Global Stability of Thermal Convection in Navier-Stokes-Voigt Fluids With Couple Stresses Saturating a Porous Medium

This study investigates the global stability of thermal convection in Navier-Stokes-Voigt fluids with couple stresses saturating a porous medium, focusing on the effects of medium permeability and couple stresses. We employ both nonlinear and linear approaches to analyze the system using energy and normal mode analysis method, respectively. The Rayleigh number is calculated using the Galerkin method, yielding consistent results that indicate global stability and the absence of subcritical regions. Convection is limited to a stationary state, adhering to the principle of exchange of stabilities. Our findings reveal that while the Kelvin-Voigt parameter significantly influences energy decay, it does not affect convection modes. Couple stresses contribute to the stabilization of the fluid system, whereas medium permeability introduces a destabilizing effect. Notably, configurations with rigid-rigid boundary surfaces enhance thermal stability, making them particularly advantageous for convection in this context. This research has important implications across various fields, including petroleum engineering, groundwater hydrology, biomedical engineering, geothermal energy, civil engineering, and environmental engineering.