Magnetic field and Soret effect on mixed convection Williamson fluid model through a vertical channel using artificial neural network

Purpose This study aims to analyze the mixed convection of Williamson fluid through a vertical channel, taking into account the effects of both the Soret phenomenon and a magnetic field along with a first-order chemical reaction. An “artificial neural network” (ANN) is used to carry out the investigation. The aim is to examine the impact of various physical parameters on velocity, temperature and concentration profiles as well as on skin friction, heat and mass transfer rates. Design/methodology/approach ANNs are used to solve the flow problem. A multilayer perceptron neural network with tunable parameters is used for the trial functions. These parameters are adjusted to find the best solution. The Adam optimization algorithm (adaptive moment estimation) is applied to adjust the parameters of the trial solution. Findings The authors assess the convergence and accuracy of the findings by comparing them with the exact spectral quasi linearization method, resulting in satisfactory outcomes. The graphs demonstrate how changes in different parameter factors affect the velocity, temperature and concentration curves. The outcome demonstrates that the axial velocity and concentration profiles decrease as the magnetic parameter value increases. The axial velocity and concentration trends amplify as the Hall parameter increases. Meanwhile, a spike in the Williamson and Soret parameters enhances these profiles, except for the temperature profile. The results indicate that raising the value of the chemical reaction parameter drops the velocity, temperature and concentration profiles. The skin friction coefficient and heat transfer amount increase with the rise of the Soret number. Originality/value The current finding from this study can be applied in various engineering and industrial processes where non-Newtonian fluids are involved, such as in chemical processing, petroleum engineering and materials manufacturing. The use of a feed-forward multilayer perceptron neural network, along with the ADAM optimization technique, presents a novel methodology for addressing complex nonlinear equations contributing to the advancements in computational fluid dynamics.