A two-phase model for studying the complex interplay between natural convection and magnetic field in aluminum-oxide/water nanofluid

Abstract

While previous experimental studies revealed the existence of optimal heat transfer performance in natural convection of magnetohydrodynamic (MHD) nanofluid flows, it is believed that this phenomenon is not unique in different levels of magnetic flux density. In order to prove this speculation, we numerically investigate the influence of the magnetic field on steady natural convection of aluminum-oxide (Al2O3) nanofluids inside an enclosure. The MHD flow model without the consideration of nanofluids is well validated against theoretical, numerical, and experimental results. The nanofluid in the present investigation has temperature-dependent physical properties and is modeled by a two-phase mixture considering thermophoresis and Brownian diffusion. While varying the volume fraction of nanoparticles from 0 to 6%, we methodically examine the effect of the Hartmann number on the heat transfer performance through the thermal behavior map in terms of the Hartmann–Rayleigh plane. Depending on the combination of magnetic intensity and buoyancy-induced flow, the nanofluid heat transfer with the addition of various concentrations of nanoparticles can be categorized into two patterns separated by a critical Hartmann number: the presence of a maximum Nusselt number (Type A) and continuously increased heat transfer rates (Type B) over a wide range of the Rayleigh number from 103 to 106 and the Hartmann number from 0 to 300. Described by a piecewise-defined function, the critical Hartmann number is exponentially proportional to the Rayleigh number from 104 to 106 and rises linearly in a logarithmic scale with elevating the Rayleigh number from 103 to 104.