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Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 709836, 16 pages
Research Article

Extended Stokes' First Problem of an Oldroyd-B Fluid for Relatively Moving Half-Planes

Division of Mathematics, General Education Center, Chienkuo Technology University, 500 Changhua City, Taiwan

Received 20 October 2010; Accepted 31 January 2011

Academic Editor: Horst Ecker

Copyright © 2011 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.


An Oldroyd-B fluid suddenly disturbed by relatively moving half-planes is theoretically studied in this paper. This new problem, extended from the traditional Stokes' problem, recently attracts a great deal of attention due to its potential applications in engineering. Using integral transformations and dividing the original system into two subsystems, the exact solution is derived and shown in a series form. In addition to the general understanding of velocity developments, the effects of the relaxation time and the retardation time on the velocity profiles are examined in a series of figures. It is found that above two rheological parameters influence the induced flow in an opposite way. Other interesting characteristics are also elucidated from present results.