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

• Published in: Mathematical problems in engineering Vol. 2015; no. 2015; pp. 1 - 8
• Main Author: Pazanin, Igor
• Format: Journal Article
• Language: English
• Published: Cairo, Egypt Hindawi Publishing Corporation 01.01.2015; John Wiley & Sons, Inc
• Subjects: Approximation; Asymptotic methods; Asymptotic properties; Asymptotic series; Distortion; Engineering; Fluid flow; Geometry; Incompressible flow; Incompressible fluids; Law; Mathematical analysis; Mathematical models; Pipe; Pipe flow; Pressure dependence; Pressure distribution; Spherical coordinates; Transformations; Viscosity
• ISSN: 1024-123X; 1563-5147
• DOI: 10.1155/2015/905406

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 withrespect 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 theeffective flow.