Laminar filmwise condensation of nanofluids over a vertical plate considering nanoparticles migration

• An exact analytical solution for nanoparticle distribution inside the condensation film is obtained.
• Effects of nanoparticle migration on heat transfer enhancement in the film are studied.
• Thermophoresis and Brownian motion effects on the cooling performance are studied.
• It is shown that alumina nanoparticles reveal better performance than titanium.

This is an investigation on developing the transport phenomenon of the nanofluids falling condensate film, taking into account the effects of nanoparticle migration. The intensity and direction of nanoparticle migration are able to manage the thermophysical properties of nanofluids, as well as the control of flow, heat transfer, and mass transfer, in order to improve the cooling performance. Thus, Brownian motion and thermophoretic diffusivity have been considered by using the modified Buongiorno model to observe the effects of nanoparticle slip velocity relative to the base fluid. Our outcomes have been obtained for different parameters, including the ratio of Brownian motion to thermophoretic diffusivity NBT, saturation nanoparticle volume fraction ϕsat  , and normal temperature difference γ=(Tsat−Tw)/Twγ=(Tsat−Tw)/Tw. It is revealed that increasing ϕsat and decreasing γ enhance the heat transfer rate and the nanoparticle volume fraction inside the condensate film. In addition, as the nanoparticle diameter increases, its migration grows in the film, which intensifies the nanoparticle volume fraction on the cold wall. Further, inclusion of alumina nanoparticles signifies a better cooling performance than titania.