International Journal of Mathematics and Mathematical Sciences
Volume 17 (1994), Issue 3, Pages 515-536
doi:10.1155/S0161171294000761
The effect of Coriolis force on nonlinear convection in a porous medium
Department of Theoretical and Applied Mechanics, University of Illinois at Urbana-Champaign, Urbana 61801, Illinois, USA
Received 6 January 1993
Copyright © 1994 D. H. Riahi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Nonlinear convection in a porous medium and rotating about vertical axis is studied in this paper. An upper bound to the heat flux is calculated by the method initiated first by Howard [6] for the case of infinite Prandtl number.
For Ta≪0(1), the rotational effect is not significant. For 0(1)≪Ta≪0(RlogR), the Nusselt number decreases with increasing Ta for a given Rayleigh number R. The flow has always a finite number of modes, but with increasing Ta in this region, the number of modes decreases. The functional dependence of the Nusselt number on R and Ta is found to have discontinuities as the number of modes N* reduces to N*−1. For 0(RlogR)≪Ta≪0(R), the Nusselt number is proportional to RTa(logRTa). The stabilizing effect of rotation is so strong that the optimal solution has left with only one horizontal mode. For Ta=0(R), the Nusselt number becomes 0(1) and the convection is inhibited entirely by rotation for Ta>1π2R.