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 Nu¯i on the inner cylinder wall decreases as the nanofluid volume fraction increases. This decrease in Nu¯i 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 Nu¯i to increase, while increasing Ha number and increasing the magnetic field causes Nu¯i 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 Nu¯i versus Ra, φ, Ha, and λ are derived for the axial and radial magnetic fields cases.