Windows and routes to chaos in mixed convection in confined spaces

A simplified model of mixed convection in confined spaces is developed through approximating the solution of the governing equations in the low mode Fourier series and Chebyshev polynomials. Bifurcation structure of the simplified model dependent on two main system parameters, namely Re and Ar, is numerically investigated. Re is chosen as the bifurcation parameter. The results of the numerical experiments show that the routes to chaotic solution are different in three ranges of Ar. In addition, quasiperiodic windows are found in the chaotic regime for middle values of Ar and frequency locking appears in mixed convection with higher Ar.