The second grade fluid flow problem in an infinite pipe

Article type: Research Article

Authors: Klovienė, N. | Pileckas, K.^;

Affiliations: Faculty of Mathematics and Informatics, Vilnius University, Vilnius, Lithuania. E-mails: konstantinas.pileckas@mif.vu.lt, neringa.kloviene@gmail.com

Note: [] Corresponding author: K. Pileckas, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko Str. 24, Vilnius, 03225 Lithuania. Tel.: +37052193050; Fax: +37052151585; E-mail: konstantinas.pileckas@mif.vu.lt

Abstract: The non-stationary equations describing the motion of the second grade fluid are studied in an infinite three-dimensional pipe of arbitrary cross-section. For sufficiently small data the existence of the unique Poiseuille type solution having a given time-dependent flow rate (flux) is proved. The velocity field U has all three components. However, we show that components U1, U2 are secondary in comparison with the axial velocity U3.

Keywords: Poiseuille solution, pipe flow, non-stationary solutions, second grade fluid flow

DOI: 10.3233/ASY-121159

Journal: Asymptotic Analysis, vol. 83, no. 3, pp. 237-262, 2013