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

Mathematical Problems in Engineering. 2015;2015 DOI 10.1155/2015/905406


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Journal Title: Mathematical Problems in Engineering

ISSN: 1024-123X (Print); 1563-5147 (Online)

Publisher: Hindawi Limited

LCC Subject Category: Technology: Engineering (General). Civil engineering (General) | Science: Mathematics

Country of publisher: United Kingdom

Language of fulltext: English

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Igor Pažanin (Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia)


Blind peer review

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Time From Submission to Publication: 26 weeks


Abstract | Full Text

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 ε (representing the ratio of the pipe’s thickness and its length) into the problem and perform asymptotic analysis with respect to ε. 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.