The purpose of this examination is to assess the effect of Stephan blowing and thermal radiation on chemical reactive flow of Williamson nanofluid flow across a sheet with Marangoni convection. Rapid advancements in technology have led to tremendous growth in the domains of machine learning and artificial intelligence. In order to solve the mathematical formulation including heat sources and chemical reactive flow using the Bayesian-Regularization approach, this study creates a machine learning model based on ANN (artificial neural networks). With error estimates of 2.51 × 10⁻¹², 1.51 × 10⁻¹², and 7.41 × 10⁻¹³ across all three scenarios, the model achieves remarkable test performance by utilizing the BRO-DNN (Bayesian-Regularization Optimizer-Deep Neural Network), exhibiting great accuracy and dependability. Numerous industrial and technical domains where heat and mass movement are important have substantial uses for the suggested paradigm. Williamson nanofluid dynamics' incorporation of Stefan blowing and thermal radiation effects is very helpful for improving heating and cooling systems, such as those used in sophisticated industrial processes, thermal energy storage, and electronic device cooling. In applications involving porous media and composite materials, the thermal non-equilibrium approach improves forecast accuracy. The precision of numerical solutions is also increased by combining the Bayesian-Regularization Optimizer with a Deep Neural Network, which makes it advantageous for machine learning-based predictive modelling in biomedical applications, aerospace thermal management, and renewable energy systems like solar collectors.

This study analyzes the impact of local thermal non-equilibrium on the bioconvection flow of hybrid nanofluid across a slender extending sheet containing gyrotactic bacteria using artificial neural networks trained using a Bayesian regularization backpropagation approach (ANN-BRS). The effects of magnetic fields, thermal radiation, and Hall current are all things related to fluid flow. The suggested model has particular applicability in microscale drug delivery systems, where gyrotactic microorganisms and hybrid nanofluid can be employed to control nutrition and medication dispersion under non-equilibrium temperature circumstances. It can be used in lab-on-chip and organ-on-chip technologies to improve bio-mixing and accurate heat control. The model also applies to micro-solar collectors and porous micro-heat exchangers, which use hybrid nanoparticles to boost thermal efficiency. It can also be used in bioreactors and biomedical cooling systems, where local thermal non-equilibrium effects and ANN-based prediction allow for precise control of heat, mass, and microbe transfer, resulting in optimal performance. Similarity transformations are used to convert the original nonlinear PDEs into non-dimensional ODEs and the bvp4c program is applied to numerically resolve the resulting boundary-value problem. The training, testing, and validation processes yield the expected outcomes for every scenario based on the chosen data points. Regression analysis, histograms of error, and mean square error (MSE) metrics are employed to assess the ANN-BRS model's outcome. The liquid phase heat thermal profile increases as the interphase heat transfer parameter values rise, while the solid phase thermal profile decreases.

This study scrutinizes the effect of thermal radiation and Stefan blowing on the chemical reactive flow of Boger nanofluid across a stretched sheet with Darcy Forchheimer medium and heat generation using an intelligent computational framework based on Artifice neural network—Bayesian regularization. Furthermore, Brownian motion and thermophoresis properties have been examined. The suggested model of how Stefan blowing affects the chemical reactive flow of a Boger nanofluid with thermophoresis effects and Brownian motion has useful applications in a number of industrial and engineering operations. In chemical reactors, nano-coating technologies, and polymer processing, this model is essential for improving heat and mass transport processes. While the Boger nanofluid model accurately depicts non-Newtonian behaviour pertinent to biofluids and complex lubricants, Stefan blowing consideration offers insights on evaporation or suction effects. For the purpose of maximizing nanoparticle dispersion in cooling systems, fuel cells, and medicinal devices like targeted drug delivery systems where exact control over particle motion and chemical reactivity is crucial, Brownian motion and thermophoresis are also critical. The velocity profile improves as the Stefan blowing parameter values rise, but the thermal and concentration profiles decrease.

The current study examines the properties of heat radiation on the Darcy Forchheimer flow of carbon nanotube/water based hybrid nanofluid across a Riga plate in the occurrence of oxytactic microbes, employing a novel intelligent numerical computing paradigm based on the legacy of neural networks with the intelligent Bayesian regularization (NN-IBR) method. The AI-driven neuro-computing model for improving the thermal behavior of a carbon nanotube (CNT) hybrid nanofluid in wastewater treatment has a wide range of applications. It has the potential to dramatically improve thermal management efficiency in wastewater treatment plants, improve pollutant removal through optimal heat and mass transfer, and minimize energy consumption in treatment operations. This model can also be used in sustainable water recycling, industrial effluent treatment, and smart environmental management systems, where intelligent prediction and control of nanofluid performance is critical for accomplishing environmentally friendly and cost-effective operations. The Homotopy analysis approach is used to classify the obtained equations. The concentration profile increases as the activation energy parameter values upsurge.