an:05950216
Zbl 1221.76017
Jamil, M.; Fetecau, Constantin; Imran, M.
Unsteady helical flows of Oldroyd-B fluids
EN
Commun. Nonlinear Sci. Numer. Simul. 16, No. 3, 1378-1386 (2011).
00281869
2011
j
76A05
Oldroyd-B fluid; helical flows; velocity field; time-dependent shear stresses; Hankel transforms
Summary: The unsteady helical flow of an Oldroyd-B fluid, in an infinite circular cylinder, is studied by using finite Hankel transforms. The motion is produced by the cylinder that, at time \(t = 0^{+}\), is subject to torsional and longitudinal time-dependent shear stresses. The solutions that have been obtained, presented under series form, satisfy all imposed initial and boundary conditions. The corresponding solutions for Maxwell, second grade and Newtonian fluids are obtained as limiting cases of general solutions. Finally, the influence of the pertinent parameters on the fluid motion is underlined by graphical illustrations.