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Mathematical Problems in Engineering
Volume 2015, Article ID 905406, 8 pages
http://dx.doi.org/10.1155/2015/905406
Research Article

Asymptotic Analysis of the Curved-Pipe Flow with a Pressure-Dependent Viscosity Satisfying Barus Law

Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia

Received 24 November 2014; Accepted 20 March 2015

Academic Editor: Ana Carpio

Copyright © 2015 Igor Pažanin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Curved-pipe flows have been the subject of many theoretical investigations due to their importance in various applications. The goal of this paper is to study the flow of incompressible fluid with a pressure-dependent viscosity through a curved pipe with an arbitrary central curve and constant circular cross section. The viscosity-pressure dependence is described by the well-known Barus law extensively used by the engineers. We introduce the small parameter (representing the ratio of the pipe’s thickness and its length) into the problem and perform asymptotic analysis with respect to . The main idea is to rewrite the governing problem using the appropriate transformation and then to compute the asymptotic solution using curvilinear coordinates and two-scale asymptotic expansion. Applying the inverse transformation, we derive the asymptotic approximation of the flow clearly showing the influence of pipe’s distortion and viscosity-pressure dependence on the effective flow.