## 1 Introduction
The result showed that the Nusselt number and entropy generation increase, and the Bejan number decreases with increasing Raleigh number. Moreover, the heat transfer rate and entropy generated were reduced, and the Bejan number increases by increasing the angle of the magnetic field. [PERSON] et al. [37] conducted an experimental study on the convective heat transfer characteristics of Fe\({}_{3}\)O\({}_{4}\) magnetic nanofluids in a circular tube subjected to a magnetic field. When the 0.5 vol% Fe\({}_{3}\)O\({}_{4}\) magnetic nanofluid had a Re of 1080 and magnetic field strengths of 415 and 700 G, the Nu number increased by 4.36% and 7.19%, respectively. [PERSON] et al. [38] analyzed convective heat transfer and entropy generation of graphene-Fe\({}_{3}\)O\({}_{4}\) hybrid nanofluid. The results indicated that the local convective heat transfer increased by up to 82%, and the total entropy production rate was reduced by 41% compared with water. [PERSON] et al. [39] experimented on forced convective heat transfer in laminar flow using a Fe\({}_{3}\)O\({}_{4}\)-MWCNT hybrid nanofluid in a constant magnetic field. Under the same Re of 548, the Nu number of a 0.5 vol% Fe\({}_{3}\)O\({}_{4}\)-1.35 vol% MWCNT hybrid nanofluid exhibited a maximum increase of 20.5% compared with the scenario without a magnetic field. Similarly, [PERSON] et al. [40] conducted an experiment on forced convective heat transfer in laminar flow for a Fe\({}_{3}\)O\({}_{4}\)-MWCNT hybrid nanofluid. When the Re was 500, the Nu number and pressure drop of 0.9 vol% Fe\({}_{3}\)O\({}_{4}\)-1.35 vol% MWCNT hybrid nanofluids increased by 109.31% and 25.02%, respectively, when compared to the scenario without a magnetic field. [PERSON] et al. [41] investigated the effect of a constant magnetic field on Ag/MgO/H\({}_{2}\)O nanofluid in a cavity form. The result showed that heat transfer was limited by the increase in Ha number, and therefore, the magnetic field can be used as a heat transfer controller. [PERSON] et al. [42] conducted an experimental study on the preparation of the liquid paraffin-Fe\({}_{3}\)O\({}_{4}\) mixture and further developed models using an artificial neural network for the prediction of thermal conductivity and viscosity. [PERSON] et al. [43] developed a new approach using an enhanced artificial neural network on functionalised-MWCNTs-Fe\({}_{3}\)O\({}_{4}\)/EG hybrid nanofluid. The proposed method provides more precise results in less time. In addition, [PERSON] et al. [44] investigated the thermal conductivity and stability of graphene oxide-Al\({}_{2}\)O\({}_{3}\) hybrid nanofluid. The result showed that the pH, dispersant, ultrasonication power, and duration affect the stability of the hybrid nanofluid. Previous studies have demonstrated that nanofluids can increase the efficiency of heat exchange systems through forced convective heat transfer. In addition, studies on forced convective heat transfer characteristics using hybrid nanofluids consisting of two or more nanoparticles have been conducted. The magnetic field effect on the forced convective heat transfer characteristics using Fe\({}_{3}\)O\({}_{4}\) magnetic nanofluids has also been studied. However, the research on hybrid magnetic nanofluids is insufficient, and it can hardly be found in the literature. Although hybrid magnetic nanofluids may improve the forced convective heat transfer characteristics through the synergistic effect of two or more nanoparticles, most studies on the effect of magnetic fields focused on single magnetic nanofluids. To date, no study has been conducted to confirm the synergistic effect of hybrid magnetic nanofluids by comparing the improvement rate of convective heat transfer of hybrid magnetic nanofluids with that of single magnetic nanofluids. Generally, producing single and hybrid magnetic nanofluids for each concentration and experimentally confirming the characteristics of forced convective heat transfer according to changes in the magnetic field are time-consuming.