In this paper, the scenario leading to chaos in natural convection of Cu-water nanofluid inside an inclined square enclosure with the aspect ratio equal to unity is numerically investigated. The enclosure is heated from one part of the side and cooled through two other opposite half sides. The governing equations and the corresponding boundary conditions are solved numerically using the finite difference method. The effect of Rayleigh number and the volume fraction on natural convection flow are analyzed. The obtained results indicate that the mode of fluid flow which is initially stationary, passes by a periodic mode across a supercritical Hopf bifurcation, then quasi periodic at two incommensurable frequencies, before reaching the final stage of chaotic convection for both pure fluid and nanofluid. The sequences of bifurcation are presented graphically; it was found that the presence of suspended nanoparticles inside the base fluid causes significantly the delay of this transition.

Stability and transition problems of two dimensional laminar external flow over a flat plate with wall suction and blowing are studied numerically using the temporal linear stability theory. The flow is assumed similar two-dimensional laminar boundary-layer. The mean velocity profiles are obtained numerically for the case of suction or blowing. The stability equation is given in a general form which can be applied to Chebyshev domain and in boundary layer domain and solved numerically by the Chebyshev collocation spectral method. The neutral stability curves and the critical Reynolds numbers are presented.

This paper investigates the effect of fins orientations of a horizontal two fins annular tube heat exchanger on enhancing the heat transfer during the melting process of n-eicosane, as phase change material (PCM) used in thermal storage systems. Based on the enthalpy-porosity method, two-dimensional model is performed and solved by Ansys Fluent. The impact of the fins orientation on melting rate, thermal conduction and natural convection, as the angle of the system varied from 0º (vertical fins) to 90º (horizontal fins) are discussed. Numerical predictions are validated by comparison with experimental data and numerical results reported in the literature. Good agreements are achieved. The results show that at initial time of the melting process, the conduction heat transfer is dominant. During the melting process, the heat transfer in the horizontal fins is more effective while the upper half of PCM melts and less effective as the lower half of PCM melts because fin arrangement resists natural convection occurs. However, the effectiveness of heat transfer and convection in the vertical fins is almost constant during the entire melting process. From comparison, better heat transfer performance is achieved with vertical fins system; complete melting was reduced 250% compared to horizontal fins case.

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