Brownian motion and thermophoresis effects on slip flow of alumina/water nanofluid inside a circular microchannel in the presence of a magnetic field

• Forced convection of alumina/water nanofluid inside a circular microchannel.
• Nanoparticles migration effects on fluid flow and heat transfer.
• Brownian motion and thermophoresis effects on nanoparticles migration.
• Nanoparticles move from the walls towards to core region of the microchannel.

The current study is a theoretical investigation of the laminar flow and convective heat transfer of alumina/water nanofluid inside a circular microchannel in the presence of a uniform magnetic field. A modified two-component four-equation nonhomogeneous equilibrium model was employed for nanofluids, which fully accounted for the effect of the nanoparticle volume fraction distribution. Because of the microscopic roughness in circular microchannels and also the non-adherence of the fluid–solid interface in the presence of nanoparticle migration, known as slip condition, the Navier's slip boundary condition is considered at the walls. The results indicated that nanoparticles migrate from the heated walls (nanoparticles depletion) towards the core region of the microchannel (nanoparticles accumulation) and construct a non-uniform nanoparticles distribution. The ratio of the Brownian to thermophoretic diffusivities (NBT) has relatively significant effects both on the distribution of the nanoparticles and the convective heat transfer coefficient of nanofluids. It was further observed that for smaller nanoparticles, the nanoparticle volume fraction is more uniform and abnormal variations in the heat transfer rate vanish. Moreover, in the presence of the magnetic field, the near wall velocity gradients increase, enhancing the slip velocity and thus the heat transfer rate and pressure drop increase.