Abstract
We consider the onset of convection in an inclined anisotropic porous layer heated from below. To date the principle axes of the permeability and diffusivity tensors have been assumed to be aligned with the coordinate directions. Therefore particular emphasis is laid upon how the basic flow and criteria for the onset of convection are altered by the presence of oblique principle axes. When these axes are not aligned with the coordinate directions and when the ratios of the principle permeabilities or diffusivities are not too large or too small, we find that there is always a smooth transition in the orientation of the most dangerous mode of instability as the inclination increases from the horizontal. In more extreme cases there may be sudden changes in the orientation, Darcy–Rayleigh number and wavenumber.
Similar content being viewed by others
References
S. Bories M. Combarnous (1973) ArticleTitleNatural convection in a sloping porous layer J. Fluid Mech. 57 63–79
S. Bories M. Combarnous J. Y. Jaffrennou (1972) ArticleTitleObservation des différentes formes d’écoulements thermoconvectifs dans une couche poreuse inclinée C.R. Acad. Sci. Paris A275 857–860
S. Bories L. Monferran (1972) ArticleTitleCondition de stabilité et échange thermique par convection naturelle dans une couche poreuse inclinée de grande extension C. R. Acad. Sci. Paris B274 4–7
A. Postelnicu D. A. S. Rees (2001) ArticleTitleThe onset of convection in an anisotropic porous layer inclined at a small angle from the horizontal Int. Com. Heat Mass Transfer 28 641–650
D. A. S. Rees (2002) ArticleTitleThe onset of Darcy-Brinkman convection in a porous layer: an asymptotic analysis Int. J. Heat Mass Transfer 45 2213–2220 Occurrence Handle10.1016/S0017-9310(01)00332-5
D. A. S. Rees A. P. Bassom (2000) ArticleTitleThe onset of Darcy–Bénard convection in an inclined layer heated fom below Acta Mechanica 144 103–118 Occurrence Handle10.1007/BF01181831
D. A. S. Rees A. Postelnicu (2001) ArticleTitleThe onset of convection in an inclined anisotropic porous layer Int. J. Heat Mass Transfer 44 4127–4138
D. A. S. Rees L. Storesletten (2002) ArticleTitleThe linear instability of a thermal boundary layer with suction in an anisotropic porous medium Fluid Dyn. Res. 30 155–168 Occurrence Handle10.1016/S0169-5983(02)00035-7
L. Storesletten M. Tveitereid (1999) ArticleTitleOnset of convection in an inclined porous layer with anisotropic permeability Appl. Mech. Engng. 4 575–587
M. Trew R. McKibbin (1994) ArticleTitleConvection in anisotropic inclined porous layers Transport Porous Media 17 271–283 Occurrence Handle10.1007/BF00613587
J. E. Weber (1974) ArticleTitleThermal convection in a tilted porous layer Int. J. Heat Mass Transfer 18 474–475
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Rees, D.A.S., Storesletten, L. & Postelnicu, A. The Onset of Convection in an Inclined Anisotropic Porous Layer with Oblique Principle Axes. Transp Porous Med 62, 139–156 (2006). https://doi.org/10.1007/s11242-005-0618-8
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s11242-005-0618-8