Numerical and artificial neural network time-series modeling of Casson–Jeffrey nanofluid flow over linear and nonlinear stretching surfaces in porous media

This study investigates the synergistic influence of magnetohydrodynamics, thermal radiation and porous medium on the transport of Casson-Jeffrey hybrid nanofluid over both linear and nonlinear stretching sheets. The governing equations are solved numerically using the Runge–Kutta with Shooting method and the outcomes are validated with a multilayer perceptron artificial neural network in neural network time series. The key controlling parameters include magnetic number, Casson parameter, Jeffrey parameter, buoyancy ratio, radiation parameter, brownian motion, thermophoresis, prandtl number and heat generation. The results demonstrate that increasing the magnetic parameter from 0.1 to 0.4 enhances the skin friction magnitude by approximately 12% for linear stretching and 15% for nonlinear stretching. Similarly, raising the radiation parameter from 0.1 to 0.4 increases skin friction magnitude by about 10% in the linear case and 25% in the nonlinear case. In contrast, the Nusselt number decreases when the brownian motion parameter rises from 0.1 to 0.4, leading to an almost 11% reduction in both linear and nonlinear flows. Thermophoresis effects further suppress the heat transfer rate, showing a 5% decline when its value increases from 0.1 to 0.4. Neural network validation confirms the accuracy of the solver, with regression coefficients very close to unity R ≈ 0 . 9999 and mean square error values as low as 1 . 84 × 1 0 − 6 . These findings underline the physical importance of magnetic, radiative, and porous medium effects in hybrid nanofluid transport and demonstrate the effectiveness of artificial intelligence tools for predictive modeling. Future research can extend this framework to unsteady, three-dimensional and experimentally validated configurations.