Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Zeitschrift für Naturforschung A

A Journal of Physical Sciences

Editor-in-Chief: Holthaus, Martin

Editorial Board: Fetecau, Corina / Kiefer, Claus

12 Issues per year


IMPACT FACTOR 2016: 1.432

CiteScore 2017: 1.30

SCImago Journal Rank (SJR) 2017: 0.403
Source Normalized Impact per Paper (SNIP) 2017: 0.632

Online
ISSN
1865-7109
See all formats and pricing
More options …
Volume 70, Issue 5

Issues

A Direct Comparison between the Negative and Positive Effects of Throughflow on the Thermal Convection in an Anisotropy and Symmetry Porous Medium

Akil J. Harfash / Ahmed K. Alshara
Published Online: 2015-04-14 | DOI: https://doi.org/10.1515/zna-2015-0049

Abstract

The linear and nonlinear stability analysis of the motionless state (conduction solution) and of a vertical throughflow in an anisotropic porous medium are tested. In particular, the effect of a nonhomogeneous porosity and a constant anisotropic thermal diffusivity have been taken into account. Then, the accuracy of the linear instability thresholds are tested using a three dimensional simulation. It is shown that the strong stabilising effect of gravity field. Moreover, the results support the assertion that the linear theory, in general, is accurate in predicting the onset of convective motion, and thus, regions of stability.

Keywords: Anisotropic Porous Media; Finite Differences; Linear Instability; Nonlinear Stability; Throughflow

References

  • [1]

    B. Straughan, Mathematical Aspects of Penetrative Convection, Longman, New York 1993.Google Scholar

  • [2]

    P. H. Roberts, J. Fluid Mech. 30, 33 (1967).Google Scholar

  • [3]

    P. C. Matthews, J. Fluid Mech. 188, 571 (1988).Google Scholar

  • [4]

    B. Straughan and D. W. Walker, Proc. R. Soc. Lond. A 452, 97 (1996).Google Scholar

  • [5]

    A. J. Harfash, Transp. Porous Med. 101, 281 (2014).Google Scholar

  • [6]

    A. J. Harfash, Transp. Porous Med. 102, 43 (2014).Google Scholar

  • [7]

    A. J. Harfash, Transp. Porous Med. 103, 361 (2014).Google Scholar

  • [8]

    M. C. Kim, Korean J. Chem. Eng. 30, 1207 (2013).Google Scholar

  • [9]

    M. M. Rashidi, S. Abelman, and N. Freidooni Mehr, Int. J. Heat Mass Trans. 62, 515 (2013).Google Scholar

  • [10]

    S. Noreen, Z. Naturforsch. A 70, 3 (2015).Google Scholar

  • [11]

    N. S. Akbar and A. W. Butt, Z. Naturforsch. A 70, 23 (2015).Google Scholar

  • [12]

    M. Sheikholeslami, R. Ellahi, M. Hassan, and S. Soleimani, Int. J. Numer. Meth. Heat Fluid Flow 24, 1906 (2014).Google Scholar

  • [13]

    M. Sheikholeslami, M. G. Bandpy, R. Ellahi, and A. Zeeshan, J Magn. Magn. Mater. 369, 69 (2014).Google Scholar

  • [14]

    A. Zeeshan, R. Ellahi, and M. Hassan, Eur. Phys. J. Plus 129, 261 (2014).Google Scholar

  • [15]

    R. Ellahi, A. Riaz, S. Abbasbandy. T. Hayat, and K. Vafai, Therm. Sci. J. 18, 1247 (2014).Google Scholar

  • [16]

    D. A. Nield and A. Bejan, Convection in Porous Media. 4th Ed., Springer-Verlag, New York 2013.Google Scholar

  • [17]

    S. Abbasbandy, T. Hayat, R. Ellahi, and S. Asghard, Z. Naturforsch. A 64, 59 (2009).Google Scholar

  • [18]

    T. Hayat, R. Ellahi, and F. M. Mahomed, Z. Naturforsch. A 64, 531 (2009).Google Scholar

  • [19]

    A. J. Harfash and A. A. Hill, Int. J. Heat Mass Trans. 72, 609 (2014).Google Scholar

  • [20]

    I. S. Shivakumara and A. Khalili, Transp. Porous Med. 53, 245 (2003).Google Scholar

  • [21]

    I. S. Shivakumara and S. Sureshkumar, J. Geophys. Eng. 4, 104 (2007).CrossrefGoogle Scholar

  • [22]

    D. A. Nield and A. V. Kuznetsov, Transp. Porous Med. 87, 765 (2011).Google Scholar

  • [23]

    A. A. Hill, S. Rionero, and B. Straughan, IMA J. App. Math. 72, 635 (2007).Google Scholar

  • [24]

    F. Capone, M. Gentile, and A. A. Hill, Acta Mech. 208, 205 (2009).Google Scholar

  • [25]

    A. J. Harfash, J. Non-Equilib. Thermodyn 139, 123 (2014).Google Scholar

  • [26]

    A. J. Harfash, Transp. Porous Media, 106, 163 (2015).Google Scholar

  • [27]

    B. Straughan, The Energy Method, Stability, and Nonlinear Convection. Springer, Series in Applied Mathematical Sciences, Vol. 91, 2nd Ed. (2004).Google Scholar

About the article

Corresponding author: Akil J. Harfash, Department of Mathematics, College of Sciences, University of Basrah, Basrah, Iraq, E-mail:


Received: 2015-02-02

Accepted: 2015-03-18

Published Online: 2015-04-14

Published in Print: 2015-05-01


Citation Information: Zeitschrift für Naturforschung A, Volume 70, Issue 5, Pages 383–394, ISSN (Online) 1865-7109, ISSN (Print) 0932-0784, DOI: https://doi.org/10.1515/zna-2015-0049.

Export Citation

©2015 by De Gruyter.Get Permission

Comments (0)

Please log in or register to comment.
Log in