Hopf bifurcation in mixed convection flow inside a rectangular cavity

In the present paper, a study of mixed convection inside a rectangular cavity has been carried out. The Reynolds number (Re) has been kept at 100 while the Grashof number (Gr) has been varied between 0, image, image and aspect ratio (AR) (height/width) = 0.5, 1 and 2 keeping the Prandtl number (Pr) = 1. The two vertical walls are maintained at cold temperature image. In one case the top-moving wall is maintained at hot image and the bottom is cold image and in the other case, the top is cold image and the bottom is hot image. The integral form of the governing equations are solved numerically using finite-volume method. SIMPLE algorithm with higher-order upwinding scheme is used. Results are presented in the form of local and average Nusselt number distribution for the range of Grashof number and aspect ratio. The streamlines and isothermal lines are also presented. A Hopf bifurcation has been observed at image for aspect ratio 2. A periodic oscillation of the total kinetic energy (TKE) occurs with the period 4.368 non-dimensional time.