Optimization using response surface methodology for Eyring-powell fluid flow with Cattaneo-Christov heat flux and cross diffusion effects

The optimization of heat transfer in engineering applications has significant implications for product performance and efficiency. This study investigates the flow and heat transfer characteristics of Eyring-Powell fluid over a curved sheet, incorporating complex phenomena such as magnetic dipoles, Cattaneo-Christov heat flux, and cross-diffusion effects. Navier's slip and melting boundary conditions are applied to model realistic physical constraints. The study employs response surface methodology (RSM) and sensitivity analysis to evaluate the parametric influences on skin friction and the Nusselt number, providing statistical insights into their behavior. Using similarity transformations, the governing partial differential equations are converted into ordinary differential equations, which are numerically solved using the Runge-Kutta-Fehlberg 4th-5th order method. Key findings include the reduction in velocity due to higher Eyring-Powell parameters, ferrohydrodynamic interactions, and slip effects. Similarly, increased melting and ferrohydrodynamic interactions lower the fluid temperature, while the Dufour number enhances it. The concentration is positively influenced by higher Soret numbers. Statistical results demonstrate a perfect fit with a squared-R coefficient of 100 %, and the Pareto chart identifies critical points at 2 for skin friction and the Nusselt number. Sensitivity analysis reveals negative sensitivity for most parameters across ferrohydrodynamic interaction levels, except for the Prandtl number, which exhibits positive sensitivity at low and medium Eyring-Powell parameter levels but turns negative at higher levels. This work provides a robust framework for understanding and optimizing the thermofluidic behavior of non-Newtonian fluids under complex physical conditions, offering valuable insights for industrial applications.