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.