## 1 Introduction  
Poor thermal conductivity of base fluids (commonly mineral oils, water and/or glycols) establishes a barrier to the creation of advanced energy-efficient heat-transfer equipment. Therefore, improving the efficiency of heat transfer of these conventional fluids is nowadays a critical issue at the industrial level. Generally, nanofluids are considered as a novel kind of heat-transfer fluid with nanosized additives dispersing into conventional working fluids [1]. The impact of using heat-transfer fluids with dispersed nanoparticles with important effects on intrinsic parameters and thermal performance behaviours [2; 3; 4] has opened the door for the improvement of energy-efficient heat-transfer devices [5; 6; 7; 8]. The presence of nanomaterials in the fluid implies changes in thermal conductivity, which is the most crucial factor influencing heat transfer and plays a significant role in the advancement of heat-transfer systems [8]. Other key parameters such as thermal diffusion, density, and surface tension are also directly involved in numerous industrial applications associated with solar- and thermal-energy supply, heat pipes, or cooling fluids [9; 10; 11; 12; 13; 14; 15; 16]. Nanoparticles are nanosized materials with unique characteristics that make them attractive, particularly their outstanding thermophysical properties when compared with bulk materials [5; 6]. Due to the nano sizes and very large specific surface areas of these particles, nanofluids overcome problems related to systems of microparticles and base fluids [7]. Nanoparticles of diverse materials have been used for the production of nanofluids [17; 18], with the promise of a rather large surface/volume ratio and a large number of nanoparticles interacting with the surrounding fluid to promote heat flow. Furthermore, the nanometric size minimizes the gravitational effects, thus avoiding problems related to sedimentation. Therefore, metals--Cu, and Fe [17], metal oxides--Al\({}_{2}\)O\({}_{3}\), CuO, SiO\({}_{2}\), TiO\({}_{2}\), and ZrO\({}_{2}\), carbon materials--carbon nanotubes and graphene--or hybrid nanoparticles [18], among others, were used in the design of nanofluids. On the other hand, the aggregation of nanoparticles has become a challenge in the field of nanofluids. Aggregation refers to the clumping or sticking together of the dispersed colloid particles to form aggregates or flocks [19]. These structures, made up of primary particles, can remain loosely tied together, and have been demonstrated to have both beneficial and detrimental effects in the final thermophysical properties of nanofluids [20; 21]. In addition, the stability of nanoparticle aggregation in the dispersion is crucial and significant analyses must be undertaken in this area [22; 23]. However, since there is a lack of control over the possible aggregation of nanoparticles above a maximum concentration when dispersed in base fluids intended for use in heat exchangers, the impact of controlled aggregation on the thermal characteristics of nanofluids has not yet been sufficiently investigated. To shed some light on this, we have recently opened a line of research focused on the effect of a controlled aggregation of nanosized iron oxide on the properties of nanofluids [24]. Nevertheless, finding an effective way to exert control over an aggregation process is not an easy task, considering the two steps necessary: firstly, bringing together the nanoparticles and secondly, keeping a similar number of them sticked when they do make contact to form clusters. Furthermore, when clusters are formed, the ideal case is that they grow solely by adding more individual nanoparticles, but cluster-cluster aggregation can also occur [19].