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

International Journal of Nonlinear Sciences and Numerical Simulation

Editor-in-Chief: Birnir, Björn

Editorial Board: Armbruster, Dieter / Bessaih, Hakima / Chou, Tom / Grauer, Rainer / Marzocchella, Antonio / Rangarajan, Govindan / Trivisa, Konstantina / Weikard, Rudi

8 Issues per year


IMPACT FACTOR 2016: 0.890

CiteScore 2016: 0.84

SCImago Journal Rank (SJR) 2016: 0.251
Source Normalized Impact per Paper (SNIP) 2016: 0.624

Mathematical Citation Quotient (MCQ) 2016: 0.07

Online
ISSN
2191-0294
See all formats and pricing
More options …
Volume 17, Issue 5

Issues

Nonhomogeneous Porosity and Thermal Diffusivity Effects on a Double-Diffusive Convection in Anisotropic Porous Media

Akil J. Harfash
Published Online: 2016-07-19 | DOI: https://doi.org/10.1515/ijnsns-2015-0139

Abstract

A model for double-diffusive convection in anisotropic and inhomogeneous porous media has been analysed. In particular, the effects of variable permeability, thermal diffusivity and variable gravity with respect to the vertical direction, have been studied. The validity of both the linear instability and global nonlinear energy stability thresholds are tested using three dimensional simulation. Our results show that the linear theory produce a good predicts on the onset of instability in the basic steady state. It is known that as Rc increases the onset of convection is more likely to be via oscillatory convection as opposed to steady convection, and the three dimensional simulation results show that as Rc increases, the actual threshold moving toward the nonlinear stability threshold and the behaviour of the perturbation of the solutions becomes more oscillated.

Keywords: double-diffusive; variable permeability; thermal diffusivity; finite differences; anisotropic porous media

MSC 2010: 76S05; 76Rxx; 35B35

References

  • [1] D. A. Nield and A. Bejan, Convection in porous media, 4th ed., Springer-Verlag, New York, 2013.Google Scholar

  • [2] G. Castinel and M. Combarnous, Natural convection in an anisotropic porous layer, Int. Chem. Eng. 17 (1977), 605–614.Google Scholar

  • [3] J. F. Epherre, Criterion for the appearance of natural convection in an anisotropic porous layer, Int. Chem. Eng. 17 (1977), 615–616.Google Scholar

  • [4] O. Kvernvold and P. A. Tyvand, Nonlinear thermal convection in anisotropic porous media, J. Fluid Mech. 90 (1979), 609–624.Google Scholar

  • [5] Y. Shiina, M. Hishida and P. A. Tyvand, Critical Rayleigh number of natural convection in high porosity anisotropic horizontal porous layers, Int. J. Heat Mass Transfer 53 (2010), 1507–1513.Google Scholar

  • [6] A. J. Harfash, Convection in a porous medium with variable gravity field and magnetic field effects, Transp. Porous Media 103 (2014), 361–379.Google Scholar

  • [7] A. J. Harfash, Stability analysis of penetrative convection in anisotropic porous media with variable permeability, J. Non-Equilib. Thermodyn. 39 (2014), 123–133.Web of ScienceGoogle Scholar

  • [8] A. J. Harfash, Magnetic effect on convection in a porous medium with chemical reaction effect, Transp. Porous Media 106 (2015), 163–179.Google Scholar

  • [9] A. J. Harfash and A. K. Alshara, Chemical reaction effect on double diffusive convection in porous media with magnetic and variable gravity effects, Korean J. Chem. Eng. 32 (2015), 1046–1059.Web of ScienceGoogle Scholar

  • [10] A. J. Harfash and A. K. Alshara, Magnetic field and throughflow effects on double-diffusive convection in internally heated anisotropic porous media, Korean J. Chem. Eng. 32 (2015), 1970–1985.Web of ScienceGoogle Scholar

  • [11] A. J. Harfash and A. K. Alshara, A direct comparison between the negative and positive effects of throughflow on the thermal convection in an anisotropy and symmetry porous medium, Z. Naturforsch. A 70 (2015), 383–394.Web of ScienceGoogle Scholar

  • [12] M. C. Kim, Nonlinear numerical simulation on the onset of Soret-driven motion in a silica nanoparticles suspension, Korean J. Chem. Eng. 30 (2013), 831–835.Web of ScienceGoogle Scholar

  • [13] M. C. Kim, Analysis of onset of buoyancy-driven convection in a fluid layer saturated in anisotropic porous media by the relaxed energy method, Korean J. Chem. Eng. 30 (2013), 1207–1212.Web of ScienceGoogle Scholar

