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Convective Instability in Slip Flow in a Vertical Circular Porous Microchannel

  • Abstract The paper represents an analysis of convective instability in a vertical cylindrical porous microchannel performed using the Galerkin method. The dependence of the critical Rayleigh number on the Darcy, Knudsen, and Prandtl numbers, as well as on the ratio of the thermal conductivities of the fluid and the wall, was obtained. It was shown that a decrease in permeability of the porous medium (in other words, increase in its porosity) causes an increase in flow stability. This effect is substantially nonlinear. Under the condition Da > 0.1, the effect of the porosity on the critical Rayleigh number practically vanishes. Strengthening of the slippage effects leads to an increase in the instability of the entire system. The slippage effect on the critical Rayleigh number is nonlinear. The level of nonlinearity depends on the Prandtl number. With an increase in the Prandtl number, the effect of slippage on the onset of convection weakens. With an increase in the ratio of the thermal conductivities of the fluid and the wall, the influence of the Prandtl number decreases. At high values of the Prandtl numbers (Pr > 10), its influence practically vanishes.

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Author:Andriy Alexandr Avramenko, Igor V Shevchuk, Andrii I. Tyrinov
Parent Title (English):Transport in Porous Media
Publisher:Springer Netherlands
Document Type:Article
Date of first Publication:2021/07/01
Date of Publication (online):2023/04/20
Tag:Civil Engineering; Classical and Continuum Physics; Geotechnical Engineering & Applied Earth Sciences; Hydrogeology; Hydrology/Water Resources; Industrial Chemistry/Chemical Engineering
Page Number:18
Institutes:Informatik und Ingenieurwissenschaften (F10) / Fakultät 10 / Institut Allgemeiner Maschinenbau
Dewey Decimal Classification:600 Technik, Medizin, angewandte Wissenschaften
Open Access:Open Access
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International