Frequency response of three-dimensional natural convection of nanofluids under microgravity environments with gravity modulation

Abstract

The present study performed three-dimensional numerical simulations of natural convection generated by nanofluids between plates under microgravity with gravity modulation. The Rayleigh number was fixed at $3\times {10}^6,$ and the dimensionless frequency of the gravity modulation was varied from F = 0 to 10² for the volume fraction $\varphi =0$–0.05. From an unsteady analysis, we clarified the time variation of three-dimensional thermal convection structures under gravity modulation and the frequency response of the heat transfer characteristics to the gravity modulation. When the frequency of gravity modulation and the volume fraction of nanoparticles are changed, two- or three-dimensional roll-shaped thermal convection occurs, and vortex pairs form between thermal plumes. For a low volume fraction of $\varphi =0.01,$ the fluid follows the low-frequency gravity modulation of F = 1 well. Therefore, the thermal convection repeatedly develops and decays as the gravity acceleration increases and decreases. At high-frequency gravity modulation of $F={10}^2,$ since the followability of the fluid is poor, the convection remains during one cycle of gravity modulation. At the low frequency of F = 1 and low volume fraction of $\varphi =0.01,$ the instantaneous Nusselt number is 1.0–1.1 times higher than that at $\varphi =0$ over one period. For the time-averaged characteristics, the heat transfer coefficient is lower at low frequencies than at high frequencies regardless of the volume fraction. At the low volume fraction of $\varphi =0.01,$ the average Nusselt numbers for the low frequencies of F = 1 and F = 5 are 1.0–1.01 times higher than that at $\varphi =0,$ and the decrease in heat transfer coefficient owing to nanoparticles is suppressed. At $\varphi =0.05$ for each frequency, the Nusselt number is much lower than that for $\varphi =0.$ Therefore, for low-frequency gravity modulations that make damping difficult, using nanofluids with a low volume fraction of $\varphi =0.01$ can prevent the decrease in the heat transfer coefficient.

Keywords:

• Gravity modulation
• heat transfer
• microgravity
• nanofluid
• natural convection

Acknowledgments

The numerical results in this research were obtained using supercomputing resources at the Cyberscience Center, Tohoku University. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. We would like to express our gratitude to Associate Professor Yosuke Suenaga of Iwate University for his support of our laboratory. The authors wish to acknowledge the time and effort of everyone involved in this study.

Conflicts of interest

The authors have no conflicts to disclose.

Authors’ contributions

H. Yanaoka conceived and planned the research, and developed the numerical method and calculation codes. R. Inafune performed the simulations. H. Yanaoka and R. Inafune contributed equally to analyzing data, reaching conclusions, and writing the article.