Response Surface Methodology for Soret-Dufour Model of Walter-B Fluid Flow over a Stretchable Channel for Industrial Applications

Optimization of the transport mechanisms in non-Newtonian fluids is fundamental to enhance the thermal efficiency of a wide range of engineering systems. In this study, Soret-Dufour effects on the flow of Walter’s-B fluid in a stretchable porous channel are investigated. The main focus is to optimize the surface drag by using response surface methodology and sensitivity analysis. The model integrates a magnetic field, buoyancy, linear radiation, a porous medium, heat generation, chemical reaction, and second-order slip with suction/injection. The resulting nonlinear governing equations are solved by utilizing the Runge-Kutta-Fehlberg approach employed in a shooting technique, while RSM-ANOVA is used to identify dominant parameters. These outcomes show that the skin friction varies from − 7.5407 to − 7.8544 , with minimum drag magnitude occurring at R e = 1 , M = 0.5 , and K p = 1 , corresponding to variation in the surface approximately around 4%. Enhancing porosity reduces the surface drag, and also magnetic parameters suppress the local shear. The radiation and cross-diffusion effects cause a rise in thermal and concentration components. ANOVA consequences reveal that porosity K p is the most influential parameter ( 66.8 % ) , followed by R e ( 29.0 % ) and M ( 1.6 % ) , with p < 0.001 indicating a substantial model significance. Markedly, controlling porosity is identified as the most effective strategy for reducing surface drag and improving a system’s performance. These conclusions are applicable to several industrial processes, such as polymer extrusion, surface coating operations, and heat dissipation management in porous channel configurations.