Response surface methodology for Darcy–Forchheimer convective flow of Williamson nanofluid: A sensitivity analysis

Abstract

This paper explores the Response Surface Method (RSM) for the Darcy–Forchheimer convective flow of Williamson nanofluid. The convective nanofluid flow is optimized using the Response Surface Methodology, and the effective parameters in the flow are explored through sensitivity analysis. The current study is investigated in two dimensions. Firstly, a mathematical model is developed for the Williamson nanofluid under the influence of Darcy–Forchheimer effects and convection over a stretching sheet. The developed model is simplified by similarity variables, and numerical results are obtained through the bvp4c MATLAB function. Secondly, an empirical relation is developed for heat and mass transport by variance analysis through the RSM approach for dimensionless variables that appeared in the flow model. Sensitivity analysis is performed for heat and mass transfer against the dimensionless variables, namely the inertia coefficient $(0.1\le Fr\le 3.5)$, porosity parameter $(1\le \beta \le 3)$, and radiation parameter $(1\le Rd\le 4)$. The findings show that the inertia coefficient, porosity parameter, and radiation parameter are dominant in the flow model for heat and mass transport. Furthermore, the radiation parameter is more prominent than the inertia and porosity parameters for mass transport, while the opposite behavior is observed for heat transport.