Nonlinear and linear analysis for thermal convection in partially-ionized plasma saturating a porous medium in the presence of magnetic field

The influence of a magnetic field on thermal convection in partially-ionized plasma has profound implications in both astrophysical and laboratory environments. This study explores the impact of a magnetic field on thermal convection within a compressible, partially-ionized plasma layer saturating a porous medium, confined by various combinations of bounding surfaces. Additionally, the effects of medium permeability, collisional frequency and compressibility on the onset of thermal convection are examined. The study employs both nonlinear analysis, using the energy method, and linear analysis, via the normal mode approach, with eigenvalue problems formulated for each. Numerical analysis is performed using the Galerkin-weighted residual method. The findings highlight the significant role of collisional frequency in energy dissipation. Validation of the principle of exchange of stability in the linear analysis suggests the absence of oscillatory convection modes. Results demonstrate that the Rayleigh-Darcy number is the same across both nonlinear and linear analyses, indicating no subcritical region and confirming global stability. Furthermore, the study shows that the magnetic field, medium permeability and compressibility all contribute to delaying the onset of thermal convection. It also concludes that partially-ionized plasma confined between rigid-rigid boundaries exhibits greater thermal stability compared to other boundary configurations.