Physics-informed computational modelling for thermal analysis of Casson nanofluid flow over linear and nonlinear stretching surfaces

Thermal transport analysis of non-Newtonian nanofluids is essential for the design of advanced energy systems, manufacturing processes and biomedical thermal devices. This study investigates Casson nanofluid flow over linear and nonlinear stretching sheets under the combined effects of nonlinear thermal radiation, magnetic field, internal heat generation, Brownian motion, thermophoresis, porous medium resistance, convective boundary conditions and activation energy. The governing nonlinear boundary layer equations are transformed into coupled ordinary differential equations using similarity transformations and solved numerically to examine the velocity, temperature and concentration fields. The results reveal that nonlinear stretching significantly enhances the thermal boundary layer and increases the skin friction coefficient and Nusselt number compared with the linear stretching case. To enable rapid prediction, supervised machine learning models are trained using the numerical dataset. Among the models considered, artificial neural networks (ANNs) provide the best predictive performance. For the linear stretching case, the ANN achieves validation errors of RMSE ≈ 0.106 for the skin friction coefficient and RMSE ≈ 0.085 for the Nusselt number, with corresponding coefficients of determination of approximately 0.58 and 0.70. The close agreement between numerical and ANN predictions demonstrates the effectiveness of the proposed hybrid framework for efficient prediction and optimization of heat transfer in nanofluid thermal systems.