Computational analysis and neural network validation of Jeffrey nanofluid flow over a moving vertical flat plate with chemical reaction and couple stress: a non-Fourier heat flux model

Abstract This study aimed to develop a unified mathematical model that couples couple stress rheology, chemical reaction, thermal radiation, and non-Fourier heat conduction with the Buongiorno two-phase nanoparticle transport model for magnetohydrodynamic Jeffrey nanofluid flow over a moving vertical flat plate, addressing a gap left by previous works that treated these phenomena in isolation. The governing partial differential equations were transformed into ordinary differential equations and solved numerically using the bvp4c solver in MATLAB. Grid independence testing confirmed convergence beyond 200 mesh points, and relative errors remained below 0.1 % against established benchmark solutions. An artificial neural network trained with the Levenberg-Marquardt algorithm was used as a consistency check on the computed dataset; the network reproduced the bvp4c outputs with correlation coefficients close to unity and mean squared errors between 10 –10 and 10 –12 . The results reveal that increasing the couple stress parameter and Deborah number both reduced fluid velocity, the former through heightened resistance to rotational deformation and the latter through stronger elastic memory effects. Temperature increased with thermal radiation and thermophoresis but decreased with the thermal relaxation parameter, since the fluid requires finite time to respond to boundary heating. Concentration declined with rising chemical reaction and Brownian motion parameters, reflecting accelerated species consumption and enhanced diffusive mixing respectively. The skin friction coefficient increased with the couple stress parameter, while the Nusselt number decreased as thermophoresis intensified. These findings provide practical design guidance for heat exchangers, drag control in maritime and aerospace applications, nanoparticle-based drug delivery, solar thermal collectors, and continuous casting processes, where accurate prediction of flow and transport behaviour directly influences operational efficiency and product quality.