Effect of gravity modulation on rotating porous layer filled with Jeffrey fluid via artificial neural network

This study used linear and weakly nonlinear stability theories to investigate the influence of time-dependent gravity modulation on the thermosolutal instability of a Jeffrey fluid-saturated with a rotating horizontal porous layer heated from below using an artificial neural network. Four types of gravity modulation are considered in this research. For the unmodulated case, linear stability analysis was conducted using the Galerkin technique to determine the critical thermal Rayleigh number at the onset of stationary convection. The study explores the impact of the Jeffrey fluid parameter, Taylor number, Darcy number, and solute Rayleigh number on the onset of convection. We further validate the obtained critical thermal Rayleigh numbers using an artificial neural network model via the Levenberg–Marquardt algorithm. The disturbance is expanded as a power series in the amplitude of convection, assuming it to be small. A nonlinear cubic Ginzburg–Landau equation is derived using the third-order system for weakly nonlinear analysis. It is used to explore heat and mass transfer of the system, and these are presented in terms of Nusselt and Sherwood numbers, obtained from the amplitude equation. The study also analyzes the Jeffrey fluid parameter, amplitude modulation, Darcy number, and solute Rayleigh number, which influence the Nusselt and Sherwood numbers, thereby promoting instability. Notably, the frequency modulation and Taylor number are found to have a stabilizing effect on the system, leading to enhanced stability.