Thermal performance prediction of unsteady magnetohydrodynamic cross fluid flow over a porous oscillating surface via finite difference and neural network methods

Purpose The study aims to evaluate and predict the influence of different wall motions on heat transfer rate and fluid friction in unsteady magnetohydrodynamic flow of a nonNewtonian Cross fluid. In addition, it seeks to develop a hybrid numerical–artificial intelligence framework to accurately predict the flow field, thermal distribution and concentration field, enhancing predictive accuracy and computational efficiency in thermal engineering applications. Design/methodology/approach The governing nonlinear equations for unsteady MHD flow of a nonNewtonian Cross fluid are solved using the finite difference method, and the resulting data set is used to train an artificial neural network to predict the flow field, thermal distribution and concentration field. Findings A detailed case study of wall kinematics demonstrates that steady wall motion provides a baseline thermal response, whereas pure oscillatory motion enhances heat transfer by 29.4% due to intensified near-wall mixing. Ramp-oscillatory motion yields the maximum thermal enhancement, increasing heat transfer by 73.2%, while phase-shifted oscillations improve thermal transport by approximately 65% and concurrently reduce fluid friction, indicating superior thermo-hydrodynamic performance. Mass transfer remains insensitive to wall kinematics. The ANN predictions achieve high accuracy with absolute errors in the range of 10−4 to 10−5. Originality/value The study presents a hybrid numerical–artificial intelligence framework for predicting heat transfer and fluid friction in unsteady MHD flow of a nonNewtonian Cross fluid. This approach provides an efficient and accurate strategy for analyzing the effects of complex wall motions, offering insights for thermal optimization and predictive control in oscillatory nonNewtonian flow systems.