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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 N bt 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.

A stagnation-point flow of a Powell–Eyring nanofluid along a vertical stretching surface is examined. The buoyancy force effect due to mixed convection is taken into consideration along with the Brownian motion and thermophoresis effect. The flow is investigated under active and passive controls of nanoparticles at the surface. The associating partial differential equations are converted into a set of nonlinear, ordinary differential equations using similarity conversions. Then, the equations are reduced to first-order differential equations before further being solved using the shooting method and bvp4c function in MATLAB. All results are presented in graphical and tabular forms. The buoyancy parameter causes the skin friction coefficient to increase in opposing flows but to decrease in assisting flows. In the absence of buoyancy force, there is no difference in the magnitude of the skin friction coefficient between active and passive controls of the nanoparticles. Stagnation has a bigger influence under passive control in enhancing the heat transfer rate as compared to when the fluid is under active control. Assisting flows have better heat and mass transfer rates with a lower magnitude of skin friction coefficient as compared to opposing flows. In this case, the nanofluid parameters, the Brownian motion, and thermophoresis altogether reduce the overall heat transfer rates of the non-Newtonian nanofluid.

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