Central composite design in predicting heat transfer rate on the time-dependent flow of Williamson nanofluid with chemical reaction: A response surface methodology

The unsteady magnetohydrodynamic motion of non-Newtonian nanofluids via a permeable surface has attracted considerable interest due to its wide range of commercial applications. Particularly, in several industrial processes, cooling of electronic devices, polymer extrusion as well as biomedical engineering areas its utility is vital. The cross-diffusion of thermal and solutal is critical as they influence the distribution of migration of the nanoparticles, affecting the thermal properties. This study focuses on the magnetised flow of a Williamson nanofluid through a porous matrix embedded in a permeable, expanding surface. The simultaneous interaction of Brownian and thermophoresis along with the thermal radiation shows influential characteristics in enhancing the thermal properties. Further, the interaction of the heat source/sink along with chemical species enriches the flow phenomena. In practical scenario, the porous medium along with stretching surface used in filtration, oil recovery, chemical reactors, etc. The designed governing dimensional form of the equations is re-constructed into non-dimensional form by using appropriate transformations. Further, numerical simulation is carried out by utilizing shooting along with Runge-Kutta fourth-order technique. Moreover, results demonstrate that both Brownian and thermophoresis significantly enhances the particle concentration and temperature distribution and the existence of magnetism and chemical reaction further modifies the flow characteristics. Further, a statistical approach embedding central composite design is executed for the efficient heat transfer rate utilizing various influencing terms. It is revealed that the significant enhancement is projected for the variation the heat source but the magnetization decelerates the response of Nusselt number throughout.