<p>In this article, both local non-similarity and global non-similarity solutions of the governing equations for momentum and thermal transport of Williamson nanofluid over a curved surface are reported. Effects of magnetic field, Joule heating, Brownian motion, and thermophoresis are taken into account. The problem is model using conservation laws of mass, momentum, energy, and nanoparticle concentration. The boundary layer approach, along with suitable dimensionless variables, simplifies the governing partial differential equations. The resulting equations for local non-similar and non-similar solutions are solved numerically. The flow features are presented and discussed for both curved and flat surfaces. The obtained velocity, temperature profiles, skin friction, local Nusselt number, and Sherwood number for different values of parameter are presented and discussed. Numerical values of skin friction, the Nusselt number, and Sherwood number are presented in tabular form. The results are validated with existing literature. A comparative analysis between local non-similarity solutions and global non-similarity solutions shows that flow and heat transfer features are strongly influenced with streamwise coordinate.</p>