The heat transport mechanisms and stagnation point of the MHD Williamson nanofluid are investigated in the presence of Brownian motion and thermophoresis diffusion past a permeable stretching/shrinking cylinder. Both the conditions of velocity slip and heat source/sink effects are considered. The governing partial differential equations are converted into a system of coupled ordinary differential equations using suitable similarity transformation and then solved numerically via shooting scheme together with Runge-Kutta-Fehlberg method. The effect on drag coefficient, heat and mass transport rates as well as the dimensionless velocity, temperature and concentration fields of the physical boundaries objectives of the study, are graphically delineated and thoroughly discussed. As nanoparticle concentration increases at the outer surface of the boundary layer, the rising patterns of Nusselt number as well as skin friction are observed. Dual solutions with the critical value of the mass transfer parameter (0