Effect of rotation on thermal convection in a Navier–Stokes–Voigt fluid saturating a porous medium using dual-temperature conditions

This study examines thermal convection thresholds in a rotating Navier–Stokes–Voigt fluid saturating a porous medium, incorporating thermal non-equilibrium through two temperature equations for the fluid and solid phases. The Coriolis term is included in the Navier–Stokes equations to represent rotational influences. Stability is assessed through both nonlinear and linear frameworks using the energy method and normal mode analysis, respectively, leading to eigenvalue problem formulations. The analysis explores results for three different combinations of free and rigid bounding surfaces. The study further explores the impact of the viscoelastic parameter on energy dissipation, showing exponential decay under the influence of the Kelvin–Voigt parameter, underscoring the importance of viscoelastic properties in the convection process. Identical Darcy–Rayleigh numbers are obtained in both analyses, confirming global stability and indicating the reliability of the system under the conditions analyzed. An asymptotic approach is applied to provide deeper insight into system behavior under extreme thermal conditions. Additionally, graphical results illustrate the effects of variables such as rotation, medium permeability, heat transfer, and porosity on the onset of thermal convection. This work enhances understanding of convection in rotating, non-equilibrium complex fluids, supporting applications like geothermal energy and polymer processing.