Study of the effects of three types of time-periodic vertical oscillations on the linear and nonlinear realms of Rayleigh-Bénard convection in hybrid nanoliquids

In the paper, the effect of time-periodic gravity modulation with trigonometric sine, triangular, and square waves-forms on Rayleigh Bénard convection in water-alumina nanoliquids and water-alumina-copper hybrid nanoliqiuds is studied by using a single-phase model. Using a perturbation method, linear stability analysis is performed for all the three wave-forms. A generalized Lorenz model that has the influence of nanoliquids and modulation incorporated in it is derived using a truncated Fourier series representation. The Lorenz model is then transformed into a Ginzburg-Landau model using the method of multiscales, and the solution is used to study heat transport. For trigonometric sine, triangular and square wave-forms of modulations comparison are made on their effect on the onset of convection and the heat transport. The linear stability analysis reveals that the critical Rayleigh number obtained in the case of a triangular wave-form is less compared to the value obtained in the cases of trigonometric sine and square wave-forms. This leads to an enhanced heat transfer situation in the case of triangular wave-form compared to that in the other two wave-forms. It is also found that such an enhancement in heat transport increases with amplitude and decreases with the modulation frequency. Thus, the modulation is found to be a regulating mechanism on heat transport. Further, it is observed that water-alumina-copper facilitates maximum heat transport compared to that by water-alumina and water, leading to the conclusion that hybrid nanoliquids facilitate enhanced heat transport compared to that by mono nanoliquids.