Nanomaterial flow has fascinated the concern of scientists across the globe due to its innovative applications in various manufacturing, industrial, and engineering domains. Bearing aforementioned uses in mind, the focal point of this study is to examine the Carreau nanofluid flow configured by the Riga surface with Arrhenius catalysts. Microorganisms are also suspended in nanofluid to strengthen the density of the regular fluid. Time-dependent coupled partial differential equations that represent the flow dynamics are modified into dimensionless patterns via appropriate non-dimensional variables, and handled through an explicit finite difference approach with stability appraisal. The performances of multiple flow variables are examined graphically and numerically. Representation of 3D surface and contour plots for heat transportation and entropy generation are also epitomized. The findings express that the modified Hartmann number strengthens the motion of nanomaterial. Reverse outcomes for heat transport rate and entropy are seen for the radiation variable. Concentration diminishes for chemical reaction variable. Activation energy enhances the concentration of nanomaterial, whereas reduction happens in the movement of microbes for bio-Lewis number. Greater Brinkman variable heightens the entropy.

In the automotive, electronics, and energy sectors, heat exchangers and cooling systems can be improved by the flow dynamics of thermally enriched nanomaterials across enlarged surfaces. In biomicrosystems, bionanocooling units, and the petroleum sector, the fluid’s stabilizing properties derive from the presence of microorganisms. Using nonlinear radiation, Arrhenius catalysts, and thermal convection, this work focuses on the electrically induced nanobioconvective migration of Maxwell fluid‐containing organisms across an exponentially grown surface. Using suitable transformations, the governing equations are converted into dimensionless forms to create a mathematical framework for nanofluids based on the Buongiorno model. After a stability analysis, the reformulated flow problems are solved using a finite difference approach, and the computational outcomes are verified against previous research. The results show that larger buoyancy ratios and magnetic components decrease the velocity of the nanofluid, while increasing viscosity and radiation increase its thermal energy. Furthermore, unpredictable motion and enhanced thermophoresis reduce heat transmission. Compared to linear radiation, nonlinear thermal radiation has a far bigger effect on thermal fields. Additionally, fewer dispersed bacteria result in a lower motile microbe density when the Peclet number ( Pe ) is larger. When it comes to estimating microbe density ( Nd ), the model’s statistical validation yields a 99.95% R ² at a 95% confidence level, indicating its dependability. Pe and Ae show the highest and lowest sensitivity to the motile density function in Maxwell fluid, respectively. By improving the circumstances for microbial growth in nanofluid settings, the findings of this study aid in the optimization of biofuel production.

In this study, an integrated finite-difference and deep neural network analysis of the simultaneous multiphysics of coupled momentum, heat, nanoparticle, and pollutant transport in a Sutterby tri-hybrid nanofluid over a quadratically radiative Riga surface is developed. The Fe₃O₄, Al₂O₃, and TiO₂ nanoparticles are considered, and a mixture of propylene glycol and water is used, along with electroosmotic forcing, electromagnetic actuation, nonlinear thermal radiation, viscous dissipation, Brownian motion, thermophoresis, and pollutant transport. The key novelty is the ability to formally connect these strongly coupled nonlinear transport processes with a deep neural network (DNN) surrogate model to allow for the rapid and accurate prediction of complex thermo-fluid and mass-transfer responses. The governing equations are then transformed into nonlinear equations and solved numerically using a finite difference method (FDM) coded in FORTRAN to produce high fidelity numerical data sets that are used to train a feed-forward back-propagation deep neural network (DNN) implemented in Python with PyTorch. The optimized DNN successfully predicted the velocity, temperature, field of nanoparticles, and pollutant concentration, with the RMSE less than (3.2 × 10⁻²) and (R² > 0.987), which indicates that the optimized DNN possesses high predictive accuracy and reliability. The fluid motion is improved by the increased electroosmotic and electromagnetic parameters due to increased electrokinetic and Lorentz forces, and the increased Brinkman number increases the fluid viscous dissipation heating and raises the temperature field. The enhanced Brownian motion facilitates the migration of nanoparticles and greatly affects coupled heat and mass transport while pollutant-related parameters control concentration distributions. The proposed DNN framework has the potential of being an efficient surrogate for fast simulations, parametric evaluation, and optimization for nonlinear multiphysics systems, and has direct applications to thermal management systems in industry, microfluidic processing, electrochemical technologies, electromagnetic flow-control devices, industrial wastewater treatment systems, and pollutant removal systems.