A note on the stability of convection in a vertical slot

Abstract

The study of natural convection in a rectangular cavity whose side walls are maintained at different fixed temperatures can be regarded as one of the classical problems of thermal convection (see Batchelor 1954; Elder 1965 and Gill 1966). One aspect of this problem is the question of stability of the laminar flow solution for given values of the three governing parameters, the Rayleigh numberA= γgΔTL³/κν, the aspect ratioh=H/Land the Prandtl number σ = ν/κ. HereHis the height andLthe width of the cavity,Tis the temperature difference between the two walls andgthe acceleration due to gravity. The fluid filling the container has coefficient of expansion γ, thermal diffusivity κ and kinematic viscosity ν. Instead of studying the stability of the exact laminar flow solution, which is not a parallel flow, the stability of the following solution of the governing eauations is examined instead: