Abstract
The effect of an anisotropic permeability on thermal boundary layer flow in porous media is studied. The convective flow is induced by a vertical, uniformly heated surface embedded in a fluid-saturated medium. A leading-order boundary layer theory is presented. It is shown that the thickness of the resulting boundary layer flow is different from that obtained in an isotropic porous medium. In general, an anisotropic permeability induces a fluid drift in the spanwise direction, the strength of which depends on the precise nature of the anisotropy. Conditions are found which determine whether or not the boundary layer flow is three-dimensional.
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References
Castinel, G. and Combarnous, M.: 1974, Critère d'apparition de la convection naturelle dans une couche poreuse anisotrope horizontale,C. R. Acad. Sci. Ser. B 287, 701–704.
Chang, I. D. and Cheng, P.: 1983, Matched asymptotic expansions for free convection about an impermeable horizontal surface in a porous medium,Int. J. Heat Mass Transf. 26, 163–174.
Cheng, P. and Chang, I. D.: 1976, Buoyancy induced flows in a porous medium adjacent to impermeable horizontal boundaries,Int. J. Heat Mass Transf. 19, 1267–1772.
Cheng, P. and Hsu, C. T.: 1984, Higher order approximations for Darcian free convection about a semi-infinite vertical flat plate,Trans. A.S.M.E. J. Heat Transf. 106, 143–151.
Cheng, P. and Minkowycz, W. J.: 1977, Free convection about a vertical flat plate imbedded in a porous medium with application to heat transfer from a dike,J. Geophys. Res. 82 2040–2044.
Daniels, P. G. and Simpkins, P. G.: 1984, The flow induced by a heated vertical wall in a porous medium,Q. J. Mech. Appl. Math. 37, 339–354.
Epherre, J. F.: 1975, Critère d'apparition de la convection naturelle dans une couche poreuse anisotrope,Rev. Thermique 168, 949–950.
Kvernvold, O. and Tyvand, P. A.: 1979, Nonlinear thermal convection in anisotropic porous media,J. Fluid Mech. 90, 609–624.
McKibbin, R.: 1984, Thermal convection in layered and anisotropic porous media: A review in R. A. Wooding and I. White, (eds),Convective Flows in Porous Media, DSIR, Wellington, New Zealand, pp. 113–127.
Nield, D. A. and Bejan, A.: 1992,Convection in Porous Media, Springer-Verlag, Berlin.
Rees, D. A. S. and Riley, D. S.: 1985, Free convection above a near horizontal semi-infinite heated surface embedded in a saturated porous medium,Int. J. Heat Mass Transf. 28, 183–190.
Riley, D. S. and Rees, D. A. S.: 1985, Non-Darcy natural convection from arbitrarily inclined heated surfaces in saturated porous media,Q. J. Mech. Appl. Math. 38, 277–295.
Storesletten, L.: 1993, Natural convection in a horizontal porous layer with anisotropic thermal diffusivity,Transport in Porous Media 12, 19–29.
Tyvand, P. A. and Storesletten, L.: 1991, Onset of convection in an anisotropic porous medium with oblique principal axes,J. Fluid Mech. 226, 371–382.
Wooding, R. A.: 1978, Large-scale geothermal field parameters and convection theory,New Zealand J. Sci. 27, 219–228.
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Rees, D.A.S., Storesletten, L. The effect of anisotropic permeability on free convective boundary layer flow in porous media. Transp Porous Med 19, 79–92 (1995). https://doi.org/10.1007/BF00716050
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DOI: https://doi.org/10.1007/BF00716050