# Thermal Conductivity of Nanofluids: A Review on Prediction Models, Controversies and Challenges
## 1 Introduction  
Technological development in the past decades led to the increase in demand for novel cooling fluids able to surpass the conventional ones--air and water--to improve the lifespan of the electronic components [1]. One type of fluid that has been increasingly investigated is nanofluid (NF), as seen in Figure 1. Introduced in 1995 by [PERSON], nanofluids consist of a colloidal dispersion of nanoparticles (NPs) with 1-100 nm of dimension in a base fluid (BF) [2, 3]. The NPs usually used in the NFs are oxides, metals, nitrides, and non-metals like carbon nanotubes and graphene, while the BF are often water, ethylene glycol, oils, and polymer solutions [4]. NFs contribute to the improvement of heat transfer processes, and to reduce and optimize thermal systems [5].Different properties, such as wettability and thermal conductivity, can be adjusted by altering the NPs concentration, making nanofluids suitable for a wide range of applications. Local concentration can be controlled using magnetic NPs under the action of an applied magnetic field [6]. Nevertheless, preparation and use of NFs still have some limitations. Sedimentation and aggregation of the particles are difficult to control andmay accelerate corrosion of the components and increase the dynamic viscosity of the NFs. Also, the synthesis of nanomaterials is still an expensive process [5].On top of that, there is no general consensus regarding the exact concentration and type of particle required for the NFs best performance. In spite of these difficulties, new and more competitive preparation techniques have been developed. For example, titanium dioxide NFs can be obtained nowadays by the Vapor Deposition Technique (VDT) [7]. Due to the previously mentioned advantages, NFs have been applied to a wide variety of fields [6; 7; 8; 9]. For instance, some NFs were used to cool electronic parts such as CPUs [10] and transformers [11], motor engines [12] and nuclear reactors [13]. In space technologies, they were tested to improve cooling mechanisms, and also as fuel [14] and for machining and grinding techniques as lubricant and cutting fluid [15]. The thermal properties of NFs were also very useful to improve the heat transport and, consequently, the thermal efficiency of systems like heat pipes [16], thermosiphons [17], heat exchangers, and chillers [6; 8], and solar panels and collectors [17]. Recently, there has been a growing interest in the use of NFs in nanomedicine. On this field, the magnetic NPs can be used not only to improve the potential of diagnostic techniques but also in hyperthermia treatments or as drug carriers [18; 19; 20; 21].Also, the use of NFs to study the heat transfer mechanisms in cavities, like the free natural convection, has grown tremendously [22]. One of the most relevant properties of NFs is the thermal conductivity. The thermal conductivity of NFs is influenced by shape, size, concentration and surface resistance of the NPs and by the viscosity, pH, temperature, and other characteristics of the base fluid [23]. Several theoretical models and experimental methods were developed to measure this property. The most common measuring methods are the transient hot-wire method followed by the 3\(\omega\) method, the steady-state parallel plate method and the temperature oscillation method. Despite the growing number of studies, there are still disparities between data generated by the theoretical models and experimental measurements as well as between measurements derived from the same method (reproducibility of results) [3]. In this work, the main experimental methods used by researchers to measure the thermal conductivity of nanofluids will be presented. The study will discuss the parameters that may be interfering with the accuracy of the results like the aforementioned factors, and  
Figure 1: Number of scientific journal articles presented in the Science Direct database published between January of2000 and September of 2020. (Search date: 10.09.2020) (Please read the data availability statement).