Multiple solutions and stability analysis in MHD non‐Newtonian nanofluid slip flow with convective and passive boundary condition: Heat transfer optimization using RSM‐CCD

Abstract

This study explores the effect of Williamson nanofluid in the presence of radiation and chemical reaction caused by stretching or shrinking a surface with convective boundary conditions. After implementing two‐component model and Lie group theory, the transformed ODEs are solved using the Runge–Kutta Dormand–Prince (RKDP) shooting approach technique. The dual solutions are predicted for certain range of physical nanofluid parameters, such as Williamson parameter (), stretching/shrinking parameter (), and suction parameter () with different slip and magnetic M parameters. Contour plots are generated for the stable branch of the Nusselt number () for different combinations, providing insights into the heat transfer characteristics. The eigenvalue problem is solved in order to predict flow stability. The optimization of heat transfer in nanoliquid is conducted by RSM‐CCD. The resulting quadratic correlation enables the prediction of the optimal Nusselt number for , , and . This investigation is motivated by various applications including manufacturing processes, thermal management systems, energy conversion devices, and other engineering systems where efficient heat transfer is crucial.