Abstract
In this paper, we study the effects of the Lorentz force and the induced anisotropic thermal conductivity due to a magnetic field on the flow and the heat transfer of a ferro-nanofluid. The ferro-nanofluid is modeled as a single-phase fluid, where the viscosity depends on the concentration of nanoparticles; the thermal conductivity shows anisotropy due to the presence of the nanoparticles and the external magnetic field. The anisotropic thermal conductivity tensor, which depends on the angle of the applied magnetic field, is suggested considering the principle of material frame indifference according to Continuum Mechanics. We study two benchmark problems: the heat conduction between two concentric cylinders as well as the unsteady flow and heat transfer in a rectangular channel with three heated inner cylinders. The governing equations are made dimensionless, and the flow and the heat transfer characteristics of the ferro-nanofluid with different angles of the magnetic field, Hartmann number, Reynolds number and nanoparticles concentration are investigated systematically. The results indicate that the temperature field is strongly influenced by the anisotropic behavior of the nanofluids. In addition, the magnetic field may enhance or deteriorate the heat transfer performance (i.e., the time-spatially averaged Nusselt number) in the rectangular channel depending on the situations.
Highlights
With the rapid development of nanotechnology, various nanofluids have been devised and applied in thermal engineering [1]
We study the flow and heat transfer in a magnetic nanofluid whose viscosity depends on the volume fraction of the nanoparticles, and thermal conductivity shows anisotropy; the specific forms of these two transport properties are based on existing experimental data
Under the continuous frame nanofluids can be mathematically modeled by using three different approaches [4,49]: (1) single phase approach where the nanofluid is treated as a conventional single-phase fluid suspension with variable properties; (2) single phase non-homogenous model where the movement of the nanoparticles is modeled by a concentration-flux transport equation [4]; (3) two-fluid approach, such as Mixture theory approach [50,51,52], where the two components are coupled through interaction forces
Summary
With the rapid development of nanotechnology, various nanofluids have been devised and applied in thermal engineering [1]. Compared to the conventional nonmagnetic nanofluids, MNFs show several unique features, such as the possibility of controlling the flow or the thermo-physical properties of MNFs using external magnetic fields and providing a more intensive thermo-magnetic convection compared to pure gravitational convection [22] To investigate these advantages, many studies, focusing on different geometries, have been performed. For magnetic nanofluids (MNFs), the nanoparticles tend to assemble into chains or rings; as a result, the heat flux along the magnetic field is enhanced dramatically [40] This indicates that the thermal conductivity of MNFs shows some degree of anisotropy. We study the flow and heat transfer in a magnetic nanofluid whose viscosity depends on the volume fraction of the nanoparticles, and thermal conductivity shows anisotropy; the specific. Two specific problems are solved numerically and the results for temperature distributions are discussed for a range of dimensionless numbers
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