ANN-driven prediction for 3D bioconvection flow of radiative Carreau ternary hybrid nanofluids across a porous stretching sheet with Buongiorno model

This study presents a novel numerical and artificial neural network (ANN) investigation of three-dimensional magnetohydrodynamic (MHD) bioconvective flow of a Carreau ternary hybrid nanofluid (THNF) over a bidirectional-stretching Riga plate embedded in a porous medium. The mathematical model adopted is derived from the Buongiorno model and includes the effects of thermal radiation, Joule heating, Brownian motion, thermophoresis, heat generation/absorption, activation energy, and binary chemical reaction. Similarity variables are introduced into the governing partial differential equations to convert them into ordinary differential equations, which are then solved numerically using the MATLAB solver bvp4c. A Levenberg-Marquardt-based backpropagation neural network (LMS-BPNN) is trained to predict the key transport properties, using 70% of the data for 15% of training to validate and test the network. The results show that the velocity profiles decrease with the increase of the Weissenberg number because of the dominant elastic forces, and the temperature profile increases with the increase of the Brownian motion and thermophoresis parameters. The Nusselt number increases with the increase of Brownian motion and thermophoresis, while the skin friction coefficient increases with the increase of the magnetic and chemical reaction parameters. The results obtained from ANN agree fairly well with the numerical results, and the mean square error value is in the range of \(1 0^{-9}\) to \(1 0^{-8}\). The high agreement between the numerical and ANN predictions with previous studies demonstrates the accuracy and robustness of the proposed computational framework, which has the potential to predict complex transport phenomena in advanced thermal systems.