Magnetohydrodynamic Williamson fluid flow in ureteral tubes with heat and mass transfer in electromagnetic therapy: numerical and artificial neural network analysis

Ureteral peristalsis, responsible for transporting urine, is easily interfered with by mechanical and physical factors. Because of the ionic constituents, urine is electrically conducting and thus is sensitive to electromagnetic fields. The present study investigates the effects of magnetic therapy on urine flow when solid nanoparticles are suspended in urine, relevant to conditions such as kidney stones or targeted drug delivery. This study investigates the influence of magnetic fields on the flow behavior of a specialized nanofluid, analogous to urine laden with suspended nanoparticles, within a ureter-like conduit. Instead of relying on conventional methodologies, a mathematical modeling framework is employed to analyze the combined effects of body forces and thermal transport on fluid dynamics. Particular emphasis is placed on the interplay between electromagnetic effects and Soret-driven thermodiffusion to elucidate their coupled impact. Furthermore, a trained artificial neural network is utilized to predict and validate the flow characteristics. The study investigates a two-phase system using Williamson liquid and small particles under magnetic forces, considering factors like wall slip, viscous dissipation, and Soret thermodiffusion. The equations are scaled down in dimensionless notation and solved using a finite difference method (FDM), with stability confirmed across various mesh sizes and time steps. Over 1,000 simulations explore key parameters: magnetic strength (0–5), magnetic parameter (0–5), Weissenberg parameter (0.1–1.5), suspension parameter (up to 0.6), and Prandtl number (0.7–7.0). Neural Network algorithm(NNA) through Levenberg–Marquardt backpropagation method (LMBP) then learns patterns through trial-and-error tuning to improve output predictions. Key results show nanoparticles slow down the main flow; meanwhile, slippery effects help move particles along the edges, amplifying skin friction and pressure changes. When the Weissenberg parameter rises, fluid speed increases, but heat spreads decay. Moreover, the proposed predictive framework demonstrates excellent performance, yielding low mean squared error (MSE), strong correlation metrics, and high regression accuracy, thereby establishing its effectiveness as a reliable surrogate modeling approach. This study provides key insights into improving electromagnetic treatment in urinary care. The tested neural network runs quickly and behaves like a smart calculator for predicting fluid movement, with potential applications in targeted drug-delivery systems and in the treatment of urinary infections by fine-tuning treatment settings. This study is the first to consider ureteral peristalsis, electromagnetic forces, viscous heating, thermodiffusion, and wall slip in particulate non-Newtonian flow. By addressing the two-phase nature of clinically relevant flows, including both fluid and particles, it advances beyond traditional models that oversimplify bodily fluids, particularly urine.