Levenberg–Marquardt neural networks (LMNNs) for free convective Casson fluid flow in partially heated square cavity with rectangular heat source

The study of Casson fluid in cavities is relevant in different fields like biomedical simulations, chemical processing, lubrication, reactor design, and microfluidic devices, to mention just a few. Therefore, it remains always a topic of great interest for researchers to explore the flow field aspects of Casson fluid in both theoretical and experimental frames. Owing to such motivation, we offered an integration of neural networks with the finite element method to study the free convective Casson thermal flow field in a partially heated square cavity rooted with a rectangular heat source. The heat source is uniformly heated, and the bottom wall is taken with non-uniform heating. The right and left walls are engaged cold. The top wall is considered adiabatic. The flow equations are mathematically modeled and solved by using a hybrid meshed based finite element method. The Nusselt number along the rectangular heat source is predicted by an AI-based neural network model. The performance of the constructed neural network model is tested through regression coefficients and mean square error. The artificial neural network (ANN) model appears to be well-trained and capable of reliably forecasting heat transfer in this system, based on the close match between the ANN predictions and the real data of the Nusselt number. It is found that the horizontal and vertical velocities significantly increase as the Rayleigh number rises, indicating more intense convective flow. Furthermore, the Nusselt number significantly rises along the rectangular heat source for higher Rayleigh numbers.