Investigating the Effect of Gravity Modulation on Weakly Nonlinear Magnetoconvection in a Nonuniformly Rotating Nanofluid Layer

This paper investigates the impact of gravity modulation on weakly nonlinear magnetoconvection in a nanofluid layer that is nonuniformly rotating. The fundamental equations are obtained for the Cartesian approximation of the Couette flow using the Boussinesq approximation and gravitational modulation. The weakly nonlinear regime is analyzed using the method of perturbations with respect to the small supercritical parameter of the Rayleigh number, considering the effects of Brownian motion and thermophoresis in the nanofluid layer. Heat and mass transfer are evaluated in terms of finite amplitudes and calculated from the Nusselt numbers for the fluid and the volume concentration of nanoparticles. The findings demonstrate that gravitational modulation, nonuniform rotation, and differences in the volume concentration of nanoparticles at the layer boundaries can effectively control heat and mass transfer. Additionally, the negative rotation profile has a destabilizing effect. The study shows that the modulated system conveys more heat and mass than the unmodulated system.