# Effect of trigonometric sine, square and triangular wave-type time-periodic gravity-aligned oscillations on Rayleigh–Bénard convection in Newtonian liquids and Newtonian nanoliquids

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## Abstract

The influence of trigonometric sine, square and triangular wave-types of time-periodic gravity-aligned oscillations on Rayleigh–Bénard convection in Newtonian liquids and in Newtonian nanoliquids is studied in the paper using the generalized Buongiorno two-phase model. The five-mode Lorenz model is derived under the assumptions of Boussinesq approximation, small-scale convective motion and some slip mechanisms. Using the method of multiscales, the Lorenz model is transformed to a Ginzburg–Landau equation the solution of which helps in quantifying the heat transport through the Nusselt number. Enhancement of heat transport in Newtonian liquids due to the presence of nanoparticles/nanotubes is clearly explained. The study reveals that all the three wave types of gravity modulation delay the onset of convection and thereby to a diminishment of heat transport. It is also found that in the case of trigonometric sine type of gravity modulation heat transport is intermediate to that of the cases of triangular and square types. The paper is the first such work that attempts to theoretically explain the effect of three different wave-types of gravity modulation on onset of convection and heat transport in the presence/absence of nanoparticles/nanotubes. Comparing the heat transport by the single-phase and by the generalized two-phase models, the conclusion is that the single-phase model under-predicts heat transport in nanoliquids irrespective of the type of gravity modulation being effected on the system. The results of the present study reiterate the findings of related experimental and numerical studies.

## Keywords

Nanoliquid Two-phase model Rayleigh–Bénard convection Lorenz model Ginzburg–Landau equation Gravity modulation Triangular Sinusoidal Square Wave forms Onset Heat transfer## Notes

### Acknowledgements

The authors are grateful to the Bangalore University for support. The authors are grateful to the Reviewers of the paper and the Editor for their valuable comments.

### Compliance with ethical standards

### Conflict of interest

The authors declare that they have no conflict of interest.

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