Stabilizing mechanisms in couple-stress porous media: roles of throughflow and gravity variation

This study examines the stability mechanism for couple-stress porous layer under the combined influence of throughflow and variable gravity. We analyse the onset of convective instability under the interactive influence of vertical throughflow and time-varying variable gravity, considering three distinct gravitational profiles: linear, parabolic, and exponential. Employing linear stability theory, the critical Rayleigh number is established with eigenvalue equations solved via dual methodologies: An analytical approach based on the regular perturbation technique, using the wave number as the perturbation parameter. and a numerical Galerkin approach. Both methods exhibit exceptional agreement, underscoring the robustness of the findings. A key contribution of this work is the comparative analysis of different gravity profiles, revealing that the exponential variation provides the strongest stabilizing effect, while the parabolic variation is the least effective. Furthermore, the study identifies a symmetric dependence of the critical Rayleigh number on the throughflow parameter, indicating that stability is governed by the magnitude of throughflow rather than its direction. In addition, a detailed analysis of vertical seepage velocity eigenfunctions highlights that advective transport is enhanced by increasing throughflow intensity and couple-stress effects. These findings offer insights into controlling convective instabilities in porous media applications such as geothermal energy extraction and oil recovery.