Marangoni convection in layers of water-based nanofluids under the effect of rotation

A linear stability analysis is performed for the onset of Marangoni convection in a horizontal layer of a nanofluid heated from below and affected by rotation. The top boundary of the layer is assumed to be impenetrable to nanoparticles with their distribution being determined from a conservation co...

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Bibliographic Details
Published in:Open mathematics (Warsaw, Poland) Poland), 2021-09, Vol.19 (1), p.1029-1046
Main Authors: Bakhsh, Abeer H., Abdullah, Abdullah A.
Format: Article
Language:English
Subjects:
76E06
76E09
76E25
Brownian motion
Chebyshev approximation
Chebyshev method
Diffusion effects
linear stability
Marangoni convection
Material properties
Nanofluids
Nanoparticles
Probability distribution functions
Rotation
Stability analysis
Thermophoresis
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Summary:A linear stability analysis is performed for the onset of Marangoni convection in a horizontal layer of a nanofluid heated from below and affected by rotation. The top boundary of the layer is assumed to be impenetrable to nanoparticles with their distribution being determined from a conservation condition while the bottom boundary is assumed to be a rigid surface with fixed temperature. The motion of the nanoparticles is characterized by the effects of thermophoresis and Brownian diffusion. A modification model is used in which the effects of Brownian diffusion and thermophoresis are taken into consideration by new expressions in the nanoparticle mass flux. Also, material properties of the nanofluid are modelled by non-constant constitutive expressions depending on nanoparticle volume fraction. The steady-state solution is shown to be well approximated by an exponential distribution of the nanoparticle volume fraction. The Chebyshev-Tau method is used to obtain the critical thermal and nanoparticle Marangoni numbers. Different stability boundaries are obtained using the modified model and the rotation.
ISSN:2391-5455
2391-5455
DOI:10.1515/math-2021-0073