Whilst, the magnetic susceptibility of paramagnetic fluids also have the temperature dependency. It has an inverse dependency on the absolute temperature, which is called Curie’s law. This suggests that the magnitude of magnetic force depends on local temperature. Rest of aforementioned phenomena are derived from this characteristic, thus they belong to so-called ‘magneto-thermal convection’. Various investigations have been reported so far to clarify the fundamental characteristics in pure magneto-thermal convection or in mixed convection. Kaneda et al. [15] found that the natural convection of air in a cubic enclosure is suppressed when the magnet is placed above the enclosure. In contrast, it is enhanced by placing the magnet below the enclosure.
In case of the magneto-thermal wind phenomenon, a spontaneous flow in a pipe is generated by supplying both heat source and magnetic field without pumps or blowers [10]. The case under the presence of main flow was also studied [16]. However, these are limited in two-dimensional and flow without gravity or vertical system. The heat transfer characteristic has not been discussed in such system.
In this study, the effect of the external magnetic field on heat transfer is numerically investigated for a heated laminar pipe flow. Followed by the schematics and governing equations, the case without gravity is firstly discussed especially for the effect of the magnet location and its strength. The effect of additional force of the gravity is then studied.