Stability analysis of magneto-LTNE porous convection in Kelvin–Voigt fluid

The stability of Darcy–Brinkman–Bénard model for Kelvin–Voigt fluids is investigated using a local thermal non-equilibrium (LTNE) configuration. The study considers physically realistic rigid surfaces, with the lower surface heated from below. The effects of spatially varying gravitational force and constant magnitude Lorentz force on the onset of convection are investigated. A systematic analysis is conducted on two porous materials: Sander sandstone and aluminum metallic foam (AL1050). Our mathematical model comprises the Kelvin–Voigt–Navier–Stokes equation, coupled with a two-equation, thermal non-equilibrium model of energy. The Fourier modes technique is used for linear instability analysis, while the energy method is applied for nonlinear stability analysis. The differential eigenvalue problems arising from linear and nonlinear theories are solved using the Spectral Collocation-QZ method. We determine the critical conditions for the onset of convection, examining the impact of the Darcy number, Darcy–Hartmann number, and inter-phase heat transport parameter. The results reveal a notable disparity between linear and nonlinear stability thresholds, with the latter being consistently lower. This discrepancy indicates the existence of a subcritical instability region. Our findings demonstrate that increased magnitudes of Lorentz and gravitational forces postpone the initiation of convective motion, thereby stabilizing the fluid system. This stabilization is reflected in higher Darcy–Rayleigh numbers, which potentially contribute to enhanced heat transfer rates. Similarly, an increase in the Darcy number leads to elevated Darcy–Rayleigh numbers, potentially improving thermal stability and heat transfer efficiency. Furthermore, we found that the subcritical instability regime expands significantly when both porosity and gravity field intensity reaches sufficiently high levels. •Mathematical model is developed for LTNE convection in Kelvin–Voigt fluid.•Global nonlinear stability analysis of conduction solution has been performed.•Conditions for the onset of convection are provided.•Existence of subcritical instability convection is demonstrated.•Differential eigenvalue problems are solved using the QZ-algorithm.