Stagnation-Point Casson Fluid Flow with Variable Properties and Heat Flux: An Adaptive PINN Approach

The objective of this research is to explore the nature of non-linear flow and heat transfer of the Casson fluid at the stagnation region in view of variable surface heat flux, viscous dissipation, and temperature-dependent thermal properties of the fluid. The model developed here represents the influence of non-linear rheological behavior, surface thermal loading, viscous heating, and variations in fluid properties on flow dynamics. The nonlinear boundary layer equations are reduced to a dimensionless form and solved using the Residual-Based Adaptive Parametric Physics-Informed Neural Network (RAP-PINN) method. This is an improvement on traditional numerical solution methods, which repeatedly solve each parameter combination separately. The new approach incorporates the physics into the training algorithm and places more importance on regions where there are higher residual errors. This allows the network to learn the physics-based solution for different governing parameters while keeping the accuracy of the solution high. An investigation of the influence of velocity ratio parameter, Casson parameter, Eckert number, and variable property parameters on the velocity, nanoparticle concentration, and temperature profiles along with their respective heat and mass transfer behaviors is conducted. Comparison with already published results shows very good consistency, which once again verifies the efficiency, accuracy, and reliability of the presented RAP-PINN approach in solving the present nonlinear problem. The suggested model can be used especially in the fields of thermal management, coating and polymer processing, cooling processes, and other engineering applications that involve non-Newtonian fluids under non-uniform thermal boundary conditions.