Hybrid numerical-data-driven modeling and optimization of thermo fluid transport in magnetized Eyring–Powell fluid

Purpose Accurate prediction and optimization of nonlinear thermofluid transport are essential for the design of advanced thermal engineering systems. This study aims to develop a hybrid computational–optimization–data-driven framework for modeling coupled transport phenomena in magnetized Eyring–Powell fluids with variable thermophysical properties. The optimization analysis investigates coupled thermofluid transport in an unsteady magnetized Eyring–Powell fluid over a vertical surface with temperature-dependent viscosity and thermal conductivity. The primary objective is to analyze, optimize and predict convective heat transfer using response surface methodology (RSM) based on a central composite design. Design/methodology/approach The governing nonlinear partial differential equations are solved numerically using an explicit finite difference method to obtain the flow, thermal, concentration and entropy generation fields. The resulting numerical data are subsequently used to construct linear, quadratic and interaction regression models for the Nusselt number (Nu) as functions of the magnetic parameter (M), Eckert number (Ec), heat source/sink parameter (δ), Dufour number (Du) and the Eyring–Powell fluid parameter (K). The adequacy of the proposed regression model is evaluated through analysis of variance. In addition, an artificial neural network (ANN) based on the Levenberg–Marquardt back-propagation algorithm is developed to predict the transport behavior under various operating conditions. Findings The developed quadratic RSM model demonstrates excellent statistical significance (F = 596,513.10), (p < 0.001) and predicts the Nusselt number with relative errors below 0.156%, while the heat source/sink parameter is identified as the dominant factor governing heat transfer (F = 9.33 × 106). The predictive capability of the ANN is validated through mean squared error, error histogram and absolute error analyses, confirming its high prediction accuracy. Physically, increasing the Eyring–Powell fluid parameter (K) enhances both the fluid velocity and temperature fields, whereas higher dynamic viscosity suppresses the flow by reducing the fluid velocity. Originality/value The proposed numerical–optimization–ANN framework offers an efficient tool for predicting and optimizing convective heat transfer in magnetized non-Newtonian fluid systems, with potential applications in thermal management, energy conversion, polymer extrusion and process engineering.