The aim of this study is to analyze the mixed convection under Soret effect in a liquid layer subjected to adverse temperature and concentration gradients and slip conditions. Theoretical linear stability analysis and numerical methods were performed to study the convective and absolute instabilities of the transverse rolls. It is found that, for convective instabilities, the problem has analytical solution and is a Galilean transformation of natural convection. The throughflow makes the rolls to propagate and the frequency shift is proportional to Reynolds number. For higher Rayleigh numbers, advection breaks Galilean invariance, and absolute instabilities settle. At the threshold of absolute instability, the presence of throughflow breaks the symmetry by the rotational invariance, and the system selects among an infinite number of unstable modes, the progressive waves, in the direction of the flow.
| Published in | American Journal of Mechanics and Applications (Volume 3, Issue 3) |
| DOI | 10.11648/j.ajma.20150303.11 |
| Page(s) | 19-26 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Mixed Convection, Horizontal Liquid Layer, Critical Rayleigh, Linear Stability Analysis
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APA Style
A. Kadiri, H. Ben Hamed, H. Beji. (2015). Linear Stability Analysis of Mixed Convection Under Soret Effect in Bounded Horizontal Fluid Layer with Slip Conditions. American Journal of Mechanics and Applications, 3(3), 19-26. https://doi.org/10.11648/j.ajma.20150303.11
ACS Style
A. Kadiri; H. Ben Hamed; H. Beji. Linear Stability Analysis of Mixed Convection Under Soret Effect in Bounded Horizontal Fluid Layer with Slip Conditions. Am. J. Mech. Appl. 2015, 3(3), 19-26. doi: 10.11648/j.ajma.20150303.11
AMA Style
A. Kadiri, H. Ben Hamed, H. Beji. Linear Stability Analysis of Mixed Convection Under Soret Effect in Bounded Horizontal Fluid Layer with Slip Conditions. Am J Mech Appl. 2015;3(3):19-26. doi: 10.11648/j.ajma.20150303.11
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Download@article{10.11648/j.ajma.20150303.11,
author = {A. Kadiri and H. Ben Hamed and H. Beji},
title = {Linear Stability Analysis of Mixed Convection Under Soret Effect in Bounded Horizontal Fluid Layer with Slip Conditions},
journal = {American Journal of Mechanics and Applications},
volume = {3},
number = {3},
pages = {19-26},
doi = {10.11648/j.ajma.20150303.11},
url = {https://doi.org/10.11648/j.ajma.20150303.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajma.20150303.11},
abstract = {The aim of this study is to analyze the mixed convection under Soret effect in a liquid layer subjected to adverse temperature and concentration gradients and slip conditions. Theoretical linear stability analysis and numerical methods were performed to study the convective and absolute instabilities of the transverse rolls. It is found that, for convective instabilities, the problem has analytical solution and is a Galilean transformation of natural convection. The throughflow makes the rolls to propagate and the frequency shift is proportional to Reynolds number. For higher Rayleigh numbers, advection breaks Galilean invariance, and absolute instabilities settle. At the threshold of absolute instability, the presence of throughflow breaks the symmetry by the rotational invariance, and the system selects among an infinite number of unstable modes, the progressive waves, in the direction of the flow.},
year = {2015}
}
TY - JOUR T1 - Linear Stability Analysis of Mixed Convection Under Soret Effect in Bounded Horizontal Fluid Layer with Slip Conditions AU - A. Kadiri AU - H. Ben Hamed AU - H. Beji Y1 - 2015/06/16 PY - 2015 N1 - https://doi.org/10.11648/j.ajma.20150303.11 DO - 10.11648/j.ajma.20150303.11 T2 - American Journal of Mechanics and Applications JF - American Journal of Mechanics and Applications JO - American Journal of Mechanics and Applications SP - 19 EP - 26 PB - Science Publishing Group SN - 2376-6131 UR - https://doi.org/10.11648/j.ajma.20150303.11 AB - The aim of this study is to analyze the mixed convection under Soret effect in a liquid layer subjected to adverse temperature and concentration gradients and slip conditions. Theoretical linear stability analysis and numerical methods were performed to study the convective and absolute instabilities of the transverse rolls. It is found that, for convective instabilities, the problem has analytical solution and is a Galilean transformation of natural convection. The throughflow makes the rolls to propagate and the frequency shift is proportional to Reynolds number. For higher Rayleigh numbers, advection breaks Galilean invariance, and absolute instabilities settle. At the threshold of absolute instability, the presence of throughflow breaks the symmetry by the rotational invariance, and the system selects among an infinite number of unstable modes, the progressive waves, in the direction of the flow. VL - 3 IS - 3 ER -
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