Journal of Applied Sciences1812-56541812-5662Asian Network for Scientific Information10.3923/jas.2008.218.229Aklouche BenouaguefS. ZeghmatiB. BouhadefK. DaguenetM. 2200882In this study, we investigated numerically the transient natural convection in a square cavity with two horizontal adiabatic sides and vertical walls composed of two regions of same size maintained at different temperatures. The flow has been assumed to be laminar and bi-dimensional. The governing equations written in dimensionless form and expressed in terms of stream function and vorticity, have been solved using the Alternating Direction Implicit (ADI) method and the GAUSS elimination method. Calculations were performed for air (Pr = 0.71), with a Rayleigh number varying from 2.5x105 to 3.7x106. We analysed the effect of the Rayleigh number on the route to the chaos of the system. The first transition has been found from steady-state to oscillatory flow and the second is a subharmonic bifurcation as the Rayleigh number is increased further. For sufficiently small Rayleigh numbers, present results show that the flow is characterized by four cells with horizontal and vertical symmetric axes. The attractor bifurcates from a stable fixed point to a limit cycle for a Rayleigh number varying from 2.5x105 to 2.51x105. A limit cycle settles from Ra = 3x105 and persists until Ra = 5x105. At a Rayleigh number of 2.5x105 the temporal evolution of the Nusselt number Nu(t) was stationary. As the Rayleigh number increases, the flow becomes unstable and bifurcates to a time periodic solution at a critical Rayleigh number between 2.5x105 and 2.51x105. After the first HOPF bifurcation at Ra = 2.51x105, the oscillatory flow undergoes several bifurcations and ultimately evolves into a chaotic flow.]]>Berge, P. and Y. Pomeau, 19981998Bratsun, D.A., A.V. Zyuzgin and G.F. Putin, 200324835852De Vahl Davis, G.,19833249264Douamna, S., M. Hasnaoui and B. Abourida, 199938797807Gollub, J.P. and S.V. Besson, 1980100449470Grassberger, P. and I. Procaccia, 198350346346Ishida, H., S. Kawase and H. Kimoto, 20064950355048Jahnke, C.C., V. Subramanyan and D.T. Valentine, 19984123072320Kuang, J.L., P.A. Mechan and A.Y.T. Leung, 20062714081414Lamsaadi, M., M. Naimi and M. Hasnaoui, 200616779802Le-Quere, P. and M. Behnia, 199835981107Mukutmoni, D. and K.T. Yang, 1993115360366Ndame, A.,19921992Prasad, Y.S. and M.K. Das, 20075035833598Schuster, H.G., 19841st Edn.,pp: 31-36pp: 31-36Shu, C. and H.A. Week, 200231209226Skouta, A., M. Randriazanamparany and M. Daguenet, 200140352365Victorri, G. and P. Blondeaux, 1991324922495Yoo, J.S. and S.M. Han, 200027231245Yu, P. and A.Y.T. Leung, 200316277300