Characteristics of stephan blowing and thermal radiation on williamson nanofluid with thermal non-equilibrium effect using bayesian-regularization optimizer-deep neural network

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.