Influence of internal heat and chemical reaction on magneto-convection in a Jeffrey fluid under magnetic field modulation

This study aims to investigates the influence of internal heat and chemical reactions, combined with vertical magnetic field modulation, on the nonlinear magneto-convection of a Jeffrey fluid in a horizontally porous layer subjected to differential heating. The problem is critical for understanding stability in porous systems under combined thermal, magnetic, and reactive effects, relevant to energy storage, geophysics, and industrial processes. Linear stability analysis is employed, solving the generalized eigenvalue problem using the Galerkin technique to determine the critical thermal Rayleigh number RTc for a wide range of parameters. Results reveal that increased magnetic field strength (Q) raises RTc, significantly delaying convection onset. A weakly nonlinear stability analysis is conducted to explore the system’s nonlinear behavior. Expanding small-axisymmetric disturbances in a power series of convection amplitude leads to deriving a nonautonomous nonlinear cubic Ginzburg–Landau equation. Numerical solutions of this equation yield the Nusselt and Sherwood numbers as functions of key parameters. The results demonstrate that increases in the Jeffrey fluid parameter, modulation frequency, magnetic field, and Darcy number lead to reductions in both heat and mass transfer, thereby enhancing system stability. The findings highlight the stabilizing role of magnetic field modulation and the interplay between fluid and porous medium properties, providing novel insights into controlling convection in magneto-reactive systems. This work extends previous efforts by incorporating non-linear magnetic field modulation effects and elucidating their quantitative impact on heat and mass transfer metrics, revealing critical nonlinear dynamics with implications for astrophysical phenomena such as heat transport in stellar interiors and planetary systems.