2.3.6. Roughness-to-Particle Size Ratio

The ratio of the nanoparticle dimension to the average roughness of the heating surface can also be linked to the heat transfer behavior. With the use of extended ratios, the deposition of nanoparticles can further enhance the average roughness of the surface or, alternatively, reduce the average roughness. The authors Shoghl et al. [6] found a heat

transfer decrement using zinc oxide and alumina nanoparticles dispersed in water. This deterioration was the consequence of the surface roughness decrease as compared with the heat transfer improvement that occurs with carbon nanotubes because of a notorious surface roughness enhancement. The authors reported that any improvement or any degradation of the boiling thermal performance was affected by the nature of the nanoparticles and the relative nanoparticle size ratio to the initial heating surface roughness. In addition, the researchers Narayan et al. [9], Shahmoradi et al. [64], and Wen et al. [65], among others, highlighted that the nucleate boiling enhancement generated by increasing the surface roughness factor was only viable with a well-defined range of size of the nanoparticle. For instance, the authors Narayan et al. [9] introduced the "surface interaction" factor, which represents the ratio of the average surface roughness to the average nanoparticle size, to address the capability of a given nanofluid to improve its nucleate boiling performance. In the cases where the nanoparticles are significantly smaller than the surface roughness features, having a "surface interaction" parameter considerably greater than one, the boiling heat transfer improved appreciably as the smaller particles deposited onto the initial nucleation sites and divided these initial single nucleation points into multiple ones. Nevertheless, in the cases where this interaction parameter had a value near one, the heat transfer was limited as most of the nanoparticles deposited in active nucleation points with approximated relative size and hindered the bubble nucleation. On the other hand, if the referred parameter presented a value considerably smaller than one, the heat transfer decrement was less intense than that verified with the parameter value around one, given that the larger nanoparticles decreased the number of the nucleation points being deactivated. Moreover, the "surface interaction" parameter is also of relevance in interpreting the boiling HTC degradation with augmented concentration of nanoparticles. In this direction, Shahmoradi et al. [64] found a decrement in the HTC for a water-based alumina nanofluid with the "surface interaction" parameter with values lower than one. Such decrement clearly worsened with enhanced nanoparticle volume fraction below 0.1. The researchers explained the worsening deterioration with the additional thermal resistance provided by the deposited layer of nanoparticles. Furthermore, Wen et al. [65] revealed that any augment in the boiling heat transfer was strongly influenced by the relative size of the particles dispersed in the working fluid and the initial dimensions of the superficial elements. Nevertheless, the researchers also highlighted that, since the surface modification by the nanoparticles was a cumulative phenomenon in time, the heat transfer trend was believed to continuously alter with successive pool-boiling experiments with only one heating surface. Moreover, Vafaei [66] reported an increment in the heating surface cavities' dimensions in the cases where the deposited nanoparticles were larger than the valleys of the surface roughness profile. The reported enhancement promoted the activation of nucleation points and improved the HTC at low heat fluxes. On the other hand, when the settled nanoparticles were smaller than the valleys of the surface roughness profile, the heating surface activation decreased, rendering a less effective boiling performance.
