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. dependence critical Rayleigh number on Darcy, Knudsen, and Prandtl numbers, as well ratio thermal conductivities fluid wall, was obtained. It shown that decrease permeability medium (in other words, increase its porosity) causes flow stability. This effect is substantially nonlinear. Under condition Da > 0.1, porosity practically vanishes. Strengthening slippage effects leads to entire system. level nonlinearity depends number. With number, onset convection weakens. influence decreases. At high values numbers (Pr 10),