MHD mixed convection in a vertical annulus filled with Al₂O₃-water nanofluid considering nanoparticle migration

In the current study, an MHD mixed convection of alumina/water nanofluid inside a vertical annular pipe is investigated theoretically. The model used for the nanofluid mixture involves Brownian motion and thermophoretic diffusivities in order to take into account the effects of nanoparticle migration. Since the thermophoresis is the main mechanism of the nanoparticle migration, different temperature gradients have been imposed using the asymmetric heating. Considering hydrodynamically and thermally fully developed flow, the governing equations have been reduced to two-point ordinary boundary value differential equations and they have been solved numerically. It is revealed that the imposed thermal asymmetry would change the direction of nanoparticle migration and distorts the velocity, temperature and nanoparticle concentration profiles. Moreover, it is shown that the advantage of nanofluids in heat transfer enhancement is reduced in the presence of a magnetic field.