The effect of Coriolis force on nonlinear convection in a porous medium

Author:

Riahi D. H.1

Affiliation:

1. Department of Theoretical and Applied Mechanics, University of Illinois at Urbana-Champaign, Urbana 61801, Illinois, USA

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.ForTa0(1), the rotational effect is not significant. For0(1)Ta0(RlogR), the Nusselt number decreases with increasingTafor a given Rayleigh numberR. The flow has always a finite number of modes, but with increasingTain this region, the number of modes decreases. The functional dependence of the Nusselt number onRandTais found to have discontinuities as the number of modesN*reduces toN*1. For0(RlogR)Ta0(R), the Nusselt number is proportional toRTa(logRTa). The stabilizing effect of rotation is so strong that the optimal solution has left with only one horizontal mode. ForTa=0(R), the Nusselt number becomes0(1)and the convection is inhibited entirely by rotation forTa>1π2R.

Publisher

Hindawi Limited

Subject

Mathematics (miscellaneous)

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