Polynomial degree impact on prediction accuracy in Casson-Williamson fluid with Cattaneo-Christov

• Partial Differential Equations model reflecting the behavior of the Casson-Williamson fluid. • Similarity transformation to covert highly non-linear partial differential equations into ordinary differential equations. • Numerical Framework to find solution for ODE system. • Polynomial approximation of degree one and two. • Analysis of fluid properties and heat transfer including thermophoresis, and heat flux overflow and thermal profiles. A discussion on the 3D incompressible steady laminar boundary layer flow over a porous sheet due to the CattaneoChristov heat flux model and magnetohydrodynamic (MHD) effects are present, and artificial intelligence-based tools are used to predict the boundary layer flow, with a comparative analysis of degree 1 (linear model) polynomial approaches and degree 2 (linear model). The results have established that degree 2 polynomials are found to be more accurate than linear regressions in making precise predictions on flow behavior for its complexity. Important parameters under analysis include the fluid properties of Casson and Williamson, thermophoresis, heat flux overflow, and thermal profiles. With an increase in the Casson and Williamson fluid parameters, the velocity profile becomes smaller, showing improved resistance in flow. As thermophoresis parameter values are increased, the concentration profile increases while the boundary layer thickness decreases with improved mass transfer. The comparison among the polynomial models can be analyzed by referring to Table 2. The prediction performance metrics, such as R-squared and modified R-squared values, are displayed in Table 3. The nonlinear polynomial approach's success is demonstrated by the maximum value of 0.9912 for the Casson fluid parameter. The MSE values vary between 10 − 8 to 10 − 10 indicating strong reliability and accuracy of the ANN model. The results have significant engineering applications in designing thermal-fluid systems, such as polymer extrusion processes, cooling systems for electronic devices, and enhanced oil recovery techniques, where fluid flow and heat transfer control are critical.