Stability of natural convection flow in a tall vertical enclosure under non-Boussinesq conditions

Abstract

We have examined the linear stability of the fully developed natural convection flow in a differentially heated tall vertical enclosure under non-Boussinesq conditions. The three-dimensional analysis of the stability problem was reduced to a two-dimensional one by the use of Squire's theorem. The resulting eigenvalue problem was solved using an integral Chebyshev collocation method. The influence of non-Boussinesq effects on the stability was studied. We have investigated the dependence of the critical Rayleigh number on the temperature difference. The results show that two different modes of instability are possible, one of which is new and due entirely to non-Boussinesq effects. Both types of instability are oscillatory, and the critical disturbance wave speed is zero only in the Boussinesq limit.