Multi-parameter-based Box–Behnken design for optimizing energy transfer rate of Darcy–Forchheimer drag and mixed convective nanofluid flow over a permeable vertical surface with activation energy

The optimization of energy transfer rate in Darcy–Forchheimer inertial drag and mixed convective nanofluid motion over a vertical permeable surface with Arrhenius kinetics is obtained by utilizing a multi-parameter-based Box–Behnken design. The proposed investigation aims to enhance thermal management systems, with a particular focus on advanced cooling technologies and geothermal energy extraction. Precise control of heat transfer is essential in these applications. The integration of Brownian motion and thermophoresis effects elucidate the study for the energy transfer characteristics of the nanofluid flow. The employment of the Darcy–Forchheimer drag effects in the porous medium and the mixed convection is considered for the combined influence of buoyancy and forced convection. Activation energy is incorporated for the simulation of chemical reaction that is useful in various industrial purpose. Numerical technique such as shooting-based Runge–Kutta is adopted for the solution of transmuted dimensionless equations obtained by using adequate similarity rules. A critical parametric analysis is projected for the contributing factor with a strong validation comparing with earlier study. The robust Box–Behnken design, a statistical experimental design is utilized for the exploration of the influence of multi parameters involving radiating heat, Eckert number, Brownian motion, thermophoresis, and thermal Biot number. Further, the important outcomes are; the flow through permeable surface give rise to the impact of suction enhances the fluid velocity and the stronger thermal convection with increasing thermal Biot number also favors in enhancing the heat transport phenomenon.