## 1 Introduction
Recently, several studies have been conducted on the effect of the magnetic field on Fe\({}_{3}\)O\({}_{4}\) nanofluids. [PERSON] et al. [24; 25] experimentally studied the effect of a magnetic field on the convective heat transfer characteristics of Fe\({}_{3}\)O\({}_{4}\) nanofluids. At 40 \({}^{\circ}\)C with a 3 vol% and a magnetic field of 0 G, the convective heat transfer coefficient increased by 1.2-2.3% in the laminar flow region and 4.7-5.6% in the turbulent flow region. The experimental results confirmed that Fe\({}_{3}\)O\({}_{4}\) nanofluids increased the heat transfer coefficients by 4.2% and 8.1% for a constant magnetic field strength at 800 G and a gradient magnetic field, respectively. In addition, [PERSON] et al. [26; 27] analyzed the flow of Fe\({}_{3}\)O\({}_{4}\) nanofluids in an elliptical cylinder and inside a moving wall in the presence of an external magnetic field using a simulation. The results indicated that the heat transfer improved as the Re increased, but the heat transfer decreased as the Hartmann number increased. [PERSON] et al. [28] prepared Fe\({}_{3}\)O\({}_{4}\) nanofluids using the solvothermal method and observed that the heat transfer characteristics of magnetic nanofluids significantly improved when an external magnetic field was applied. [PERSON] et al. [29] modeled the convective heat transfer characteristics of Fe\({}_{3}\)O\({}_{4}\) magnetic nanofluids in a rectangular channel using four magnets. When a magnetic field was applied, the average convective heat transfer coefficient increased by 40.8% and 58.2% compared with the Fe\({}_{3}\)O\({}_{4}\) magnetic nanofluid without a magnetic field and pure water, respectively. [PERSON] et al. [30] studied the convective heat transfer characteristics of nanofluids in a new test section consisting of a wavy circular cylinder and a rhombus. The results indicated that the shape of the nanoparticles also affected heat transfer improvement. [PERSON] et al. [31] experimentally investigated the heat transfer and flow performance of a magnetic nanofluid in a vertical tube under the magnetic quadrupole effect. The result showed that the maximum enhancement of 23.4%, 37.9%, and 48.9% in the local heat transfer coefficient for the magnetic nanofluid with 2 vol% of Fe\({}_{3}\)O\({}_{4}\) in the presence of quadrupole magnets at three different positions for Re of 580 and the enhancement in heat transfer coefficient was decreased with increase in Re. [PERSON] et al. [32] numerically investigated the magnetohydrodynamic natural convection of Fe\({}_{3}\)O\({}_{4}\)-water nanofluid in a round diagonal corner square cavity. The effect of various parameters such as Rayleigh number, Hartmann number on the nanofluid flow, and heat transfer was evaluated and discussed. The magnetic field effect on micro cross jet injection of water/Al\({}_{2}\)O\({}_{3}\) nanofluids in a microchannel was investigated by [PERSON] et al. [33]. The nanofluid jet was used for the heat transfer enhancement under homogeneous magnetic field strength with Ha of 0, 20, and 40. [PERSON] et al. [34] conducted an experimental study on the effect of inclational angle on the heat transfer enhancement of a ferrofluid under the influence of a magnetic field. The heat transfer coefficient of the heat pipe was improved by increasing the input heat flux. The inclination angle of the heat pipe plays a significant role in the performance of the heat pipe. The same author has studied the effect of magnetic field on the heat transfer rate of kerosene/Fe\({}_{2}\)O\({}_{3}\) nanofluid in a heat pipe [35]. The experimental results showed that the temperature difference between the surface and the vapour core of the evaporator section was 3.1 and 2 \({}^{\circ}\)C for with and without the influence of the magnetic field. [PERSON] et al. [36] numerically investigated the effect of radiation on the convective heat transfer rate and entropy generation of the nanofluid in a diagonal rectangular chamber.