Abstract
The onset of thermal convection in an isothermally heated, horizontal porous layer saturated with viscoelastic liquid was analyzed analytically under the linear theory. An existing constitutive model, which is rather simple, was employed to examine the effects of relaxation times. It is shown clearly that oscillatory instabilities can set in before stationary modes are exhibited. The peculiar behavior of the frequency at the critical state was discussed in connection to polymeric liquids.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Akhatov, I. S. and Chembarisova, R. G.: 1993, The thermoconvective instability in hydrodynamics of relaxational liquids, in: G. Gouesbet and A. Berlemont (eds), Instabilities in Multiphase Flows, Plenum Press, New York, pp. 277-287.
Alisaev, M. G. and Mirzadjanzade, A. K.: 1975, For the calculation of delay phenomenon in filtration theory, Izvestya Vuzov, Neft i Gaz. 6, 71-77.
Cheng, P.: 1978, Heat transfer in geothermal systems, Adv. Heat Transfer 14, 1-105.
Combarnous, M. and Bories, S.: 1975, Hydrothermal convection in saturated porous media, Adv. Hydrosci. 10, 231-307.
Horton, C. W. and Logers, F. T.: 1945, Convection currents in a porous medium, J. Appl. Phys. 16, 367-370.
Katto, Y. and Masuoka, T.: 1967, Criterion for onset of convection in a saturated porous medium, Int. J. Heat Mass Transfer 10, 297-309.
Kolkka, R. W. and Ierley, G. R.: 1987, On the convected linear stability of a viscoelastic Oldroyd-B fluid heated from below, J. Non-Newtonian Fluid Mech. 25, 209-237.
Lapwood, E. R.: 1948, Convection of a fluid in a porous medium, Proc. Camb. Phil. Soc. 44, 508-521.
Lee, G. J., Choi, C. K. and Kim, M. C.: 1993, The onset of convection in viscoelastic fluid layers cooled from above, Proc. of the 1st Int. Conf. on Transport Phenomena in Processing, Honolulu, pp. 774-784.
Lorenz, E. N.: 1963, Deterministic nonperiodic flow, J. Atmos. Sci. 20, 130-141.
Manole, D. M. and Lage, J. L.: 1993, The inertial effect on the natural convection flow within a fluid-saturated porous medium, Int. J. Heat Fluid Flow 14, 376-384.
Nield, D. A. and Bejan, A.: 1999, Convection in Porous Media, 2nd edn, Springer-Verlag, New York.
Nield, D. A., Manole, D. M. and Lage J. L.: 1993, Convection induced by thermal and solutal gradients in a shallow horizontal layer of a porous medium, J. Fluid Mech. 257, 559-574.
Straugehan, B.: 2001, A sharp nonlinear stability threshold in rotating porous convection, Proc. R. Soc. Lond. A 457, 87-93.
Vadasz, P.: 1998, Coriolis effect on gravity-driven convection in a rotating porous layer heated from below, J. Fluid Mech. 376, 351-375.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Yoon, DY., Kim, M.C. & Choi, C.K. The Onset of Oscillatory Convection in a Horizontal Porous Layer Saturated with Viscoelastic Liquid. Transport in Porous Media 55, 275–284 (2004). https://doi.org/10.1023/B:TIPM.0000013328.69773.a1
Issue Date:
DOI: https://doi.org/10.1023/B:TIPM.0000013328.69773.a1