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Heat Transfer Research
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Heat Transfer Research

DOI: 10.1615/HeatTransRes.2015010733
pages 277-293

LINEAR STABILITY ANALYSIS OF POISEUILLE−RAYLEIGH−BENARD FLOW AFFECTED BY A VERTICAL MAGNETIC FIELD AND A TEMPERATURE FIELD

Chan Liu
Laboratory of Liquid Metal Modeling for Multiphysical Fluid Mechanics (LLiMM-MFM), School of Physics, University of Chinese Academy of Sciences, Beijing 101408, China
Ming-Jiu Ni
Laboratory of Liquid Metal Modeling for Multiphysical Fluid Mechanics (LLiMM-MFM), School of Physics, University of Chinese Academy of Sciences, Beijing 101408, China
Nian-Mei Zhang
Laboratory of Liquid Metal Modeling for Multiphysical Fluid Mechanics (LLiMM-MFM), School of Physics, University of Chinese Academy of Sciences, Beijing 101408, China

SINOPSIS

The temporal instability of the Poiseuille−Rayleigh−Benard flow subjected to a vertical magnetic field has been investigated by a Chebyshev collocation method. The magnetic field and the temperature gradient are two main factors that affect the stabilities. The magnetic field strongly stabilizes the two- and three-dimensional perturbations in basic flow. When heated from below, the buoyancy driven by a temperature gradient destabilizes the flow. For three-dimensional perturbations, the effects of spanwise disturbance on the instability are investigated. With a small temperature gradient, the increase of the oblique angle γ leads to larger critical Reynolds numbers; but with a great temperature gradient, the increase of γ results in smaller critical Rayleigh numbers. When affected by a weak magnetic field, two-dimensional disturbances are more unstable. Meanwhile, for a moderate or strong magnetic field, three-dimensional disturbances can cause the instability at a smaller Reynolds number than two-dimensional ones.


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