Effects of the magnetic field on the cylindrical Couette flow and heat transfer of a nanofluid

Abstract

This paper documents the effects of magnetic field on the flow and heat transfer of a nanofluid confined between two cylinders. The inner ring is assumed rotary (representing shaft) while the outer ring was considered fixed (representing the housing). In addition to the single-phase approach, the two-phase model of Buongiorno is used to numerically solve the mass, momentum and energy equations by taking the Brownian and thermophoresis effects into account. The effects of several physical parameters such as the NBT (ratio of Brownian to thermophoretic diffusivities), nanoparticles bulk volume fraction (φb) and the Hartman number on the nanoparticles’ distribution, shear stress and heat transfer at the two rings are reported. It is clearly shown that the magnetic field, changes the linear variation of nanoparticles volume fraction in absence of magnetic field to a non-linear trend in which existence of a minima can be observed. The results indicate that the magnetic field has significant effects on the inner and outer rings’ shear stress and heat transfer such that the Hartman number variations outweighed other parameters’ variations such as NBT and the nanoparticles volume fraction. The results exhibit that increment in the magnetic field drastically reduces the outer ring shear stress and heat transfer magnitude. For example, in the case of Ha = 20, the outer ring shear stress and heat transfer are reduced about 86% and 11 %, respectively in comparison with the case of absent magnetic field (Ha = 0) when NBT=25 and φb=0.05.