Effects of magnetic field strength and direction on anisotropic thermal conductivity of ferrofluids (magnetic nanofluids) at filmwise condensation over a vertical cylinder

Brownian diffusion and thermophoresis are two primary sources of nanoparticle migration in nanofluids which have considerable impact on thermophysical properties of ferrofluids (magnetic nanofluids). Furthermore, orientation and intensity of magnetic fields influence the thermal conductivity of ferrofluids and make them anisotropic. In this paper, a theoretical investigation on filmwise condensation of ferrofluids over a vertical cylinder in the presence of a uniform variable-directional magnetic field is investigated, taking into account the anisotropic effects of thermal conductivity. The modified Buongiorno's model is employed for the nanoparticle–fluid suspension to simulate the nanoparticle slip velocity relative to the base fluid originating from the thermophoresis (nanoparticle slip velocity due to temperature gradient) and Brownian motion (nanoparticle slip velocity due to concentration gradient). The distribution of nanoparticles inside a condensate film is analytically obtained and it is revealed that the heat transfer rate is improved further when the angle between the magnetic field and temperature gradient grows.