended Stokes’ problems.