Journal of Theoretical
and Applied Mechanics

50, 2, pp. 549-562, Warsaw 2012

Some exact solutions for Oldroyd-B fluid due to time dependent prescribed shear stress

Muhammad Jamil, Corina Fetecau, Mehwish Rana
The velocity field and the shear stress corresponding to motion of an Oldroyd-B fluid between two infinite coaxial circular cylinders are established by means of the Hankel transforms. The flow of the fluid is produced due to the time dependent axial shear stress applied on the boundary of the inner cylinder. The exact solutions, presented under a series form, can easily be specialized to give similar solutions for the Maxwell, second grade and Newtonian fluids performing the same motion. Finally, some characteristics of the motion as well as the influence of the material constants on the behavior of the fluid are underlined by graphical illustrations.
Keywords: Oldroyd-B fluid; velocity field; time-dependent shear stress; Hankel transform