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Helical flow of an Oldroyd-B fluid due to a circular cylinder subject to time-dependent shear stresses. (English) Zbl 1273.76041
Summary: Exact solutions corresponding to the unsteady helical flow of an Oldroyd-B fluid due to an infinite circular cylinder subject to torsional and longitudinal time-dependent shear stresses are established using Hankel transforms. These solutions, presented under series form in terms of Bessel functions $$J _{0}(\cdot ), \, J _{1}(\cdot )$$ and $$J _{2}(\cdot )$$, can be easily specialized to give the similar solutions for Maxwell, Second grade and Newtonian fluids performing the same motion. Some characteristics of the motion, as well as the influence of pertinent parameters on the velocity profiles, are underlined by graphical illustrations.

##### MSC:
 76A10 Viscoelastic fluids
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