Asymptotic behaviour of a class of incompressible, quasi-Newtonian fluids in thin pipes

Article type: Research Article

Authors: Ichim, Andrei

Affiliations: Université Blaise Pascal, Clermont-Ferrand II, Laboratoire de Mathématiques CNRS-UMR 6620, Campus des Cézeaux, F-63177 Aubière Cedex, France. E-mail: andrei.ichim@math.univ-bpclermont.fr

Abstract: The aim of this paper is to study the asymptotic behaviour of a wide class of incompressible quasi-Newtonian fluids flowing through a thin 3D pipe, with prescribed pressure variance at the ends. The small parameter is given by the ratio between the diameter of the cross section and the length. We prove that, if the domain satisfies a particular geometric condition at the ends, a complete asymptotic expansion can be obtained.

Keywords: quasi-Newtonian fluids, thin pipes, asymptotic expansion

DOI: 10.3233/ASY-151327

Journal: Asymptotic Analysis, vol. 95, no. 3-4, pp. 325-344, 2015