Asymptotic analysis of the nonsteady micropolar fluid flow through a curved pipe. Issue 12 (9th September 2020)

• Record Type: Journal Article
• Authors: Pažanin, Igor; Radulović, Marko
• Is Part Of: Applicable analysis. Volume 99:Issue 12(2020)
• Page Start: 2045
• Page End: 2092
• Publication Date: 2020-09-09
• Subjects: Grigory Panasenko; Micropolar fluid -- curved pipe -- nonsteady flow -- asymptotic expansion -- error analysis; 35C20 -- 35Q35 -- 76M45; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2018.1553036
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: We consider the nonsteady flow of a micropolar fluid in a thin (or long) curved pipe via rigorous asymptotic analysis. Germano's reference system is employed to describe the pipe's geometry. After writing the governing equations in curvilinear coordinates, we construct the asymptotic expansion up to a second order. Obtained in the explicit form, the asymptotic approximation clearly demonstrates the effects of pipe's distortion, micropolarity and the time derivative. A detailed study of the boundary layers in space is provided as well as the construction of the divergence correction. Finally, a rigorous justification of the proposed effective model is given by proving the error estimates.