Abstract This paper investigates the quadratic convective flow of Williamson nanoliquid with the impacts of velocity, thermal and concentration slips over a vertical wedge. Further, the magnetic effects and the Buongiorno two‐phase nanoparticle model are considered. The study of this type of flows over a vertical wedge appears in various engineering applications such as thermal insulation, engine parts of vehicles, aerospace, crude oil extraction and heat exchangers. The physical problem is formulated as a set of quadratic coupled partial differential equations (PDEs), which are dimensional. Further, the dimensionless PDEs obtained by the non‐similar transformations are solved with the aid of the implicit finite difference method and the Quasilinearization technique. The effects of slip parameters, streamwise coordinate, fluid material parameters and magnetic field on various gradients and profiles are explored through graphs. The greater values of concentration slip and thermal slip parameters improve the concentration and temperature profiles, but the fluid's velocity is reduced with the velocity slip parameter. The streamwise coordinate significantly influences the fluid's velocity more than the concentration and temperature profiles. The velocity and skin friction coefficient are pronounced more for a higher wedge angle. Also, the numerical results of this investigation compared to similar works that have been published before show that they are very consistent.
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