Stability analysis of gravity-modulated thermohaline rotating magneto-convection with internal heating and chemical reactions using artificial neural network approach

This study investigates the effect of gravity modulation on thermohaline rotating convection under a vertical magnetic field, incorporating internal heating and chemical reactions. An artificial neural network (ANN) is employed for analysis. The linear stability analysis follows the classical normal mode approach to derive the governing perturbation equations, were are then transformed into an eigenvalue problem and solved using ANN model. Additionally, integrating ANN with the Levenberg–Marquardt algorithm provides a numerical method for predicting the thermal Rayleigh number, effectively capturing complex dependencies in the data. A weakly nonlinear stability analysis is conducted using an asymptotic expansion technique to extend the investigation beyond the linear regime. This approach leads to the derivation of the Ginzburg–Landau equation, which describes the amplitude evolution of convection near the instability threshold. By solving this equation, the study provides deeper insights into how gravity modulation influences heat and mass transport. A detailed parametric study, supported by graphical interpretations, explores the combined effects of modulation amplitude, modulation frequency, internal heating, chemical reaction rate, Chandrasekhar number, and Taylor number. Interestingly, gravity modulation exhibits a dual role, it can either stabilize or destabilize the system depending on the modulation frequency and amplitude. These findings highlight the intricate interactions between external modulation and intrinsic fluid behavior, with potential applications in geophysical and industrial processes.