Convective instability of a vertical thermal boundary layer in a differentially heated cavity

The convective instability of a vertical thermal boundary layer adjacent to the sidewall of a water-filled differentially heated cavity over a range of Rayleigh numbers (5 × 107–3.44 × 109) is investigated using direct stability analysis. The results show that the dominant frequency of the convective instability changes as perturbations travel downstream due to the presence of the horizontal boundaries, which is different from that of the vertical thermal boundary layer adjacent to an infinite or semi-infinite thermal wall. The features of the convective instability of the vertical thermal boundary layer adjacent to the sidewall are described, and the dependence of the dominant frequency on the Rayleigh number is obtained. Furthermore, the dependence of the flow rate and heat transfer through the cavity on the Rayleigh number is quantified by numerical results.