<p>Drilling fluids with temperature-dependent characteristics are essential for the extraction of gasses and petroleum during deep drilling because these fluids are exposed to high temperatures and pressure. On the other hand, the clay nanoparticles regulate the fluid reaction to high temperatures by enhancing its thermal conductivity and stabilize its performance in high temperature circumstances. Therefore, the current investigation focuses on the mixed convection flow and heat-mass transfer characteristics of water-based Williamson drilling nanofluids (NF) over a vertical cylinder immersed in Darcy-Brinkman permeable medium. The Brinkman-Maxwell-Garnett model accounts the influence of clay nanoparticle dispersion in the water-based Williamson fluid. The governing set of equations are solved using Runge-Kutta (RK-4) method and their solutions are explained in a visual details. The findings suggest that the flow field declines with high porosity, inverse Darcy number, and curvature parameter by increasing permeability and reduced drag force. Variable viscosity results in decreased velocity. Variable thermal conductivity improves the thermal efficiency, while constant thermal conductivity results in a less sensitive and less thermal profile. Higher inverse Darcy number, Weissenberg number, and particle volume fraction improve the heat transfer rate. Smooth, uniform streamlines in the flow with constant viscosity show constant resistance across the region.</p>