Purpose This paper aims to analyze the effect of aspect ratio A and aspect velocity ratio a on the bifurcation occurrence phenomena in lid-driven cavity by using finite volume method (FVM) and multigrid acceleration. This study has been performed for certain pertinent parameters; a wide range of the Reynolds number values has been adopted, and aspect ratios ranging from 0.25 to 1 and various velocity ratios from 0.25 to 0.825 have been considered in this investigation. Results show that the transition to the unsteady regime follows the classical scheme of Hopf bifurcation, giving rise to a perfectly periodic state. Flow periodicity has been verified through time history plots for the velocity component and phase-space trajectories as a function of Reynolds number. Velocity profile for special case of a square cavity (A = 1) was found to be in good agreement between current numerical results and published ones. Flow characteristics inside the cavity have been presented and discussed in terms of streamlines and vorticity contours at a fixed Reynolds number (Re = 5,000) for various aspect ratios (a = 0). Design/methodology/approach The numerical method is based on the FVM and multigrid acceleration. Findings Computations have been investigated for several Reynolds numbers and aspect ratios A (0.25, 0.5, 0.75, 0.825 and 1). Besides, various velocity ratios (a = 0.25, 0.5, 0.75 and 0.825) at fixed aspect ratios (A = 0.25, 0.5 and 0.75) were considered. It is observed that the transition to the unsteady regime follows the classical scheme of Hopf bifurcation, giving rise to a perfectly periodic state. Flow periodicity is verified through time history plots for velocity components and phase-space trajectories. Originality/value The bifurcations between steady and unsteady states are investigated.

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In this paper, a numerical study of natural convection in a square enclosure with non-uniform temperature distribution maintained at the bottom wall and filled with nanofluids is carried out using different types of nanoparticles. The remaining walls of the enclosure are kept at a lower temperature. Calculations are performed for Rayleigh numbers in the range 5 × 10³ ≤ Ra ≤ 10⁶ and different solid volume fraction of nanoparticles 0 ≤ χ ≤ 0.2. An enhancement in heat transfer rate is observed with the increase of nanoparticles volume fraction for the whole range of Rayleigh numbers. It is also observed that the heat transfer enhancement strongly depends on the type of nanofluids. For Ra = 10⁶, the pure water flow becomes unsteady. It is observed that the increase of the volume fraction of nanoparticles makes the flow return to steady state.

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