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.

该论文描述了使用 Galerkin 方法对垂直圆柱形多孔微通道中的对流不稳定性进行的分析。获得了临界瑞利数对 Darcy、Knudsen 和 Prandtl 数以及流体与壁的热导率之比的依赖性。结果表明，多孔介质渗透率的降低（换句话说，其孔隙率的增加）会导致流动稳定性的增加。这种效应基本上是非线性的。在 Da > 0.1 条件下，孔隙率对临界瑞利数的影响几乎消失。滑点效应的加强导致整个系统的不稳定性增加。临界瑞利数的滑移效应是非线性的。非线性程度取决于普朗特数。随着普朗特数的增加，滑移对对流开始的影响减弱。随着流体与壁面热导率比值的增加，普朗特数的影响减小。在普朗特数较高时（Pr > 10），其影响几乎消失。