## 1 Introduction  
Nanofluids, defined as fluids containing nanometer-sized particles [1], have gained significant attention in recent years due to their enhanced thermal properties compared to conventional heat transfer fluids. The enhancement in thermal conductivity varies depending on the nature of the nanoparticles and the base fluid, with many studies observing increases ranging from 15% to 40% [2; 3]. [PERSON] et al. [4] reported that the addition of less than 1% (by volume) of nanotubes increased the thermal conductivity of the base fluid by up to approximately two times. Among nanofluids, those based on aluminum oxide (Al\({}_{2}\)O\({}_{3}\)) nanoparticles dispersed in ethylene glycol (EG) have been extensively studied for their potential applications in heat transfer systems [5; 6; 7], cooling systems [8], electronics [9], and other industrial processes [10]. [PERSON] et al. [5] have compared the cooling ability of TiO\({}_{2}\)/EG and Al\({}_{2}\)O\({}_{3}\) for double-tube heat exchangers under laminar flow conditions, demonstrating a higher thermal conductivity enhancement of Al\({}_{2}\)O\({}_{3}\) compared to TiO\({}_{2}\) in the range of 1-10% volume fraction. Therefore, accurate prediction of the thermal conductivity of EG-Al\({}_{2}\)O\({}_{3}\) nanofluids has become a top priority for reducing experimental costs, optimizing material selection, facilitating research, and customizing application solutions. Classical theoretical models, such as those of [PERSON] [11], [PERSON] [12], and [PERSON] [13; 14], offer foundational approaches to understanding the heat transfer characteristics of nanofluids. However, these models often assume idealized conditions, such as assuming nanoparticles to be perfect spheres, supposing there are no interactions between nanoparticles, and neglecting the movement of nanoparticles. This simplification often makes it difficult to capture the complex dynamics in different experimental conditions. For instance, the [PERSON] model presupposes that nanoparticles remain discrete and stationary within a continuous medium, basing its parameters solely on the volume fraction of the nanoparticles and the thermal conductivities of both the fluid and the nanoparticles. Nevertheless, this simplification overlooks critical phenomena. [PERSON] and [PERSON] [15] have highlighted that Brownian motion significantly contributes to the enhancement of thermal conductivity at small particle sizes, which traditional macroscale models do not account for. Furthermore, [PERSON] et al. [16] observed that the thermal conductivity values measured in experiments were substantially higher than those predicted by conventional models. This discrepancy can be attributed to the omission of crucial parameters such as the Hamaker constant, \(\zeta\) potential, pH, and ion concentration. It has also been reported that the aggregation effect has a non-negligible influence on the thermal behavior of nanofluids. Addressing these gaps, more advanced theoretical models and variables were considered. For example, [PERSON] et al. [17] proposed a new model considering the aggregation of nanoparticles and the presence of a nanolayer. [PERSON] et al. [18] renovated the Hamilton-Crosser model to include the shape factor and the particle-liquid interfacial layer. However, there remains a lack of consensus regarding the factors influencing the thermal conductivity of nanofluids. For example, the volume fraction of nanoparticles, known to be an important parameter for thermal conductivity enhancement, has been reported to be a positive influencing parameter [19; 20; 21; 22; 23; 24]. However, some studies indicate that thermal conductivity does not improve until the particle concentration reaches a certain threshold (i.e., the critical concentration). Once the threshold is exceeded, thermal conductivity increases linearly with further increases in concentration [25; 26]. On the contrary, [PERSON] et al. [27] reported a decrease of thermal conductivity when adding magnetite nanoparticles to water and EG.