<p>The features of mixed convection heat transfer of a couple stress Williamson nanofluid flowing across a rotating perpendicular cone are examined in this research work. The non-Newtonian nature of the Williamson fluid and the impact of couple stresses, dynamic viscosity and viscous dissipation are considered. In order to improve heat conductivity, two different nanoparticles, one is silver and other titanium dioxide, are added in the base blood. Similarity transformations are used to convert the governing partial differential equations into a collection of nonlinear ordinary differential equations, which are then solved semi-numerically using homotopy analysis method. The effect of important parameters for temperature, velocity field, skin friction and Nusselt number is carefully investigated with the help of graphs and table. The obtained results show that the couple stress and Williamson parameters have a considerable impact on the behaviour of the boundary layer and its thermal properties. This information can be used to optimize heat transfer in complex fluid engineering applications.</p>