THE EFFECT OF CORIOLIS FORCE ON NONLINEAR CONVECTION IN A POROUS MEDIUM

D. H. RIAHI

《International Journal of Mathematics and Mathematical Sciences》 1994卷 (1994/12) Pp. 515-536

https://doi.org/10.1155/S0161171294000761

摘要

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 T_α ＜＜ 0(1), the rotational effect is not significant. For 0(1) ＜＜ T_α ＜＜ 0(√R logR), the Nusselt number decreases with increasing T_α for a given Rayleigh number R. The flow has always a finite number of modes, but with increasing T_α 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(√R logR)＜＜ T_α ＜＜ 0(R), the Nusselt number is proportional to R/T_α (log R/T_α). The stabilizing effect of rotation is so strong that the optimal solution has left with only one horizontal mode. For T_α=0(R), the Nusselt number becomes 0(1) and the convection is inhibited entirely by rotation for T_α＞1/π^2 R.

關鍵字

Convection ； rotation ； nonlinear ； porous medium ； nonlinear convection