https://doi.org/10.1140/epjp/s13360-025-06175-6
Regular Article
Magnetic field and Soret effect on mixed convection Williamson fluid flow between two concentric cylinders using artificial neural network
Department of Mathematics, National Institute of Technology, 506004, Warangal, Telangana, India
Received:
7
December
2024
Accepted:
24
February
2025
Published online:
14
March
2025
This study aims to investigate the steady mixed convection Williamson fluid flow characteristics between two concentric cylinders, considering the influence of the Soret and magnetic field effect and incorporating a first-order chemical reaction. The outer cylinder is in rotation while the inner cylinder remains fixed. The outer cylinder’s motion induces the flow. A magnetic field is applied in the radial direction. Using the proper transformation, the nonlinear partial differential equations of the Williamson fluid model are transformed into ordinary differential equations. Artificial neural networks are adopted to solve the nonlinear ordinary differential equations. The multiple-layered perceptron neural network used by the trial functions has adjustable parameters like biases and weights. The trial solution’s adjustable parameters are calculated using the optimization technique of the ADAMS (Adaptive Moment Estimation Algorithm) to fulfill the governing equations. The outcomes show that solving the equations with an artificial neural network-based approach delivers considerable accuracy and efficacy compared to the analytical solutions. Moreover, graphs show how pertinent parameters affect the velocity, temperature, and concentration profiles. The findings indicate that increasing the Hall parameter results in a 
increase in the velocity profile, while the temperature profile decreases by 
. Similarly, increasing the Soret parameter leads to a 
decrease in the velocity profile and a 
decrease in the temperature profile.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
