On some helical flows of Oldroyd-B fluids.

*(English)*Zbl 1108.76008Summary: 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 \(t\).

PDF
BibTeX
XML
Cite

\textit{C. Fetecau} et al., Acta Mech. 189, No. 1--2, 53--63 (2007; Zbl 1108.76008)

Full Text:
DOI

##### References:

[9] | Rajagopal, K. R.: Mechanics of non-Newtonian fluids. In: Recent developments in theoretical fluid mechanics, Pitman Research Notes in Mathematics, vol. 291, pp. 129–162. New York: Longman 1993. · Zbl 0818.76003 |

[16] | Sneddon, I. N.: Functional analysis. In: Encyclopedia of Physics, vol. II. Berlin GĂ¶ttingen Heidelberg: Springer 1955. |

[19] | Fetecau, C., Prasad, Sharat C., Rajagopal, K. R.: A note on the flow induced by a constantly accelerating plate in an Oldroyd-B fluid. To appear in AMM (Applied Mathematical Modelling). · Zbl 1287.76047 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.