Stability analysis and Bayesian Regularization-based Artificial Neural Network for time-periodic gravity modulation in double-diffusive Micropolar fluid

An effective computational framework for predicting the onset of convection and transport behavior in complex fluid systems is provided by the stability analysis of double-diffusive micropolar fluids in conjunction with neural network modeling. The present research examined the linear and weakly nonlinear stability of a micropolar fluid layer with Boussinesq approximation, with time-periodic gravity modulation and thermal radiation. The critical thermal Rayleigh number and critical wavenumber for the onset of convection are determined by using normal mode analysis. By using a truncated Fourier series expansion, a weakly nonlinear analysis is carried out, which results in a Ginzburg-Landau amplitude equation describing finite-amplitude convection and the post-critical behavior. The resulting nonlinear system is solved numerically by the Runge-Kutta-Fehlberg method. Furthermore, a Bayesian regularization artificial neural network is developed to predict the Nusselt and Sherwood numbers with high accuracy using the numerical dataset. The results reveal that the coupling parameter, thermal radiation and heat conduction tend to stabilize the system, whereas the ratio of diffusivity and couple stress parameter tends to destabilize the system. The results of the present model can be applied to thermal management systems, geophysical flows, nuclear cooling and processing of advanced materials with micropolar fluids.