Transport in Porous Media

, Volume 62, Issue 2, pp 139-156

First online:

The Onset of Convection in an Inclined Anisotropic Porous Layer with Oblique Principle Axes

  • D. A. S. ReesAffiliated withDepartment of Mechanical Engineering, University of Bath Email author 
  • , L. StoreslettenAffiliated withDepartment of Mathematics, Agder University College
  • , A. PostelnicuAffiliated withDepartment of Thermo and Fluid Mechanics, Transylvania University of Brasov

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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.


free convection porous layer inclined layer anisotropy oblique axes instability