Physics informed neural network framework for non-similar nano-heat and solutal transport in a rheological fluid over a stretching cylinder

Accurate prediction of non-similar momentum, thermal and solutal transport phenomena in rheological fluids is crucial for the design and optimization of advanced thermal management systems, heat exchangers, polymer processing, chemical reactors, energy conversion devices and biomedical transport processes. Motivated by these engineering applications, this study presents a Physics-Informed Neural Network (PINN) framework for analyzing magnetohydrodynamic mixed convection flow of a Jeffrey fluid over a stretching horizontal cylinder embedded in a Darcy porous medium. The mathematical model incorporates the coupled effects of magnetic field, porous resistance, thermal radiation, Brownian diffusion, thermophoresis, viscous dissipation, velocity slip, internal heat generation, and Arrhenius activation energy along with chemical reaction. Owing to the non-similar nature of the governing equations, the Local Non-Similarity method is employed to transform the governing partial differential equations into a coupled system of ordinary differential equations, which is subsequently solved using a PINN implemented in PyTorch. The suggested algorithm is evaluated and tested with the help of BVP4C solver and shows good consistency with low $$\:{L}^{2}$$ error value of $$\:3.5\times\:{10}^{-3}$$ and stable convergence throughout the training phase. The results reveal that the rise in value of magnetic parameter reduce the velocity of fluid due to the Lorentz force while increase in Darcy number improves the flow due to decrease in porous effect. The thermal radiation and heat source have a major role to play in rising the temperature profile, while the increase in Schmidt number diminish the concentration distribution. The proposed LNS-PINN framework provides a computationally efficient procedure for simulating non-similar transport problems and offers a promising computational tool for engineering design and optimization of advanced systems.