Numerical and response surface methodology analysis of inclined MHD Eyring-Powell fluid flow over a curved stretching sheet with non-Fourier heat flux

This study numerically examines the steady two-dimensional flow of an Eyring-Powell fluid over a curved stretching sheet in the presence of an inclined magnetic field, an exponential heat source/sink, a Cattaneo-Christov heat flux, and homogeneous and heterogeneous chemical reactions in a non-Darcy porous medium. By applying similarity transformations, the governing nonlinear partial differential equations are simplified into ordinary differential equations, which are solved numerically using the MATLAB bvp4c solver. The velocity decreases with magnetic field strength, inclination angle, Forchheimer number, and porosity parameter but increases with the Eyring-Powell fluid parameter. Temperature decreases with thermal relaxation and curvature parameters, while magnetic field strength, heat generation, and radiation enhance it. Concentration increases with the Schmidt number and curvature, but decreases with the homogeneous and heterogeneous reaction rate. Entropy generation increases with the Brinkman number, magnetic parameter, and radiation parameter, whereas the Bejan number decreases with the Brinkman number and magnetic field strength and increases with the radiation parameter. A hybrid RSM-ANOVA framework is developed to model skin friction and the Nusselt number, demonstrating strong statistical significance ( $$p < 0.05$$ ) and high explanatory power ( $${R}^{2}=95.36 \\% $$ for skin friction and 100% for the Nusselt number). The results give significant insights into the design and optimization of non-Newtonian thermal-fluid systems with biological and engineering applications.