RSM-Based Optimization and Sensitivity Analysis of Radiative MHD Tangent Hyperbolic Nanofluid Flow Over an Exponentially Stretching Porous Sheet With Variable Heat and Mass Fluxes

Abstract

This study investigates the steady, incompressible magnetohydrodynamic (MHD) flow of a tangent hyperbolic nanofluid over an exponentially stretching porous sheet considering variable heat and mass fluxes, thermal radiation, Brownian motion, thermophoresis, porous-medium resistance, and non-Newtonian effects. Similarity transformations are applied to convert the governing partial differential equations into a nonlinear system of ordinary differential equations, which is solved numerically using MATLAB's bvp5c solver. The influences of suction/blowing, exponential stretching, magnetic field strength, Prandtl number, Schmidt number, Brownian motion, thermophoresis, thermal radiation, and tangent hyperbolic parameters on the velocity, temperature, and concentration fields are systematically examined. The results indicate that wall blowing increases the surface temperature and nanoparticle concentration, $\theta \left(0\right)$ and $\varphi \left(0\right)$, by 130.8% and 98.3%, respectively, compared with suction conditions. Increasing the exponential stretching parameter $N$ reduces $\theta \left(0\right)$ and $\varphi \left(0\right)$ by 73.3% and 62.0%, respectively. Thermophoresis enhances $\theta \left(0\right)$ and $\varphi \left(0\right)$ by 12.4% and 30.0%, whereas higher Prandtl and Schmidt numbers reduce them by 41.3% and 42.9%, respectively. The positive skin-friction magnitude is further optimized using response surface methodology (RSM) with a face-centered central composite design (CCD). The developed quadratic RSM model exhibits excellent predictive capability with $R^2=0.999506$ and adjusted $R^2=0.999062$. The normalized skin-friction magnitude ranges from 0.754773 to 1.260247, and ANOVA and sensitivity analysis identify the tangent hyperbolic parameter as the dominant factor, followed by suction/injection and Weissenberg number, with a significant interaction between the latter two parameters. The findings provide a numerical-statistical framework for optimizing tangent hyperbolic nanofluid transport in thermal management, coating processes, and enhanced oil recovery applications.