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Onset of Convection in an Anisotropic Porous Layer with Vertical Principal Axes

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Abstract

A Horton–Rogers–Lapwood problem for onset of thermal convection in a horizontal porous layer with anisotropic permeability and diffusivity is solved analytically. There is full 3D anisotropy, with the restriction that one of each set of principal axes points in the vertical direction. The porous layer has infinite horizontal extent. The upper and lower boundaries are taken to be impermeable and kept at constant temperatures. The critical Rayleigh number for the onset is calculated as a function of the five parameters governing the anisotropy: two permeability ratios, two diffusivity ratios and the angle (in the horizontal plane) between the principal axes of permeability and diffusivity.

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References

  • Beck, J.L.: Convection in a box of porous material saturated with fluid. Phys. Fluids 15, 1377–1383 (1972)

    Article  Google Scholar 

  • Castinel, G., Combarnous, M.: Critère d’apparition de la convection naturelle dans une couche poreuse anisotrope. C.R. Acad. Sci. Paris B287, 701–704 (1974)

    Google Scholar 

  • Epherre, J.F.: Critère d’apparition de la convection naturelle dans une couche poreuse anisotrope. Rev. Gén. Therm. 168, 949–950 (1975)

    Google Scholar 

  • Horton, C.W., Rogers, F.T.: Convection currents in a porous medium. J. Appl. Phys. 16, 367–379 (1945)

    Article  Google Scholar 

  • Kvernvold, O., Tyvand, P.A.: Nonlinear thermal convection in anisotropic porous media. J. Fluid Mech. 90, 609–624 (1979)

    Article  Google Scholar 

  • Lapwood, E.R.: Convection of a fluid in a porous medium. Proc. Camb. Philos. Soc. 44, 508–521 (1948)

    Article  Google Scholar 

  • Mahidjiba, A., Robillard, L., Vasseur, P., Mamou, M.: Onset of convection in an anisotropic porous layer of finite lateral extent. Int. Commun. Heat Mass Transf. 27, 333–342 (2000)

    Article  Google Scholar 

  • McKibbin, R.: Thermal convection in a porous layer: effects of anisotropy and surface boundary conditions. Transp. Porous Med. 1, 271–292 (1986)

    Article  Google Scholar 

  • Nield, D.A., Bejan, A.: Convection in Porous Media, 4th edn. Springer, New York (2013)

    Book  Google Scholar 

  • Rosenberg, N.D., Spera, F.J.: Role of anisotropy and/or layered permeability in hydrothermal convection. Geophys. Res. Lett. 17, 235–238 (1990)

    Article  Google Scholar 

  • Storesletten, L.: Natural convection in a horizontal porous layer with anisotropic thermal diffusivity. Transp. Porous Media 12, 19–29 (1993)

    Article  Google Scholar 

  • Storesletten, L.: Effects of anisotropy on convective flow through porous media. In: Ingham, D.B., Pop, I. (eds.) Transp. Phenom. Porous Media, pp. 261–283. Pergamon, Oxford (1998)

    Chapter  Google Scholar 

  • Storesletten, L.: Effects of anisotropy on convection in horizontal and inclined porous layers. In: Ingham, D.B., et al. (eds.) Emerging Technologies and Techniques in Porous Media, pp. 285–306. Kluwer, Dordrecht (2004)

    Chapter  Google Scholar 

  • Tyvand, P.A., Storesletten, L.: Onset of convection in an anisotropic porous medium with oblique principal axes. J. Fluid Mech. 226, 371–382 (1991)

    Article  Google Scholar 

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Correspondence to Peder A. Tyvand.

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Tyvand, P.A., Storesletten, L. Onset of Convection in an Anisotropic Porous Layer with Vertical Principal Axes. Transp Porous Med 108, 581–593 (2015). https://doi.org/10.1007/s11242-015-0489-6

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  • DOI: https://doi.org/10.1007/s11242-015-0489-6

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