4.4 Article

Convective Instability in Slip Flow in a Vertical Circular Porous Microchannel

Journal

TRANSPORT IN POROUS MEDIA
Volume 138, Issue 3, Pages 661-678

Publisher

SPRINGER
DOI: 10.1007/s11242-021-01639-6

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Funding

  1. NAS of Ukraine [1.7.1.892]

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This paper analyzes the convective instability in a vertical cylindrical porous microchannel using the Galerkin method, revealing that a decrease in permeability of the porous medium increases flow stability, while an increase in slippage effects leads to higher instability in the system.
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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