Effect of couple stresses on convective stability of rotating Navier–Stokes–Voigt fluid saturating a porous medium

Abstract This study aims to investigate the impact of couple stresses on the convective stability of a rotating Navier–Stokes–Voigt fluid saturating a porous medium, considering various combinations of boundary conditions. Both nonlinear and linear analyses were performed using the energy method and the normal mode analysis method, respectively. The eigenvalue problems formulated from both analyses were solved using the single-term Galerkin method to calculate the Rayleigh number. The Rayleigh numbers for nonlinear analysis and stationary convection are identical, confirming the absence of a subcritical region, ensuring global stability. The results obtained for free-free boundary conditions, in the absence of couple stresses and rotation, align with those found in Straughan’s work. The study explores the influence of key parameters such as the Kelvin–Voigt parameter, couple stress parameter, Taylor number, and Darcy–Brinkman number on the stability of the system. The results indicate that increasing the couple stresses and permeability of the medium suppresses small convection patterns, reducing the range of permissible wave numbers for oscillatory convection. Conversely, enhanced rotation and viscoelastic effects allow a broader range of wave numbers to support oscillatory convection, thereby preventing pattern merging. Couple stresses and rotational effects contribute to the stabilization of the system, while medium permeability acts as a destabilizing factor. These findings can be applied to optimize fluid dynamics and thermal management in porous media systems across diverse fields, including geophysics, engineering, petroleum recovery, and biomedical applications.