Thermosolutal convection in a rotating Navier–Stokes–Voigt fluid saturating a porous medium under thermal non-equilibrium conditions

Abstract

This study investigates the effect of rotation on viscoelastic fluid convection using the Voigt model in a porous medium under thermal nonequilibrium conditions. The analysis considers three boundary conditions with different combinations of free and rigid surfaces. The Darcy–Brinkman model is used to characterize the porous medium, and the Coriolis term is incorporated into the momentum equation to account for rotational effects. A dual-temperature model represents thermal non-equilibrium. Stability analysis is performed using both nonlinear (energy method) and linear (normal mode) approaches. The formulated eigenvalue problems are solved using single-term Galerkin method, from which explicit expressions for the Rayleigh number are derived. The critical Rayleigh number is then obtained by minimizing these expressions with respect to the wavenumber. The results establish stability thresholds and identify the key factors influencing the onset of both stationary and oscillatory convection. The global stability analysis confirms identical Rayleigh numbers for both approaches. Increasing the viscoelastic parameter \(\lambda\) stabilizes oscillatory convection, leading to its disappearance beyond \(\lambda >1.3\) (free–free), \(\lambda >0.26\) (rigid–free), and \(\lambda >0.13\) (rigid–rigid) boundary conditions, while keeping other parameters fixed, with a corresponding reduction in the wave number ranges.