Activation energy and Coriolis force impact on three-dimensional dusty nanofluid flow containing gyrotactic microorganisms: Machine learning and numerical approach

Abstract In recent times, machine learning methods have become powerful tools for solving complex problems, optimizing processes, and extracting insights from large datasets, especially in fluid dynamics. This study examines the effects of thermophoresis, Brownian motion, thermal radiation, and a non-uniform heat source on a dusty nanofluid containing gyrotactic microorganisms as it moves across a three-dimensional porous sheet. Additionally, the influence of activation energy and the Coriolis force on its biomechanics is investigated. MATLAB’s bvp4c solver is used to solve the nonlinear equations governing velocity, temperature, concentration, and microbe density. The study also includes the computation of the skin friction coefficient and the heat transfer rate, with results presented in graphical form. Furthermore, key findings indicate that an augmentation in the fluid-particle interaction parameter results in a 12.5% increase in dust fluid velocity, whereas the fluid velocity diminishes by 9.8%. A 15% augmentation in the thermophoresis parameter improves temperature and concentration profiles by 10 and 8.7%, respectively. Furthermore, Brownian motion effects result in a 7.3% increase in temperature and a 5.2% reduction in concentration. The Nusselt number has a significant association with the thermophoresis parameter, especially at elevated levels, resulting in a 11.4% increase in heat transfer efficiency. Moreover, an increased concentration of dust particles leads to a 6.5% reduction in the temperature profile for both nanofluid and dusty fluid phases. The artificial neural network methodology effectively reduces computational time when solving complex fluid dynamics problems. This theoretical analysis has applications in various fields, including biodiesel and hydrogen synthesis, oil storage, geothermal energy extraction, base fluid mechanics, oil emulsification, food processing, renewable energy, and sewage treatment systems.