Machine learning insights into heat and mass transfer in carreau hybrid nanofluid flow over stretching surface with bioconvection applications

The features of coupled flow, heat transfer, mass transport, and bioconvection of a non-Newtonian hybrid nanofluid subject to the effect of a magnetic flux, thermal radiation, viscous dissipation, nanoparticle transport, chemical reaction, and motile microorganisms over an exponentially stretching sheet are investigated. This type of multi-physics flow is of significant use in the high-technology thermal management, biomedical transport, and bio-inspired energy systems. A hybrid numerical and data-driven methodology is developed to address the highly nonlinear interactions among these effects. To reduce the governing equations to non-linear ordinary differential equations, similarity transformations are applied, and the resulting system is solved numerically using the BVP4C solver to produce high-fidelity data for parametric analysis, machine learning, and optimisation. The surrogate model used to predict surface heat transfer is a deep neural network, and the interactions between parameters and performance optimisation are investigated using response surface methodology. The findings show that the enhancement in magnetic parameters reduces velocity but increases skin friction, while the Nusselt number decreases with respect to the magnetic, radiation, and Eckert numbers owing to the effects of magnetisation, radiative heating, and viscous/Joule heating. Brownian motion, thermophoresis, chemical reaction, and bioconvection: Lewis number affects nanoparticle and microorganism concentration. The DNN with 10 inputs predicts heat transfer efficiently, with a testing R 2 = 0.997169. The novelty of the proposed approach is that bioconvection, Carreau hybrid nanofluid modelling, deep learning prediction, and optimisation are unified within a single framework, providing an effective means of designing intelligent thermal systems.