Rheological analysis and heat transfer enhancement of Williamson nanofluid in mixed convection flow over a stretching cylinder/plate

This study explores the rheological properties of Williamson nanofluids and their effects on flow dynamics within stretching cylinders and plates, aiming to enhance heat transfer processes, advance nanofluid-dependent technologies and optimize manufacturing procedures. By examining mixed convection, incompressible, unsteady magnetohydrodynamic Williamson nanofluid flow in a permeable medium with velocity slip and convective boundary conditions, the analysis incorporates magnetic fields, thermophoresis, Brownian motion, radiative heat flux and chemical reactions. Utilizing similarity transformations, the nonlinear partial differential equations governing the flow are converted into ordinary differential equations, which are then solved using the numerically efficient Keller box method. The results are rigorously validated against the existing literature. Key findings reveal that the velocity boundary layer decreases with increasing porous media, magnetic and unsteady parameters, while the heat transfer rate on the elongating cylinder's surface increases with enhanced radiative flux. These insights contribute to a deeper understanding of fluid behavior in stretching cylinder/plate geometries. Practical implications suggest that Williamson nanofluids could significantly improve oil drilling and extraction processes, maximizing recovery rates and minimizing environmental impact, and hold potential for environmental remediation applications such as groundwater treatment and wastewater management.