Numerical investigation on natural convection of Al2O3/water nanofluid with variable properties in an annular enclosure under magnetic field

Abstract

Numerical investigation of the natural convection of Al2O3-water nanofluid is carried out in a differentially heated vertical annulus under a uniform magnetic field. An in-house Fortran code has been developed to solve the system of equations governing the magneto-hydrodynamic flow. Computations are carried out for different Rayleigh numbers (104 ≤ Ra ≤ 106), nanoparticle diameter (dp = 13 and 47 nm), nanoparticle volume fraction (0 ≤ φ ≤ 0.09), radius ratio (2 ≤ λ ≤ 10), and different Hartmann numbers (0 ≤ Ha ≤ 100). According to the simulation data, nanoparticle size is crucial for evaluating nanofluid properties, such as viscosity and thermal conductivity. The computational results reveal that, for nanoparticles with a diameter dp = 47 nm, the average Nusselt number on the inner cylinder wall decreases as the nanofluid volume fraction increases. This decrease in number is observed up to a volume fraction φ = 0.05, after which it increases again. For the full range of volumetric fractions, it is shown that increasing Ra number causes to increase, while increasing Ha number and increasing the magnetic field causes to decrease. Furthermore, as the Ha number increases, the heat transfer enhancement ratio En increases mainly when the magnetic field is oriented radially. Finally, new correlations of versus Ra, φ, Ha, and λ are derived for the axial and radial magnetic fields cases