ABSTRACT
The critical Rayleigh number Ra_cr of the Hopf bifurcation that signals the limit of steady flows in a differentially heated 8:1:1 cavity is computed. The two-dimensional analog of this problem was the subject of a comprehensive set of benchmark calculations that included the estimation of Ra_cr [1]. In this work we begin to answer the question of whether the 2D results carry over into 3D models. For the case of the 2D model being extruded for a depth of 1, and noslip/no-penetration and adiabatic boundary conditions placed at these walls, the steady flow and destabilizing eigenvectors qualitatively match those from the 2D model. A mesh resolution study extending to a 20-million unknown model shows that the presence of these walls delays the first critical Rayleigh number from 3.06 × 10⁵ to 5.13 × 10⁵ .