Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 127070, 18 pages
doi:10.1155/2011/127070
Research Article

Effective Flow of Micropolar Fluid through a Thin or Long Pipe

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

Received 30 October 2010; Accepted 9 February 2011

Academic Editor: Saad A. Ragab

Copyright © 2011 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

The aim of this paper is to present the result about asymptotic approximation of the micropolar fluid flow through a thin (or long) straight pipe with variable cross section. We assume that the flow is governed by the prescribed pressure drop between pipe's ends. Such model has relevance to some important industrial and engineering applications. The asymptotic behavior of the flow is investigated via rigorous asymptotic analysis with respect to the small parameter, being the ratio between pipe's thickness and its length. In the case of circular pipe, we obtain the explicit formulae for the approximation showing explicitly the effects of microstructure on the flow. We prove the corresponding error estimate justifying the obtained asymptotic model.