Resumen de Study of a natural convection problem inside a cubical cavity from the point of view of dynamical systems
The dynamics of the natural convection flow in a cubical cavity heated from below with both adiabatic and perfectly conducting lateral walls was studied with methods from dynamical systems and bifurcations theories, A continuation procedure was developed to determine the steady solutions and bifurcations of the nonlinear governing equations aas a function of the Rayleigh number (Ra) for values of Ra up to 150000. The procedure was based on the Galerkin spectral method with a complete, divergent-free set of basis functions satisfying all boundary conditions. The convergence of the method was consistent with the number of modes used and the results compared well with numerical solutions of the equations of motion obtained by means of a fourth order accurate finite-difference solver.
Two values of the Prandtl number Pr=0.71 and Pr=130, corresponding to air and silicone oil, respectively, were studied.
Present results are in reasonable agreement with experimental data previously reported in the literature for both the adiabatic and perfectly conducting lateral walls boundary conditions. Bifurcation diagrams obtained by the parameter continuation method provide a good description of all stable convective flow patterns that coexist for different ranges of the Rayleigh number and of the transitions between them that were observed experimentally. Thus, the current study completes previously published numerical studies and provides a better and unambiguous description of previously reported experimental results.
