The influence of thermal radiation and magnetic field on mixed convection Williamson fluid flow via a vertical channel using Adam optimization technique

This study investigates the mixed convection flow of Williamson fluid through a vertical channel affected by the magnetic field and radiation effects. By employing suitable transformations, the governing partial differential equations are adapted into ordinary differential equations and solved by using the “artificial neural network”. A neural network with multiple layers of perceptrons and adjustable parameters (biases and masses) is used in the trial functions. The adjustable parameters of the trial solution are determined using the “ADAM (adaptive moment estimation algorithm) optimization technique” to satisfy the governing equations. The ANN's result shows good accuracy when compared with the analytical solutions. The primary objective is to analyze the impact of source parameters such as the magnetic field strength, thermal radiation, and Williamson fluid characteristics on velocity and temperature distributions. The velocity profile increases when increasing the radiation parameter, and cross‐flow velocity decreases when increasing the Hall parameter. The outcomes show that a boost in Weissenberg number leads to velocity profiles and friction coefficient growth, as well as heat transfer falls. Additionally, the heat transfer amount drops with a rise in the radiation parameter.Moreover, the ANN results are validated against “spectral quasi linearization method” (SQLM) solutions achieving an error margin of demonstrating the robustness of the proposed method. Parametric studies reveal that an increase in the Williamson parameter reduces the velocity gradient by approximately 10.23%, whereas the magnetic parameter enhances thermal gradients by nearly 9% due to Lorentz force effects. Furthermore, the radiation parameter enhances the temperature profile by up to 87.74%. The ANN methodology proves to be a reliable and computationally efficient approach for solving complex fluid dynamics problems paving the way for future research in machine learning‐assisted fluid flow analysis.