Central Composite Design-Based Parametric Study of Magnetically Dissipative Darcy–Forchheimer Hybrid Nanofluid Flow over an Expanding Sheet

This study investigates the effect of magnetic interactions on two-dimensional electrically conducting hybrid nanofluid flow over an expanding sheet, considering porous media and Darcy forces. In addition, the study addresses the role of Ohmic and Joule heating effects on the heat transfer processes of a copper–alumina hybrid nanofluid suspended in water. Here, Mintsa model is applied to control thermal conductivity whereas Gharesim model is applied to ascertain viscosity. Using similarity transformations, the governing conservation equations for fluid flow are converted into nonlinear ordinary differential equations. The application of the Runge–Kutta 4–5th order approach enables accurate and efficient numerical resolution of the governing system. In addition, the Response Surface Method (RSM), a robust statistical approach, is utilized to investigate the enhancement of heat transfer across multiple parameters, where optimal findings are validated through Analysis of Variance (ANOVA). The paper shows a high level of congruence with previous studies in certain instances and gives the physical meaning of the added parameters through graphs and table. Graphical representations demonstrate that augmented magnetic field strength elevated the fluid temperature of the nanofluid, resulting in heightened surface friction and thermal transfer rate. However, when the intensity of the magnetic field intensified, there was a corresponding decrease in the rate of heat transfer until a specific threshold was reached. This investigation has practical applications in improving the heat managing systems. The renewable energy management, cooling effects in electronic devices, and trade heat exchangers, by refining heat transmission efficacy and fluid performance.