Abstract

The onset of natural convection in a vertical Hele-Shaw configuration under the action of mechanical vibration is studied. Vibration is considered to be a harmonic one and its direction is considered parallel to the temperature gradient. Linear stability analysis for small Pr number leads us to the Mathieu equation. The so-called time averaged method is applied to this equation which gives us a closed form relation for the critical Ra_T number for the harmonic (synchronous) solution. The results are in a perfect agreement with published numerical results.

References

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Citation

Yazdan Pedram Razi., et al. “On the Onset of Convection in a Hele-Shaw Geometry under the Influence of Mechanical Vibrations". Clareus Scientific Science and Engineering 2.8 (2025): 02-07.

Copyright

© 2025 Yazdan Pedram Razi., et al. Licensee Clareus Scientific Publications. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license.