Instability of double-diffusive magnetoconvection in a non-Newtonian fluid layer with cross-diffusion effects

The study explores the initiation of two-dimensional double-diffusive convection in a horizontal layer of an electrically conducting non-Newtonian Navier–Stokes–Voigt fluid, subjected to a uniform vertical magnetic field and cross-diffusion effects. The numerical results are presented by obtaining the analytical solutions for both steady and oscillatory onset scenarios. The viscoelastic nature of the fluid either delays or hastens the onset of oscillatory convection depending on the strength of solute concentration. The analysis also uncovers contradictions in the linear instability characteristics with and without cross-diffusion terms, even when other input parameters are identical. Under specific conditions, three novel phenomena are observed that are not typically seen in double-diffusive cases: (i) an electrically conducting Navier–Stokes–Voigt fluid layer, initially linearly stable in the presence of a magnetic field, can become destabilized with the addition of a heavy solute to the fluid's bottom; (ii) a stable double-diffusive electrically conducting Navier–Stokes–Voigt fluid layer can be destabilized by the application of a magnetic field; and (iii) the requirement of three critical values of the thermal Rayleigh number to determine linear instability, as opposed to the usual single value owing to the existence of disconnected closed convex oscillatory neutral curves. The results are shown to align with previously published findings in the limiting cases.