Effects of nanoparticle migration on hydromagnetic mixed convection of alumina/water nanofluid in vertical channels with asymmetric heating

The effects of nanoparticle migration on mixed convection of alumina/water nanofluid inside a vertical channel in the presence of a uniform magnetic field have been investigated theoretically. Walls are subjected to different heat fluxes; qlw'' for the left wall and qrw'' for the right wall, and nanoparticles are assumed to have a slip velocity relative to the base fluid induced by the Brownian motion and thermophoresis. Considering hydrodynamically and thermally fully developed flow, the governing equations including continuity, momentum, and energy equations have been reduced to two-point ordinary boundary value differential equations and they have been solved numerically. It is shown that nanoparticles eject themselves from the heated walls, construct a depleted region, and accumulate in the core region, but they are more likely to accumulate toward the wall with the lower heat flux. In addition, inclusion of nanoparticles in the presence of a magnetic field has a negative effect on the performance.