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Zeitschrift für Naturforschung A

A Journal of Physical Sciences

Editor-in-Chief: Holthaus, Martin

Editorial Board: Fetecau, Corina / Kiefer, Claus


IMPACT FACTOR 2017: 1.414

CiteScore 2018: 1.15

SCImago Journal Rank (SJR) 2018: 0.370
Source Normalized Impact per Paper (SNIP) 2018: 0.431

Online
ISSN
1865-7109
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Volume 72, Issue 3

Issues

Analysis of the Laminar Newtonian Fluid Flow Through a Thin Fracture Modelled as a Fluid-Saturated Sparsely Packed Porous Medium

Igor Pažanin / Pradeep G. Siddheshwar
Published Online: 2016-12-19 | DOI: https://doi.org/10.1515/zna-2016-0321

Abstract

In this article we investigate the fluid flow through a thin fracture modelled as a fluid-saturated porous medium. We assume that the fracture has constrictions and that the flow is governed by the prescribed pressure drop between the edges of the fracture. The problem is described by the Darcy-Lapwood-Brinkman model acknowledging the Brinkman extension of the Darcy law as well as the flow inertia. Using asymptotic analysis with respect to the thickness of the fracture, we derive the explicit higher-order approximation for the velocity distribution. We make an error analysis to comment on the order of accuracy of the method used and also to provide rigorous justification for the model.

Keywords: Asymptotic Analysis; Darcy-Lapwood-Brinkman Equation; Error Estimates; Thin Fracture

References

  • [1]

    H. Darcy, Les fontaines publiques de la ville de Dijon, Victor Darmon, Paris, 1856.Google Scholar

  • [2]

    H. Brinkman, Appl. Sci. Res. A1, 27 (1947).Google Scholar

  • [3]

    E. R. Lapwood, Math. Proc. Camb. Phil. Soc. 44, 508 (1948).CrossrefGoogle Scholar

  • [4]

    G. Panasenko, Appl. Anal.76, 363 (2000).CrossrefGoogle Scholar

  • [5]

    O. Gipouloux and E. Marušić-Paloka, Asymptotic behavior of the incompressible Newtonian flow through thin constricted fracture, Multiscale Problems in Science and Technology, Springer, 2002, p. 189.Google Scholar

  • [6]

    E. Marušić-Paloka and I. Pažanin, Z. Angew. Math. Phys. 58, 81 (2007).CrossrefGoogle Scholar

  • [7]

    I. Pažanin, Acta Appl. Math. 116, 1 (2011).CrossrefGoogle Scholar

  • [8]

    M. C. Pereira and R. P. Silva, Discret. Contin. Dyn. S. 33, 803 (2013).Google Scholar

  • [9]

    I. Pažanin and F. J. Suarez-Grau, Comput. Math. Appl. 68, 1915 (2014).CrossrefGoogle Scholar

  • [10]

    G. Panasenko and K. Pileckas, Nonlinear Anal.-Theor. 122, 125 (2015).CrossrefGoogle Scholar

  • [11]

    D-R. Chen, D. Y. H. Pui, and B. Y. H. Liu, Aerosol Sci. Technol. 23, 579 (1995).CrossrefGoogle Scholar

  • [12]

    A. Khalilli, A. J. Basu, and M. Huettel, Acta Mech. 123, 75 (1997).CrossrefGoogle Scholar

  • [13]

    M. M. Awartani, M. H. Hamdan, and R. A. Ford, Appl. Math. Comput. 169, 749 (2005).Google Scholar

  • [14]

    N. Merabet, H. Siyyam, and M. H. Hamdan, Appl. Math. Comput. 196, 679 (2008).Google Scholar

  • [15]

    C. Conca, F. Murat, and O. Pironneau, Japan J. Math. 20, 263 (1994).Google Scholar

  • [16]

    J. G. Heywood, R. Rannacher, and S. Turek, Int. J. Numer. Methods Fluids 22, 325 (1996).CrossrefGoogle Scholar

  • [17]

    E. Marušić-Paloka, I. Pažanin, and S. Marušić, Appl. Math. Comput. 218, 7538 (2012).Google Scholar

  • [18]

    S. Marušić and E. Marušić-Paloka, Asymptot. Anal. 23, 23 (2000).Google Scholar

About the article

Received: 2016-08-26

Accepted: 2016-11-14

Published Online: 2016-12-19

Published in Print: 2017-03-01


Citation Information: Zeitschrift für Naturforschung A, Volume 72, Issue 3, Pages 253–259, ISSN (Online) 1865-7109, ISSN (Print) 0932-0784, DOI: https://doi.org/10.1515/zna-2016-0321.

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[1]
Eduard Marušić-Paloka, Igor Pažanin, and Marko Radulović
Transport in Porous Media, 2019

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