Journal of Prime Research in Mathematics

# Flow of an Oldroyd-B fluid over an infinite plate subject to a time-dependent shear stress

Nazish Shahid
Abdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan.
Mehwish Rana
Abdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan.
M. A. Imran
Abdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan.

$$^{2}$$Corresponding Author: mehwishadnanrana@gmail.com

### Abstract

The velocity field and the shear stress corresponding to the unsteady flow of an Oldroyd-B fluid due to an infinite flat plate, subject to a time-dependent shear stress, are established in integral form using the Fourier cosine transform. Similar solutions for Maxwell, Second grade and Newtonian fluids are recovered as limiting cases of general solutions. These solutions satisfy both the governing equations and all imposed initial and boundary conditions. Finally, a comparison between the four models as well as the influence of the pertinent parameters on the fluid motion is underlined by graphical illustrations.

#### Keywords:

Unsteady motion, Oldroyd-B fluids, time-dependent shear stress.