Supervised Learning Algorithm to Study the Magnetohydrodynamic Flow of a Third Grade Fluid for the Analysis of Wire Coating

Area of Science:

• Fluid Dynamics
• Computational Mathematics
• Materials Science

Background:

• Wire coating processes involve complex fluid dynamics, particularly with non-Newtonian fluids like third-grade fluids.
• Magnetohydrodynamics (MHD) plays a crucial role in processes involving electrically conducting fluids under magnetic fields.
• Accurate numerical modeling is essential for optimizing wire coating processes and understanding fluid behavior.

Purpose of the Study:

• To develop and validate an intelligent numerical computing model for analyzing magnetohydrodynamic flow of third-grade fluids in wire coating (MHD-TGFWCA).
• To implement a Levenberg-Marquardt back-propagation-based supervised neural network (LMB-SNN) for solving the governing equations.
• To assess the accuracy and effectiveness of the LMB-SNN approach through comparative analysis and performance studies.

Main Methods:

• Partial differential equations governing MHD-TGFWCA were transformed into ordinary differential equations using dimensionless parameters.
• A reference dataset was generated using Adam's numerical technique by varying key physical parameters (third-grade fluid, magnetic, and velocity ratio parameters).
• The LMB-SNN model was trained, tested, and validated using mean square error function (MSEF) optimization via Levenberg-Marquardt back-propagation.

Main Results:

• The LMB-SNN solver demonstrated high precision, with numerical outputs closely matching dataset values.
• Performance metrics including MSEF, regression plots, and error histograms confirmed the model's effectiveness.
• The study successfully validated the proposed LMB-SNN method for analyzing MHD-TGFWCA.

Conclusions:

• The Levenberg-Marquardt back-propagation-based supervised neural network (LMB-SNN) is a highly effective and accurate computational tool for modeling magnetohydrodynamic flow of third-grade fluids in wire coating.
• The developed numerical scheme provides a robust approach for analyzing complex fluid dynamics problems with significant engineering applications.
• The findings highlight the potential of intelligent numerical computing methods in advancing materials processing and fluid mechanics research.