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The onset of natural convection in a horizontal nanofluid layer heated from below
A linear stability analysis is performed for the onset of natural convection in a horizontal nanofluid layer heated from below. The motion of nanoparticles is characterized by both the thermophoresis and Brownian diffusion effects. Different from previous studies in the literature, both the dependences of thermophoresis on nanoparticle volume fraction and Brownian motion on temperature are taken into consideration in the theoretical model. The result reveals that the base flow is mainly dominated by the effect of thermophoresis and the Brownian diffusion coefficient can be treated as a constant reasonably when a finite temperature difference is imposed across the nanofluid layer. Accordingly, a novel base solution of nanoparticle volume fraction is derived. It is found that the profile of nanoparticle concentration depends heavily on the magnitude of thermophoretic diffusion, which may exhibit a nonlinear distribution across the nanofluid layer once the effect of thermophoresis is significant. The suspended nanoparticles produce a strong destabilizing effect and a tiny volume fraction of nanoparticles is sufficient to trigger the onset of convection and make the nanofluid layer become unconditionally unstable. The dispersion spectra of unstable modes are demonstrated and the most unstable mode with the maximum growth rate is explored. The growth rate of the most unstable mode is found to increase significantly with increasing nanoparticle concentration, while the influence of heat capacity ratio of nanoparticle to base fluid on the behavior of thermal convection is negligible.
The onset of natural convection in a horizontal nanofluid layer heated from below
A linear stability analysis is performed for the onset of natural convection in a horizontal nanofluid layer heated from below. The motion of nanoparticles is characterized by both the thermophoresis and Brownian diffusion effects. Different from previous studies in the literature, both the dependences of thermophoresis on nanoparticle volume fraction and Brownian motion on temperature are taken into consideration in the theoretical model. The result reveals that the base flow is mainly dominated by the effect of thermophoresis and the Brownian diffusion coefficient can be treated as a constant reasonably when a finite temperature difference is imposed across the nanofluid layer. Accordingly, a novel base solution of nanoparticle volume fraction is derived. It is found that the profile of nanoparticle concentration depends heavily on the magnitude of thermophoretic diffusion, which may exhibit a nonlinear distribution across the nanofluid layer once the effect of thermophoresis is significant. The suspended nanoparticles produce a strong destabilizing effect and a tiny volume fraction of nanoparticles is sufficient to trigger the onset of convection and make the nanofluid layer become unconditionally unstable. The dispersion spectra of unstable modes are demonstrated and the most unstable mode with the maximum growth rate is explored. The growth rate of the most unstable mode is found to increase significantly with increasing nanoparticle concentration, while the influence of heat capacity ratio of nanoparticle to base fluid on the behavior of thermal convection is negligible.
The onset of natural convection in a horizontal nanofluid layer heated from below
Ruo, An‐Cheng (author) / Yan, Wei‐Mon (author) / Chang, Min‐Hsing (author)
Heat Transfer ; 50 ; 7764-7783
2021-12-01
20 pages
Article (Journal)
Electronic Resource
English
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