Predictive modelling of conducting Casson nanofluid flow using a physics-informed neural network: effects of thermal stratification and coupled transport mechanisms

Conducting Casson nanofluid flow with thermal stratification plays vital role in advanced heat and mass transfer processes such as energy conversion, polymer processing, metallurgical operations, and biomedical applications. The simultaneous influence of magnetic fields, porous-medium resistance, Joule and Darcy dissipation, thermal radiation, Brownian motion, thermophoresis, and chemical reactions creates a strongly coupled nonlinear boundary-value problem that is difficult to solve using conventional analytical or numerical methods. To address this challenge, present study examines flow, heat-transfer, and mass-transfer behaviour of conducting Casson nanofluid over exponentially expanding permeable surface, incorporating thermal stratification along with aforementioned physical effects. Governing equations are reduced to a system of nonlinear ordinary differential equations through similarity transformations. Physics-Informed Neural Network framework is developed to obtain predictive solutions by embedding the governing equations, boundary conditions and loss function. PINN utilizes automatic differentiation and a two-stage training strategy with Adam and L-BFGS optimizers. The numerical performance of the PINN is assessed using governing-equation residual metrics, including MSE, MAE, and RMSE. The MSE ranges from 4.74 × 10 −7 to 5.55 × 10 −3 , the MAE from 4.75 × 10 −4 to 5.32 × 10 −2 , and the RMSE from 6.89 × 10 −4 to 7.45 × 10 −2 across the reported parameter cases. These metrics quantify residual satisfaction of the governing equations rather than errors relative to an external reference solution. Agreement with an independently computed boundary-value solution is assessed separately through comparisons of the solution profiles and wall quantities for selected parameter cases. Overall, the results demonstrate the applicability of the PINN framework to the coupled nonlinear conducting Casson nanofluid problem. Independent comparison with a boundary-value solution was conducted for the baseline case and the parameter variations R d = 1.5 and S c = 0.6. The agreement in the wall quantities for these selected cases supports the numerical consistency of the PINN predictions under the conditions examined. These findings are limited to the evaluated cases and do not establish convergence or low solution error across the entire parameter range.