Magnetic field and slip effects on free convection inside a vertical enclosure filled with alumina/water nanofluid

This paper deals with a theoretical investigation of natural convective heat transfer in a vertical enclosure filled with alumina/water nanofluid in the presence of a uniform magnetic field. A two-phase mixture model is used for nanofluid in the hypothesis that Brownian motion and thermophoretic diffusivities are the only significant slip mechanisms between solid and liquid phases. Because of the non-adherence of the fluid-solid interface in the presence of nanoparticle migrations, slip condition is considered at the surfaces, which appropriately represents the non-equilibrium region near the interface. Assuming a fully developed flow and heat transfer, the basic partial differential equations including continuity, momentum, and energy have been reduced to two-point ordinary boundary value differential equations and solved numerically. It is found that the nanoparticles moves from the hot wall (nanoparticles depletion) toward the cold wall (nanoparticles accumulation), constructing a non-uniform nanoparticles distribution. Then, it is shown that nanoparticle depletion at the hot wall is responsible for the controversial issue on the anomalous changes in the heat transfer rate. In addition, the slip parameter λ has a negative effect on the heat transfer rate, which is more pronounced for larger nanoparticles. The results also indicated that in the presence of the magnetic field, the near wall velocity gradients increase, enhancing the slip velocity and reduce the heat transfer rate.