Heat transfer analysis of Ethylene Glycol based hybrid nanofluid (Au–Ag) flow over a porous medium with gyrotactic microorganisms: Levenberg–Marquardt backpropagation approach

The proposed study employs the Levenberg–Marquardt backpropagation approach with artificial neural networks to examine the heat transfer in hybrid nanofluid flow over a porous embedded vertical stretching sheet in a Darcy–Forchheimer medium. This study seeks to investigate the interplay between gyrotactic microorganisms, magnetic fields, mixed convection, and temperature in hybrid nanofluids including Silver (Ag), Gold (Au), and the base fluid Ethylene Glycol ${\text{C}}_2{\text{H}}_6{\text{O}}_2$ utilizing the Cattaneo–Christov heat flux model. It improves our comprehension of their behavior and potential uses. This intricate system of highly non-linear governing equations is simplified to a set of ordinary differential equations by similarity transformations and solved numerically using the Bvp4c method. Alongside the numerical method, Artificial Neural Networks (ANNs) are utilized to precisely illustrate intricate patterns, with an Mean Square Error (MSE) of 0.00043 and strengthening the impact of the numerical findings. This study demonstrates that the utilization of Au–Ag/${\text{C}}_2{\text{H}}_6{\text{O}}_2$ hybrid nanoparticles enhances thermal conductivity, augments volume fraction, and indicates that the application of a magnetic field and thermal radiation markedly improves the dispersion of microorganisms and the formation of hybrid nanofluids, resulting in elevated heat transfer rates. Especially, ANN-based regressor for sensitivity analysis is employed to forecast essential physical parameters, including the skin friction coefficient, Nusselt number, Sherwood number, and Density of Microorganisms, while also assessing the significance of factors affecting nanofluid properties, thereby demonstrating excellent concordance with prior studies and validating the robustness of the proposed model.