## 1 Introduction
Furthermore, their analytical model predicted the phenomenon of enhanced thermal conductivity as a function of physical parameters such as chain length, size, and types of nanoparticles, fluid characteristics, magnetic field intensity, saturation magnetic moment, and nanoparticle concentration and had a good agreement with the experimental results was observed\". A review has been presented by [PERSON] and [PERSON] [21] on \"the magnetorheological fluids materials that reversibly change from liquid to near solid state under the presence of external magnetic fields. Their review highlighted the recent developments of magnetorheological fluid and nanofluid in the field of thermal behavior. Special emphasis was placed on the understanding of their thermal conductivity property by using several parameters which included particle volume fraction, shape and size of particles, materials of particles and base fluid, and magnetic field. Reference [22] showed that the increase in particle volume fraction and magnetic field strength may increase the thermal conductivity of the magnetorheological fluid. A relationship between these parameters and thermal conductivity has been developed from the theory and experiments and reported. [PERSON] et al. [22] investigated the \"Koo-Kleinstreuer-Li correlation for MHD nanofluid flowing over two vertical permeable sheets for Al\({}_{2}\)O\({}_{3}\)-water under the influence of free convection. They also used the Runge-Kutta method for the numerical solutions and discussed the effects of various physical parameters on nanofluids. Their results indicated that the enhancement in heat transfer increased the function of the Hartman number\". [PERSON] et al. [23] studied \"the effect of a magnetic field on the ferrofluid flow pattern, heat transfer, and entropy generation in a curved pipe. It was reported that a non-uniform magnetic field was applied to ferrofluid (water + 2% vol. Fe\({}_{3}\)O\({}_{4}\) nanoparticles) flow under the constant heat flux boundary condition. Governing equations were solved by the finite volume method and based on the SIMPLE algorithm. The major objective of their work was to illustrate the effects of circumferential angle (\(0^{\circ}\leq\phi\leq 180^{\circ}\)) and strengths of a magnetic field (\(0\leq\text{Mn}\leq 3\times 10^{6}\)) on the hydrothermal behavior and entropy production rate. It was found that the circumferential angle of the magnetic source played an important role in the hydrothermal performance of a curved pipe. At small magnetic numbers, the optimal circumferential location of the magnetic source was \(\phi\text{opt}=180^{\circ}\), which lead to the maximum heat transfer enhancement and hydrothermal performance and the minimal entropy generation rate. For large magnetic numbers, the optimal operating condition occurred at \(\phi=0^{\circ}\) and \(\phi=60^{\circ}\) depending on the magnetic number. Second law analysis revealed that the major source of entropy generation came from heat transfer irreversibility, which was reduced significantly by applying a magnetic field. In the range of studied parameters, the maximum heat transfer enhancement was about 29%, which occurred at \(\phi=0^{\circ}\) and \(\text{Mn}=3\times 10^{6}\)''. [PERSON] et al. [26] proposed a new type of cooling agent based on magnetic nanofluid to replace the classical cooling fluids in electrical power transformers. Reference [26] presented a mathematical model and numerical simulation results that were very useful for investigating the heat transfer performances of magnetic nanofluid. Following that study, the cooling performance of this magnetic nanofluid was tested for two types of electrical power transformers and compared to classical methods. They also presented a microactuator based on the same magnetic nanofluid\". \"While most research was focused on the enhancement of heat transfer in heat pipes using various techniques, very few people paid attention to the inherently low thermal conductivity of the working fluid and in particular nanofluids or magnetized nanofluids.