Influence of magnetic fields and bounding surface configurations on thermal convection in partially ionised plasmas: nonlinear and linear stability analyses

This study investigates the influence of a magnetic field on thermal convection within a PIP confined between distinct combinations of bounding surfaces. Nonlinear stability analysis (employing the energy method) and linear instability analysis (utilising the normal mode analysis method) are conducted and eigenvalue problems are formulated for both analyses. Numerical analysis is executed using the Galerkin-weighted residual method. Additionally, the study examines the effects of magnetic field, collisional frequency and compressibility on the onset of thermal convection. Collisional frequency plays a significant role in the decay of energy. The principle of exchange of stability is validated for linear analysis, indicating the absence of oscillatory modes of convection. The findings show that the Rayleigh number for both nonlinear and linear analyses is the same. Hence, the subcritical region is not possible, which affirms the existence of global stability. It is noteworthy that both magnetic field and compressibility contribute to the delay in the onset of thermal convection. Also, the PIP confined in rigid–rigid bounding surfaces is thermally more stable than the other configurations of the bounding surfaces.