This research examines entropy production and thermodynamic irreversibility in the steady axisymmetric boundary layer flow of an incompressible Carreau fluid along a nonlinearly stretching cylinder in a porous medium with velocity and thermal slip boundary conditions. The model incorporates higher-order nonlinear heat sources, thermal radiation, and viscous dissipation. The obtained nonlinear partial differential equations (PDEs) are converted into ordinary differential equations (ODEs) by using appropriate similarity transformations. We solve these equations numerically using 50 Chebyshev collocation points with the Spectral Quasi-Linearization Method. The study results through parametric analysis show that curvature ( \(\lambda \) ) and viscoelasticity (We) inhibit flow close to the wall and enhance flow in the outer flow region. Moreover, the thermal radiation, nonlinear heat generation, porous permeability, and viscous dissipation cause a thicker thermal boundary layer. Thermal slip, by contrast, makes the temperature distribution less uniform. The maximum entropy generation, \(N_\text {s}(\eta )\) , occurs near the surface due to strong viscous and curvature effects. Therefore, Bejan number also shows a transition from heat transfer mechanism to a fluid friction and porous resistance mechanism. Extending these results, a robust artificial neural network (ANN) surrogate model trained on high-fidelity SQLM data using Latin Hypercube Sampling, gives excellent predictive accuracy, with \(R^2\) values between 0.99999 and 1.0 and very low root-mean-square error (RMSE) across the training, validation and test datasets. This hybrid SQLM-ANN framework enables fast parametric evaluation and optimization of entropy-related quantities. Potential real-world application areas of the current study include porous heat exchangers, polymer extrusion, fiber drawing, biomedical devices, geothermal systems, and high-temperature energy conversion devices, where minimizing irreversibility is critical for energy efficiency.
