Thermohaline convection with cross-diffusion in an anisotropic porous medium. (English) Zbl 0669.76123
Using normal mode technique it has been shown that (i) values of the anisotropy parameter are important in deciding the mode of convection in a doubly diffusive fluid saturating a porous medium. (ii) Depending on the values of the Soret and Dufour parameters, an increase in anisotropy parameter either promotes or inhibits instability, (iii) cross-diffusion induces instability even in a potentially stable set-up and (iv) for certain values of the Dufour and Soret parameters there is a discontinuity in the critical thermal Rayleigh number, which disappears if the problem medium has horizontal isotropy.
References:
| [1] | Chandrasekhar, S., Hydrodynamic and hydromagnetic stability (1961), Oxford: University Press, Oxford · Zbl 0142.44103 |
| [2] | Cussler, E. L., Multicomponent diffusion (1976), Oxford, New York Amsterdam: Elsevier Scientific Publishing Company, Oxford, New York Amsterdam |
| [3] | Hurle, D. T J.; Jakeman, E., Soret-driven thermosolutal convection, J. Fluid Mech., 47, 667-687 (1971) · doi:10.1017/S0022112071001319 |
| [4] | Ingle, S. E.; Horne, F. H., The Dufour effect, J. Chem. Phys., 59, 5882-5894 (1973) · doi:10.1063/1.1679957 |
| [5] | Knobloch, Convection in binary fluids, Phys. Fluids, 23, 1918-1920 (1980) · doi:10.1063/1.863220 |
| [6] | McDougall, T. J., Double-diffusive convection caused by coupled molecular diffusion, J. Fluid. Mech., 126, 379-397 (1983) · Zbl 0547.76097 · doi:10.1017/S0022112083000221 |
| [7] | Neale, G., Degrees of anisotropy for fluid flow and diffusion (electrical conduction) through anisotropic porous media, Am. Inst. Chem. Eng. J., 23, 56-62 (1977) |
| [8] | Nield, D. A., The thermohaline Rayleigh-Jeffreys problem, J. Fluid Mech., 29, 545-558 (1967) · doi:10.1017/S0022112067001028 |
| [9] | Taslim, M. E.; Narusawa, U., Binary fluid convection and double-diffusive convection in a porous medium, ASME J. Heat Transfer, 108, 221-224 (1986) · doi:10.1115/1.3246892 |
| [10] | Tyvand, P. A., Thermohaline instability in anisotropic porous media, Water Resour. Res., 16, 325-330 (1980) · doi:10.1029/WR016i002p00325 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
