Stability Analysis of Natural Convection in Vertical Cavities with Lateral Heating

Abstract

Thermal convection of air in two-dimensional vertical cavities is considered under the boundary conditions of the left and right vertical walls kept at different temperatures and the top and bottom horizontal walls subject to thermal insulation. Linear stability analysis of thermal convection is made with the aid of the Galerkin method in which the field variables are expanded in terms of Chebyshev polynomials and linear growth rates of steady states are computed using the QR algorithm. The results of the stability analysis for air with the Prandtl number 0.71 over the range of the cavity aspect ratio A from 1 to 10 show that with increase of the temperature difference between the two vertical walls the oscillatory motion first generated by the instability of steady convection is in the form of the Tollmien-Schlichting or the internal gravity waves according as A > 3.65 or A < 3.41 while for 3.41 < A < 3.65 the internal gravity waves are first generated after the preceding spatial flow transition of the hydraulic jump.