Abstract
This paper reports the analytical results on the incompressible micropolar fluid flowing through a thin (or long) cylindrical pipe filled with porous medium. We start from the Brinkman-type system governing the filtration of the micropolar flow and perform the asymptotic analysis in the critical case characterized by the strong coupling between the velocity and microrotation. The error estimates are also derived providing the rigorous justification of the proposed effective model.
Similar content being viewed by others
References
Aero, E.L., Kuvshinsky, E.V.: Fundamental equations of the theory of elastic media with rotationally interacting particles. Trans.: Sov. Phys. Solid State 2, 1272–1281 (1961)
Allaire, A.: Homogenization of the Navier Stokes equations in open sets perforated with thiny holes I. Abstract framework, a volume distribution of holes. Arch. Ration. Mech. Anal. 113, 209–259 (1991)
Ahmed, A., Nadeem, S.: Effects of magnetohydrodynamics and hybrid nanoparticles on a micropolar fluid with 6-types of stenosis. Results Phys. 7, 4130–4139 (2017)
Bayada, G., Benhaboucha, N., Chambat, M.: New models in micropolar fluid and their applications to lubrication. Math. Mod. Meth. Appl. Sci. 15, 343–374 (2005)
Beneš, M., Pažanin, I.: Effective flow of incompressible micropolar fluid through a system of thin pipes. Acta Appl. Math. 143, 29–43 (2016)
Bonnivard, M., Pažanin, I., Suárez-Grau, F.J.: Effects of rough boundary and nonzero boundary conditions on the lubrication process with micropolar fluid. Eur. J. Mech. B/Fluids 72, 501–518 (2018)
Bonnivard, M., Pažanin, I., Suárez-Grau, F.J.: A generalized Reynolds equation for micropolar flows past a ribbed surface with nonzero boundary conditions, ESAIM: Math. Model. Numer. Anal. 56, 1255–1305 (2022)
Brinkman, H.: A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles. Appl. Sci. Res. A1, 27–34 (1947)
Darcy, H.P.G.: Les fontaines publiques de la ville de Dijon. Victor Darmon, Paris (1856)
Dupuy, D., Panasenko, G., Stavre, R.: Asymptotic methods for micropolar fluids in a tube structure. Math. Mod. Meth. Appl. Sci. 14, 735–758 (2004)
Dupuy, D., Panasenko, G., Stavre, R.: Asymptotic solution for a micropolar flow in a curvilinear channel. Z. Angew. Math. Mech. 88, 793–807 (2008)
Eringen, A.C.: Theory of micropolar fluids. J. Math. Mech. 16, 1–16 (1966)
Haghighi, A.R., Shahbazi, M.: Mathematical modeling of micropolar fluid flow through an overlapping arterial stenosis. Int. J. Biomath. 08, 1550056 (2015)
Heywood, J.G., Rannacher, R., Turek, S.: Artificial boundaries and flux and pressure conditions for the incompressible Navier-Stokes equations. Int. J. Numer. Methods Fluids 22, 325–352 (1996)
Kamel, M.T., Roach, D., Hamdan, M.H.: On the micropolar fluid flow through porous media. In: Proceedings of the 11th WSEAS International conference on mathematical methods, computational techniques and inteligent systmes, 190–197 (2009)
Khanukaeva, DYu., Fillipov, A.N., Yadav, P.K., Tiwari, A.: Creeping fow of micropolar fluid parallel to the axis of cylindrical cells with porous layer. Eur. J. Mech. B/Fluids 76, 73–80 (2019)
Khanukaeva, DYu.: Filtration of micropolar liquid through a membrane composed of spherical cells with porous layer. Theor. Comput. Fluid Dyn. 34, 215–229 (2020)
Levy, T.: Fluid flow through an array of fixed particles. Int. J. Eng. Sci. 21, 11–23 (1983)
Lukaszewicz, G.: Micropolar Fluids: Theory and Applications. Birkhäuser, Boston (1999)
Marušić-Paloka, E.: Rigorous justification of the Kirchhoff law for junction of thin pipes filled with viscous fluid. Asymptot. Anal. 33, 51–66 (2003)
Marušić-Paloka, E., Pažanin, I.: Fluid flow through a helical pipe. Z. Angew. Math. Phys. 58, 81–99 (2007)
Marušić-Paloka, E., Pažanin, I., Marušić, S.: Comparison between Darcy and Brinkman laws in a fracture. Appl. Math. Comput. 218, 7538–7545 (2012)
Mekheimer, Kh.S., El Kot, M.A.: The micropolar fluid model for blood flow through a tapered artery with a stenosis. Acta Mech. Sinica 24, 637–644 (2008)
Nield, D.A., Bejan, A.: Convection in Porous Media. Springer-Verlag, New York (2006)
Pažanin, I.: Effective flow of micropolar fluid through a thin or long pipe. Math. Probl. Eng. (2011). https://doi.org/10.1155/2011/127070
Pažanin, I.: Asymptotic behavior of micropolar fluid flow through a curved pipe. Acta Appl. Math. 116, 1–25 (2011)
Pažanin, I.: On the micropolar flow in a circular pipe: the effects of the viscosity coefficients. Theor. Appl. Mech. Lett. 1, 062004 (2011)
Sanchez-Palencia, E.: On the asymptotics of the fluid flow past an array of fixed obstacles. Int. J. Eng. Sci. 20, 1291–1301 (1982)
Srinivasacharya, D., Srikanth, D.: Flow of a micropolar fluid through cathererized artery-a mathematical model. Int. J. Biomath. 5, 1250019 (2012)
Acknowledgements
This research has been supported by the Croatian Science Foundation under the project Multiscale problems in fluid mechanics - MultiFM (IP-2019-04-1140).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The author has no conflicts of interest to declare.
Additional information
Communicated by Rosihan M. Ali.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Pažanin, I. On the Filtration of Micropolar Fluid Through a Thin Pipe. Bull. Malays. Math. Sci. Soc. 46, 186 (2023). https://doi.org/10.1007/s40840-023-01583-2
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s40840-023-01583-2