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On some helical flows of Oldroyd-B fluids. (English) Zbl 1108.76008
Summary: The velocity fields and the associated tangential stresses corresponding to some helical flows of Oldroyd-B fluids between two infinite coaxial circular cylinders and within an infinite circular cylinder are determined in forms of series in Bessel functions. At time \(t = 0\) the fluid is at rest, and the motion is produced by combined action of rotating and sliding cylinders. The solutions obtained satisfy the governing differential equations and all imposed initial and boundary conditions. For \(\lambda _{ r } = 0\), \(\lambda = 0\) or \(\lambda _{ r } = \lambda = 0\) they reduce to similar solutions for Maxwell, second-grade or Newtonian fluid, respectively (here \(\lambda\) is a characteristic relaxation time, and \(\lambda_r\) is a characteristic retardation time). Finally, for comparison, the velocity profiles corresponding to the four models are plotted for different values of \(t\).

MSC:
76A10 Viscoelastic fluids
76U05 General theory of rotating fluids
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