ABSTRACT In this study, linear instability and nonlinear stability analyses are performed to investigate double‐diffusive convection driven by radiation absorption and magnetic field effects. The Rayleigh‐Bénard configuration with realistic rigid boundaries is considered, in which the fluid layer is heated and salted from below. The mathematical model comprises the Navier‐Stokes equation for an incompressible fluid, incorporating a Kelvin‐Voigt term that describes viscoelasticity, and is coupled with convection‐diffusion equations for energy and solute concentration. Linear instability thresholds are determined using the Fourier mode approach, while nonlinear stability analysis is carried out by using the energy method. The resulting eighth‐order differential eigenvalue problems from both linear and nonlinear theories are solved using the Chebyshev Collocation Method. The nonlinear analysis produces critical Rayleigh numbers that closely match those obtained from linear instability theory. However, the discrepancy between linear and nonlinear stability thresholds indicates the existence of a subcritical instability region. The Kelvin Voigt and Hartmann numbers are found to exert a stabilizing influence, whereas radiation absorption significantly destabilizes the onset of convection.
Basavarajappa et al. (Sun,) studied this question.