Thermal Transport and Physics-Guided Optimization of MHD Buongiorno Nanofluid over a Porous Cylinder with Machine Learning Applications

The thermal and solutal transport mechanisms in non-Newtonian fluids play a substantial role in energy systems, thermal management, polymer processing, and biomedical engineering. In this study, an integrated Local Non-Similarity Physics-Informed Neural Network framework is developed to investigate the non-similar boundary layer flow, heat, and mass transport of Williamson nanofluid through a horizontal porous cylinder under the combined effects of magnetohydrodynamics and porous media. The leading nonlinear system of equations that represents the problem is transformed into a coupled ordinary differential equation using the local non-similarity method. The resulting system is solved using a Physics guided Neural Network implemented in PyTorch, where the foremost equations and boundary conditions are incorporated into a physics-based loss function without requiring labeled training data. The influences of the magnetic parameter (M), surface heating parameter (γ), Prandtl number (Pr), Schmidt number (Sc), Brownian motion parameter (N_b), and thermophoretic parameter (N_t) on the velocity, temperature, concentration, skin friction coefficient, local Nusselt number and local Sherwood number are systematically investigated. The PINN predictions show excellent agreement with benchmark numerical solutions obtained using the Scipy boundary value solver, while maintaining low L² errors, confirming the accuracy and robustness of the proposed framework. The results demonstrate that the LNS-PINN approach provides an efficient and reliable mesh-free computational methodology for solving highly nonlinear non-similar transport problems involving coupled heat and mass transfer in non-Newtonian nanofluids.