Influence of couple stress and Cattaneo-Christov heat flux on Jeffrey hybrid nanofluid flow over a moving thin needle with artificial neural network validation

This study investigated the steady flow of a Jeffrey-type hybrid nanofluid past a moving slender needle. This study introduces a new complexity by simultaneously accounting for three key physical effects: couple stress, thermal radiation, and a non-Fourier heat transfer model (Cattaneo-Christov) that incorporates a time lag for heat propagation. This specific combination of features in such a flow configuration has not been previously examined. The mathematical model, formulated using partial differential equations, was simplified into a set of coupled ordinary differential equations through similarity transformations and then solved using the bvp4c solver. Key findings show that a stronger magnetic field slows down the fluid, whereas a higher Deborah number increases the skin friction coefficient by 13.06%. When the values of the thermal relaxation parameter fell between 0 and 0.9, the heat transmission rate surged by 25.74%, and the augmentation of thermal radiation led to an elevated fluid temperature. The irreversibility analysis (entropy generation) revealed that a higher Brinkman number increases energy losses, shifting the dominant source of inefficiency from heat transfer to fluid friction. Furthermore, a Bayesian-regularised Artificial Neural Network demonstrated excellent predictive accuracy, confirming the reliability of the physical trends discovered.