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Effect of small-amplitude gravity modulation on the stability of Rayleigh–Bénard convection in nanofluids

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Abstract

Predicting the criteria for a convective flow to set up in a bottom heated fluid layer, due to density variations and the action of gravity, is essential in several physical phenomena, such as the cooling of electronic equipment and nuclear reactor design. The present article investigates the onset of convection in a nanofluid layer heated from below when the layer is subjected to a periodically modulated gravitational field of small amplitude. We assume that the layer is top-heavy, so the preferred convection mode is stationary. Our focus is on the shift in the critical Rayleigh number for constant gravitational field conditions, which is assumed to be of order square of the modulation amplitude. This shift in the Rayleigh number is obtained through a linear stability analysis of the governing system of equations. The stability criteria are obtained for three different sets of velocity boundary conditions. The effect of various parameters on the system’s stability under the modulated gravitational field is reported. The results reveal that gravity modulation significantly influences the onset of convection as through proper tuning of modulation frequency, one can further destabilize or even stabilize an unstable basic state resulting from the bottom-heating of the top-heavy layer. A comment on the inclusion of the Brownian motion effect in natural convection problems is made based on current findings and some existing studies indicating the same.

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All data generated or analysed during this study are included in this published article.

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  1. Department of Mathematics, Malaviya National Institute of Technology, Jaipur, Rajasthan, 302017, India

    Om P. Suthar

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Correspondence to Om P. Suthar.

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Suthar, O.P. Effect of small-amplitude gravity modulation on the stability of Rayleigh–Bénard convection in nanofluids. Eur. Phys. J. Plus 138, 298 (2023). https://doi.org/10.1140/epjp/s13360-023-03903-8

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