Abstract
The effect of thermal expansion on porous media convection is investigated by isolating first the solution of thermal expansion in the absence of convection which allows to evaluate the leading order effects that need to be included in the convection problem that is solved later. A relaxation of the Boussinesq approximation is applied and the relevant time scales for the formulated problem are identified from the equations as well as from the derived analytical solutions. Particular attention is paid to the problem of waves propagation in porous media and a significant conceptual difference between the isothermal compression problem in flows in porous media and its non-isothermal counterpart is established. The contrast between these two distinct problems, in terms of the different time scales involved, is evident from the results. While the thermal expansion is identified as a transient phenomenon, its impact on the post-transient solutions is found to be sensitive to the symmetry of the particular temperature initial conditions that are applied.
Similar content being viewed by others
References
Auriault, J.-L.: 1980, Dynamic behaviour of a porous medium saturated by a Newtonian fluid, Int. J. Engng Sci. 18, 775-785.
Auriault, J.-L.: 1999, Comments on the paper: local and global transitions to chaos and hysteresis in a porous layer heated from below, by P. Vadasz, Transport in Porous Media 37, 246-250.
Biot, M.A.: 1956a, Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low frequency range, The J. Acoust. Soc. America 28, 168-178.
Biot, M.A.: 1956b, Theory of propagation of elastic waves in a fluid-saturated porous solid. II. Higer frequency range, The J. Acoust. Soc. America 28, 179-191.
Gheorghita, St. I.: 1966, Mathematical Methods in Underground Hydro-Gaso-Dynamics, Romanian Academy Edn, Bucharest (in Romanian).
Levy, T.: 1979, Propagation of waves in a fluid-saturated porous elastic solid, Int. J. Engng Sci. 17, 1005-1014.
Vadasz, P.: 1999a, A note and discussion on J.-L. Ariault's letter: Comments on the paper-Local and global transitions to chaos and hysteresis in a porous layer heated from below, Transport in Porous Media 37, 251-254.
Vadasz, P.: 1999b, Local and global solutions for transitions to chaos and hysteresis in a porous layer heated from below, Transport in Porous Media 37, 213-245.
Vadasz, P. and Olek, S.: 1998, Transitions and chaos for free convection in a rotating porous layer, Int. J. Heat Mass Transfer 14, 1417-1435.
Vadasz, P. and Olek, S.: 1999a, Weak turbulence and chaos for low Prandtl number gravity driven convection in porous media, Transport in Porous Media 37, 69-91.
Vadasz, P. and Olek, S.: 1999b, Route to chaos for moderate prandtl number convection in a porous layer heated from below, Transport in Porous Media in press.
Vadasz, P. and Olek, S.: 1999c, Computational recovery of the homoclinic orbit in porous media convection, Int. J. Nonlinear Mechanics 34, 89-93.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Vadasz, P. The Effect of Thermal Expansion on Porous Media Convection Part 1: Thermal Expansion Solution. Transport in Porous Media 44, 421–443 (2001). https://doi.org/10.1023/A:1010708823008
Issue Date:
DOI: https://doi.org/10.1023/A:1010708823008