Anisotropic behavior of magnetic nanofluids (MNFs) at filmwise condensation over a vertical plate in presence of a uniform variable-directional magnetic field

Brownian motion and thermophoresis are two primary sources of nanoparticle migration in nanofluids which have considerable effects on thermophysical properties of magnetic nanofluids (MNFs). In addition, the orientation and intensity of an external magnetic field influence the thermal conductivity of MNFs and makes it anisotropic. This is a theoretical investigation on developing the transport phenomenon of the nanofluids falling condensate film, taking into account the anisotropic effects of thermal conductivity. 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. The results have been obtained for different parameters, including the Brownian motion to thermophoretic diffusion N_BT, saturation nanoparticle concentration ℙ_sat, Hartmann number Ha, magnetic field angle α, and normal temperature difference γ = (T_{sat -} T_w)/T_w. A closed form expression for the nanoparticle volume fraction distribution of MNFs inside a condensate film is obtained and it has been revealed that the heat transfer rate is improved further when an external magnetic field is aligned in the direction of the temperature gradient. Moreover, it is indicated that smaller nanoparticles make a more uniform nanoparticle distribution and enhance the heat transfer rate.