Influence of a magnetic field on double-diffusive convection in an inclined porous layer

The present study investigates the impact of a magnetic field on double-diffusive convection in an inclined porous layer, employing linear instability theory. The perturbed state is solved using the normal mode technique, and the stability eigenvalue problem is numerically analyzed for longitudinal and traveling rolls using the Runge-Kutta method coupled with the shooting method. Various dimensionless physical parameters, including solutal and thermal Rayleigh numbers, inclination angle, Hartmann number, and Lewis number, are examined for their influence on system stability. The findings reveal that, for $Le<1$, the Hartmann number, solute Rayleigh number, and inclination angle act as stabilizing factors, with greater stability observed for traveling rolls compared to longitudinal rolls. In the case of $Le=1$, the critical Rayleigh number shows a monotonic relationship with the solute Rayleigh number and inclination angle, while its relationship with the Hartmann number is non-monotonic for traveling rolls. Moreover, for $Le>1$, the Hartmann number stabilizes the system by raising the onset threshold value, favouring longitudinal modes. The solute Rayleigh number also contributes to system stability. The impact of the inclination angle on system stability is contingent upon its magnitude, with small angles favouring the stability of longitudinal rolls and larger angles leading to an initial transition from traveling to longitudinal rolls, indicating a complex non-monotonic behavior.