Advanced machine learning analysis of bioconvection in nanofluid with oxytactic microorganisms in a porous wavy enclosure under inclined periodic magnetic effects

This study investigates the bioconvection behavior of a nanofluid containing oxytactic microorganisms within a permeable wavy cavity under an external magnetic field. The analysis includes the effects of Brownian motion and thermophoresis. The dimensionless governing equations are solved using the finite-element method (FEM). A comprehensive parametric study is conducted for various dimensionless numbers: Brownian motion, Hartmann number (Ha), Rayleigh number (Ra), thermophoresis parameter, Lewis number (Le), Péclet number (Pe), nanoparticle volume fraction, bioconvection Rayleigh number (Rb), Darcy number (Da), and wall undulation. The impacts on streamlines, isotherms, and isoconcentration contours of oxygen and microorganisms are illustrated and discussed. The results indicate that cavity undulation has significant influence on the bioconvection flow and thermal transport. Increasing Ra enhances both flow circulation and bioconvective effects. Stronger thermal gradients and higher isoconcentrations of oxygen and microorganisms occur at higher Da. Furthermore, increasing Rb from 0.1 to 10 results in a 37.6% decrease in the average Nusselt number (Nuav) and a 12.1% increase in the average Sherwood number, demonstrating their influence on heat and mass transport. Both Brownian motion and thermophoresis enhance heat transfer rates. A higher Le distinctly reduces micro-organism concentration. To improve the accuracy of predictions for average Nu under fixed values of Ra, Rb, Ha, Da, Le, and Pe, an artificial neural network (ANN) combined with FEM is utilized. Optimal training is achieved at epoch 9, resulting in a mean squared error of 4.5%. The ANN demonstrates strong prediction capability with a correlation coefficient (R-value) of 0.98, confirming its excellent performance.