Nonlinear characters of natural convection around a horizontal plate in an enclosure

Numerical investigation using SIMPLE algorithm with QUICK scheme for the nonlinear phenomena of natural convection around a horizontal flat plate has been conducted. It can be found from the numerical results that flow and heat transfer around the horizontal flat plate will be steady at small Rayleigh numbers. When the Rayleigh number is over some critical value, it can be found that flow and heat transfer will be asymmetry which indicates unsteady oscillation occurs. By nonlinear analyses, it is shown that with the increase of Rayleigh number, flow and heat transfer will change from steady to unsteady state through HOPF bifurcation, and transition to chaos will occurs through multi-periodical oscillation. In the chaotic region, even though it is difficult to predict flow pattern, periodical windows still can be observed. When chaos occurs, numerical results will dramatically depended on the initial condition.