Rigorous derivation of the asymptotic model describing a nonsteady micropolar fluid flow through a thin pipe

摘要

In this paper we study a time-dependent flow of an incompressible micropolar fluid through a pipe with arbitrary cross-section. The effective behavior of the flow is found by means of rigorous asymptotic analysis with respect to the small parameter representing the pipe's thickness. The complete asymptotic expansion (up to an arbitrary order) of the solution is constructed with detailed analysis of the boundary layers provided. The convergence of the expansion is proved justifying the usage of the formally derived asymptotic model. (C) 2018 Elsevier Ltd. All rights reserved.