Active and passive controls of the Williamson stagnation nanofluid flow over a stretching/shrinking surface

A steady stagnation point flow of an incompressible Williamson nanofluid towards a horizontal linearly stretching/shrinking sheet with active and passive controls on the wall mass flux is numerically studied. The governing partial differential equations are reduced into a system of ordinary differential equations using a similarity transformation and are solved using the bvp4c package in MATLAB. The velocity, temperature and nanoparticle volume fraction profiles together with the reduced skin friction coefficient, reduced Nusselt number and reduced Sherwood number are graphically presented to visualize the effects of parameters involved in the study. Results show that temperature and nanoparticle volume fraction are decreasing functions of the stagnation parameter, r. It is also found that the diffusivity ratio Nbt and Lewis number Le have almost negligible effects on heat transfer rate in passive control. Increasing value of Williamson parameter k will increase the skin friction in both stretching and shrinking surfaces.