Z. Naturforsch. **68a,** 725 – 734
(2013)

doi:10.5560/ZNA.2013-0052

Effects of Side Walls on the Motion Induced by an Infinite Plate that Applies Shear Stresses to an Oldroyd-B Fluid

Mehwish
Rana,
Nazish
Shahid, and
Azhar
Ali Zafar

Abdus Salam School of Mathematical Sciences, GC University Lahore, Pakistan

Received April 30, 2013 / revised June 25, 2013 / published online September 18, 2013

Unsteady motions of Oldroyd-B fluids between two parallel walls perpendicular to a plate that applies two types of shears to the fluid are studied using integral transforms. Exact solutions are obtained both for velocity and non-trivial shear stresses. They are presented in simple forms as sums of steady-state and transient solutions and can easily be particularized to give the similar solutions for Maxwell, second-grade and Newtonian fluids. Known solutions for the motion over an infinite plate, applying the same shears to the fluid, are recovered as limiting cases of general solutions. Finally, the influence of side walls on the fluid motion, the distance between walls for which their presence can be neglected, and the required time to reach the steady-state are graphically determined.

*Key words:* Non-Newtonian Fluids; Shear Stress; Side Walls; Exact Solutions.