The mathematical model for heat transfer optimization of Carreau fluid conveying magnetized nanoparticles over a permeable surface with activation energy using response surface methodology

Abstract The sensitivity analysis and response surface methodology (RSM) is performed for the key parameters governed by the magneto‐flow and heat transport of the Carreau nanofluids model toward a stretching/shrinking surface in the presences Arrhenius activation energy and chemical reaction. Nanofluid that displayed Brownian motion and thermophoresis was considered with the permeable condition. The effects of different physical parameters were analyzed by employing appropriate similarity transformations in nonlinear partial differential equations and converted to the dimensionless system of ordinary differential equations. The finite difference method in bvp4c code solves the equations numerically. Associated parameters are presented graphically and interpreted against local Nusselt number, Sherwood number, and skin friction coefficient. An increase in the activation energy factor leads to increased concentration in permeable flow. The higher the activation energy lower the temperature and causes the reaction rate constant to decrease. In addition, it slows down the chemical reaction and increases the concentration characteristics. The increase of radiation and Prandtl number leads to an increase in heat transfer for the permeable surface. Furthermore, the Schmidt number and the binary reaction rate parameter increase the mass transfer for suction/injection flow. As a result, the Nusselt number's highest sensitivity is the Eckert number and the lowest to the thermophoresis parameter. The Sherwood number's positive sensitivity is observed for the Eckert number and Brownian motion parameter, whereas negatively sensitive to thermophoresis.