## 1 Introduction  
The efficiency of conventional heat-transfer fluids is augmented by using nanofluids as a novel technique [1; 2; 3; 4; 5]. During the history of heat-transfer development, due to the interesting thermal properties of nanofluids, they have been utilized in the production of heat-transfer fluids [6; 7]. Ionic liquids (ILs) are a novel group of salt-like materials that are liquid under ambient conditions [8] and have great potential for use in different industries. Although their transport properties have been widely investigated in recent years, investigations of the thermal properties are very limited in the literature [9; 10; 11; 12]. Because of their excellent thermal properties, such as high thermal conductivity (TC) and high heat capacity (\(C_{p}\)), they are recognized as an appealing candidate for heat transfer applications [13; 14]. In light of previous evidence, it is important to investigate the benefit of utilizing ILs augmented with nanoparticles. By adding only a small amount of nanoparticles into pure ILs, the thermophysical properties of ILs will be enhanced [9; 15; 16; 17; 18]. A similar idea has been observed in the chemical-enhanced oil recovery methods, which increase the amount of recovered oil by adding a very small amount of nanoparticles to the injected water [19]. This group of nanofluids with ILs as the base fluids that show higher thermophysical properties is called ion nanofluids or nanoparticle-enhanced ILs (NEILs) [16]. [PERSON] et al. [20; 21] carried out an experimental study and observed an increase in \(C_{p}\) of up to 49% compared with the base ILs when Al\({}_{2}\)O\({}_{3}\) nanoparticles were added to pyrrolidinium- and imidazolium-based NEILs. Furthermore, silver nanofluid heat transfer through a tube with twisted tape inserts was tested by [PERSON] et al. [22]. They concluded that the heat transfer rate was enhanced by dispersing nanoparticles through water. By adding multi-walled carbon nanotubes (MWCNTs) to different ion nanofluids and measuring their thermophysical properties, [PERSON] et al. concluded that the TC and \(C_{p}\) of ion nanofluids were enhanced by \(\approx\)8% and \(\approx\)9%, respectively [16; 23]. What we know about the thermophysical properties of NEILs is largely based upon empirical studies, and these data are controversial regarding their accuracy; furthermore, there is little empirical data available in the literature. Therefore, the determination of the thermophysical properties of NEILs by utilizing theoretical methods is a necessary endeavor. Computational investigations in particular have become vitally important [24; 25; 26; 27; 28; 29; 30; 31; 32; 33], where many researchers have widely implemented intelligent methods based on neuro-fuzzy neural networks to model many engineering processes [6; 34; 35; 36; 37; 38; 39] and predict the thermophysical properties of different nanofluids [40; 41; 42]. In 2013, [PERSON] et al. [43] used an interesting adaptive neuro-fuzzy inference system (ANFIS) modeling technique in a study that set out to predict the heat transfer coefficient of a nanofluid containing Al\({}_{2}\)O\({}_{3}\) under a uniform heat flux condition. Other authors have questioned the usefulness of such an approach. [PERSON] et al. [44] established a genetic algorithm-polynomial neural network and a fuzzy C-means (FCM) based neuro-fuzzy inference system to determine the TC ratio of Al\({}_{2}\)O\({}_{3}\)-based nanofluids based on the concentration and size of the nanoparticles, as well as the temperature. [PERSON] et al. [45] used artificial neural network (ANN) methods and the approximation of general function for the calculation of the thermophysical properties of quaternary ammonium-based ILs in terms of the critical temperature of the ILs and the water content. [PERSON] et al. determined the refractive index of binary solutions of IL systems based on ANN algorithms [46]. [PERSON] et al. calculated the viscosity of ILs by employing boiling temperatures based on ANN algorithms [47]. After that, [PERSON] et al.