Optimization of Chemically Reactive Radiative MHD Casson Hybrid Nanofluid Flow over a Time-Dependent Stretching Surface Using Response Surface Methodology and ANOVA

Abstract

: This study examines transient heat and mass transfer characteristics in a Casson-based hybrid nanofluid (Au–Cu/water) flowing over a time-dependent stretching elastic surface in the presence of porous media and viscous dissipation. The mathematical model further incorporates the effects of magnetic fields, thermal radiation, chemical reactions, and velocity slip conditions to capture realistic transport phenomena encountered in advanced thermal systems. Through suitable similarity transformations, the governing partial differential equations are reduced to a system of nonlinear ordinary differential equations, which are solved numerically using the MATLAB bvp4c solver. To identify optimal operating conditions, Response Surface Methodology (RSM) is employed to develop predictive correlations for skin-friction coefficient, heat transfer rate, and mass transfer rate. The statistical significance and adequacy of the developed models are assessed using Analysis of Variance (ANOVA). Validation against previously published results demonstrates excellent agreement, confirming the accuracy and robustness of the proposed formulation. The results reveal that variations in the magnetic field substantially modify the Lorentz force distribution, leading to pronounced changes in the velocity, temperature, and concentration profiles. Furthermore, magnetic field strength, slip effects, and hybrid nanofluid properties significantly influence surface shear stress, thermal transport, and concentration boundary-layer development. The RSM optimization framework successfully identifies parameter combinations that maximize heat and mass transfer performance while