Nanoparticles migration effects on magnetohydrodynamic (MHD) laminar mixed convection of alumina/water nanofluid inside microchannels

This is a theoretical study on effects of nanoparticles migration on magnetohydrodynamic mixed convective heat transfer of alumina/water nanofluid inside a vertical microchannel. Walls are subjected to different heat fluxes; q''lw for the left wall and q''rw for the right wall, and nanoparticles are assumed to have a slip velocity relative to the base fluid, induced by Brownian diffusion and thermophoresis. Scale analysis of the governing equations indicates that buoyancy effects due to the temperature distribution is insignificant, however, the buoyancy effects due to concentration distribution of nanoparticles have vast effects on flow and heat transfer characteristics. Further, it is shown that nanoparticles eject themselves from the heated walls and accumulate in the core region, but they are more likely to accumulate near the wall with lower heat flux. Also, the non-uniform nanoparticle distribution causes velocities to move toward the wall with higher heat flux and enhances heat transfer rate there. Moreover, while the nanoparticle volume fraction is smaller than 0.1, the maximum increase in the values of heat transfer rate is 37% for small nanoparticles which drops to 14% for larger nanoparticles. Applying a magnetic field leads to 42% and 30% increase in the values of heat transfer rate for small and large nanoparticles respectively. Additionally, one-sided heating serves as another causing factor for increasing the heat transfer rate which boosts it up to 80% for large nanoparticles.