Magnetohydrodynamic mixed convective flow of Al2O3–water nanofluid inside a vertical microtube

The current study is a theoretical investigation of magnetohydrodynamic (MHD) flow and mixed convective heat transfer of Al2O3–water nanofluid inside a vertical microtube. 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 due to the microscopic roughness in microtubes, the Navier׳s slip boundary condition is considered at the surfaces. Assuming a fully developed flow and heat transfer, the basic partial differential equations including continuity, momentum, and energy equations are reduced to two-point ordinary boundary value differential equations with endpoint singularities and solved numerically. The results indicate that for smaller nanoparticles, the nanoparticle volume fraction is more uniform and there is no abnormal variations in the heat transfer rate and pressure drop. Also, the heat transfer rate is enhanced in the presence of the magnetic field especially for the smaller nanoparticles. Moreover, as the magnetic field strength (Ha) intensifies, the peak of the velocity profile near the walls is increased; however, the peak of the velocity profile at the core region is decreased.