Magnetoconvective double diffusion in a Navier–Stokes–Voigt fluid with couple stresses in a porous medium

This study investigates the magnetoconvective double-diffusion in a Navier–Stokes–Voigt fluid flow in a porous medium with couple-stress effects. The system is subjected to both thermal and solutal gradients under the influence of a uniform vertical magnetic field. A comprehensive analysis is carried out by employing the normal mode technique for linear analysis and the energy method for the nonlinear regime. The nonlinear and linear stability threshold is obtained by solving the resulting eigenvalue problem via the single-term Galerkin method. To facilitate rapid parametric analysis, a multi-output artificial neural network (ANN) is trained using analytical solutions. The ANN demonstrates high predictive accuracy with R2=0.88 for rigid–rigid and R2=0.91 for rigid–free boundary conditions. Quantitative evaluation shows that increasing the couple stress parameter, solute gradient, and magnetic field strengthens system stability by elevating the critical Rayleigh number, whereas higher medium permeability promotes convection by reducing the stability threshold. The Voigt parameter suppresses oscillatory modes but has a negligible influence on stationary convection. Among the three boundary configurations, the rigid–rigid case yields the highest stability, followed by rigid–free and free–free boundaries. These findings provide quantitative insight into the interplay of viscoelasticity, magnetic field, and microstructural effects in porous double-diffusive convection.