Skip to main content Accessibility help
×
Home

Instabilities in a fluid overlying an inclined anisotropic and inhomogeneous porous layer

  • P. Deepu (a1), Sameer Dawande (a1) and Saptarshi Basu (a1)

Abstract

In this paper, linear stability analysis on a Newtonian fluid film flowing under the effect of gravity over an inclined porous medium saturated with the same fluid in isothermal condition is carried out. The focus is placed on the effect of the anisotropic and inhomogeneous variations in the permeability of the porous medium on the shear mode and surface mode instabilities. The fluid–porous system is modelled by a coupled two-dimensional Navier–Stokes/Darcy problem. The perturbation equations are solved numerically using the Chebyshev collocation method. Detailed stability characteristics as a function of the depth ratio (the ratio of the depth of the fluid layer to that of the porous layer), the anisotropic parameter (the ratio of the permeability in the direction of the basic flow to that in the direction transverse to the basic flow) and the inhomogeneity functions are presented.

Copyright

Corresponding author

Email address for correspondence: sbasu@mecheng.iisc.ernet.in

References

Hide All
Beavers, G. S. & Joseph, D. D. 1967 Boundary conditions at a naturally permeable wall. J. Fluid Mech. 30 (01), 197207.
Benjamin, T. B. 1957 Wave formation in laminar flow down an inclined plane. J. Fluid Mech. 2 (06), 554573.
Camporeale, C., Mantelli, E. & Manes, C. 2013 Interplay among unstable modes in films over permeable walls. J. Fluid Mech. 719, 527550.
Chang, M. H. 2006 Thermal convection in superposed fluid and porous layers subjected to a plane Poiseuille flow. Phys. Fluids 18 (3), 035104.
Chen, F. 1992 Salt-finger instability in an anisotropic and inhomogeneous porous substrate underlying a fluid layer. J. Appl. Phys. 71 (10), 52225236.
De Bruin, G. J. 1974 Stability of a layer of liquid flowing down an inclined plane. J. Engng Maths 8 (3), 259270.
Floryan, J. M., Davis, S. H. & Kelly, R. E. 1987 Instabilities of a liquid film flowing down a slightly inclined plane. Phys. Fluids 30, 983989.
Kandel, H. N. & Pascal, J. P. 2013 Inclined fluid-film flow with bottom filtration. Phys. Rev. E 88 (5), 052405.
Lin, S. P. 1967 Instability of a liquid film flowing down an inclined plane. Phys. Fluids 10 (2), 308313.
Liu, R. & Liu, Q. 2009 Instabilities of a liquid film flowing down an inclined porous plane. Phys. Rev. E 80 (3), 036316.
Malashetty, M. S. & Swamy, M. 2010 The onset of convection in a binary fluid saturated anisotropic porous layer. Intl J. Therm. Sci. 49 (6), 867878.
Nield, D. A. & Bejan, A. 2006 Convection in Porous Media. Springer.
Pascal, J. P. 1999 Linear stability of fluid flow down a porous inclined plane. J. Phys. D: Appl. Phys. 32 (4), 417422.
Pascal, J. P. 2006 Instability of power-law fluid flow down a porous incline. J. Non-Newtonian Fluid Mech. 133 (2), 109120.
Sadiq, I. M. R. & Usha, R. 2008 Thin Newtonian film flow down a porous inclined plane: stability analysis. Phys. Fluids 20 (2), 022105.
Shivakumara, I. S., Lee, J. & Chavaraddi, K. B. 2011 Onset of surface tension driven convection in a fluid layer overlying a layer of an anisotropic porous medium. Intl J. Heat Mass Transfer 54 (4), 9941001.
Yih, C.-S. 1963 Stability of liquid flow down an inclined plane. Phys. Fluids 6 (3), 321334.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Related content

Powered by UNSILO

Instabilities in a fluid overlying an inclined anisotropic and inhomogeneous porous layer

  • P. Deepu (a1), Sameer Dawande (a1) and Saptarshi Basu (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.