Artificial Neural Network-Based Modeling of Transient Bio-Convective Williamson Tri-Hybrid Nanofluid Flow with Gyrotactic Microorganisms over a Stretching Sheet

Abstract

In this paper, we study the unsteady magnetohydrodynamic (MHD) flow and the heat and mass transfer of a Williamson tri-hybrid nanofluid (THNF) composed of water and Al$_2$O$_3$, TiO$_2$ and Cu nanoparticles over a stretching sheet. The model incorporates thermal radiation, activation energy, chemical reaction, a heat source and the bioconvection of motile gyrotactic microorganisms. An artificial neural network (ANN) is employed for the predictive modeling of such THNF flows under these combined effects. Similarity transformations reduce the governing nonlinear partial differential equations (PDEs) to coupled ordinary differential equations (ODEs), which are solved numerically with a boundary-value-problem solver (SciPy solve_bvp). A feed-forward ANN is trained on the numerical dataset and validated through regression analysis, training convergence, comparison of numerical and predicted data, and error analysis, which results in an ANN with excellent predictive accuracy. The results show that the magnetic field, thermal radiation, Eckert number and heat source increase the temperature field, whereas the Williamson and unsteadiness parameters decrease the velocity profile. The concentration increases with the activation energy, whereas a stronger chemical reaction and a larger Schmidt number lower the concentration profile. Furthermore, the skin-friction coefficient, Nusselt number, Sherwood number and motile-microorganism density number are evaluated over a range of physical parameters. The proposed ANN-assisted framework is an efficient and reliable tool for analyzing and optimizing advanced THNF-based thermal systems.