  • [14] M. C. Kim and C. K. Choi, Density maximum effects on the onset of buoyancy-driven convection in a porous medium saturated with cold water, Int. J. Heat Mass Transfer 71 (2014), 313–320.Google Scholar

  • [15] D. Yadav, Hydrodynamic and Hydromagnetic Instability in Nanofluids, Lambert Academic Publishing, Germany, 2014.Google Scholar

  • [16] D. Yadav and G. S. Agrawal, The onset of convection in a binary nanofluid saturated porous layer, Int. J. Theor. Appl. Multiscale Mech. 2 (2012), 198–224.Google Scholar

  • [17] D. Yadav and G. S. Agrawal, The onset of double-diffusive nanofluid convection in a layer of a saturated porous medium with thermal conductivity and viscosity variation, J. Porous Media 16 (2013), 105–121.Google Scholar

  • [18] D. Yadav and M. C. Kim, Theoretical and numerical analyses on the onset and growth of convective instabilities in a horizontal anisotropic porous medium, J. Porous Media 17 (2014), 1061–1074.Google Scholar

  • [19] D. Yadav and M. C. Kim, The onset of transient Soret-driven buoyancy convection in nanoparticle suspensions with particle concentration dependent viscosity in a porous medium, J. Porous Media 18 (2015), 369–378.Google Scholar

  • [20] D. Yadav and M. C. Kim, Linear and non-linear analyses of Soret-driven buoyancy convection in a vertically orientated Hele-Shaw cell with nanoparticles suspension, Comput. Fluids 117 (2015), 139–148.Web of ScienceGoogle Scholar

  • [21] D. Yadav, D. Nam and J. Lee, The onset of transient Soret-driven MHD convection confined within a Hele-Shaw cell with nanoparticles suspension, J. Taiwan Inst. Chem. Eng. 58 (2016), 235–244.Web of ScienceGoogle Scholar

  • [22] A. J. Harfash, Three dimensional simulation of radiation induced convection, Appl. Math. Comput. 227 (2014), 92–101.Google Scholar

  • [23] A. J. Harfash, Three dimensional simulations for penetrative convection in a porous medium with internal heat sources, Acta Mech. Sinica 30 (2014), 144–152.Web of ScienceGoogle Scholar

  • [24] A. J. Harfash, Three dimensional simulations and stability analysis for convection induced by absorption of radiation, Int. J. Numer. Methods Heat Fluid Flow 25 (2015), 810–824.Google Scholar

  • [25] A. J. Harfash and A. K. Alshara, Three-dimensional simulation for problem of penetrative convection near the maximum density, J. Hydrodyn. 27 (2015), 292–303.Web of ScienceGoogle Scholar

  • [26] A. J. Harfash, Three dimensional simulations for convection induced by the selective absorption of radiation for the brinkman model, Meccanica 51 (2016), 501–515.Web of ScienceGoogle Scholar

  • [27] S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, Dover, New York, 1981.Google Scholar

  • [28] D. D. Joseph, Uniqueness criteria for the conduction-diffusion solution of the Boussinesq equations, Arch. Ration. Mech. Anal. 35 (1969), 169–177.Google Scholar

  • [29] Y. S. Li, J. M. Zhan and Y. Y. Luo, Unsteady phenomena in the double-diffusive convection flows at high Rayleigh number, Numer. Heat Transf. Part A Appl. 54 (2008), 1061–1083.Web of ScienceGoogle Scholar

  • [30] X. Liang, X. L. Li, D. X. Fu and Y. W. Ma, Complex transition of double-diffusive convection in a rectangular enclosure with height-to-length ratio equal to 4: Part I, Commun. Comput. Phys. 6 (2009), 247–268.Google Scholar

  • [31] Q. Qin, Z. A. Xia and Z. F. Tian, High accuracy numerical investigation of double-diffusive convection in a rectangular enclosure with horizontal temperature and concentration gradients, Int. J. Heat Mass Transfer 71 (2014), 405–423.Web of ScienceGoogle Scholar

  • [32] B. Zhao and Z. Tian, Numerical investigation of binary fluid convection with a weak negative separation ratio in finite containers, Phys. Fluids 27 (2015), 074102.Web of ScienceGoogle Scholar

About the article

Received: 2015-09-25

Accepted: 2016-06-06

Published Online: 2016-07-19

Published in Print: 2016-08-01


Citation Information: International Journal of Nonlinear Sciences and Numerical Simulation, Volume 17, Issue 5, Pages 205–220, ISSN (Online) 2191-0294, ISSN (Print) 1565-1339, DOI: https://doi.org/10.1515/ijnsns-2015-0139.

Export Citation

©2016 by De Gruyter. Copyright Clearance Center

Comments (0)

Please log in or register to comment.
Log in