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Mathematical Problems in Engineering
Volume 2018 (2018), Article ID 6759876, 16 pages
https://doi.org/10.1155/2018/6759876
Research Article

Asymptotic Approximation of the Nonsteady Micropolar Fluid Flow through a Circular Pipe

Department of Mathematics, Faculty of Science, University of Zagreb, Zagreb, Croatia

Correspondence should be addressed to Igor Pažanin; rh.htam@ninazap

Received 27 September 2017; Revised 2 January 2018; Accepted 29 January 2018; Published 11 April 2018

Academic Editor: Michael Vynnycky

Copyright © 2018 Igor Pažanin and Marko Radulović. 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

We study the nonsteady flow of a micropolar fluid through a thin cylindrical pipe. The asymptotic behaviour of the flow is found via asymptotic analysis with respect to the small parameter , representing the pipe’s thickness. The asymptotic approximation is derived in the form of the explicit formulae for the fluid velocity and microrotation. We also provide the numerical examples in order to visualize the effects of the micropolar nature of the fluid. The illustrations indicate the influence of the micropolarity on the effective flow of the fluid in the whole domain. In particular, those effects are most clearly observed for the velocity approximation near the boundary of the domain.