## 3 Results
### Heat Transfer Efficiency Evaluation with Mouromtseff Number  
The effectiveness of well-known Figures-of-merit, such as the _Mo_ ratio, was evaluated to assess the proposed nanofluids' convective heat transfer performance. _Mo_ ratios through the Dittus-Boelter and Simons equations were obtained from the measured experimental data and compared to the coefficient of convective heat transfer ratio. Experimental heat transfer tests were performed for the three proposed nanofluids (0.25, 1.0, and 2.0 wt%) and also the base fluid at 298, 308, and 318 K, varying the flow rate from 0.3 to 0.7 m\({}^{3}\)-h\({}^{-1}\). Base fluid and nanofluids coefficients of convective heat transfer were inferred from the measured data and are depicted in Figure 9. Both the base fluid and nanofluids exhibited increased convective heat transfer coefficients with rising temperature and flow rate. Average increments of 33% and 92% were observed with temperature increases from 298 to 318 K and flow rate increases from 0.3 to 0.7 m\({}^{3}\)-h\({}^{-1}\), respectively. However, as the nanoparticle loading increases, the convective heat transfer coefficients decreased compared to those of PG:W 30:70. Maximum average decreases of around 20% were observed for 2.0 wt% A-TiO\({}_{2}\)/PG:W 30:70 + PSS 1:4 nanofluid at 298 (Figure 9a), 308 (Figure 9b), and 318 K (Figure 9c). This is caused by a disproportionate balance between thermal conductivity and dynamic viscosity, which increases with the dispersion of the nanoparticles. Higher viscosity values, along with the turbulent mixing phenomena, boost pressure drops and hinder the thermal performance of the nanofluid. Figure 9: Experimental heat transfer coefficients, \(h\), of the base fluid, PG:W 30:70 (\(\bullet\)), and A-TiO\({}_{2}\) nanofluids at concentrations of 0.25 wt% (\(\blacktriangle\)), 1.0 wt% (\(\blacksquare\)), and 2.0 wt% (\(\blacktriangledown\))at (\(\blacktriangledown\)) 298.15K, (\(\blacktriangledown\)) 308.15 K, and (\(\blacktriangledown\)) 318.15 K as a function of the flow rate, \(\dot{V}\). Error bars indicate expanded uncertainty (\(k=2\)). Well-known FOMs, such as the _Mo_ ratio, have been employed in the literature to investigate the prospective heat transfer behaviour of nanofluids without performing experimental heat transfer tests. However, for turbulent flow conditions, the reported _Mo_ ratios in the literature did not fully correspond to the experimental convective heat transfer results. Thus, a comparison between the obtained \(Mo_{nf}/Mo_{bf}\) and the equivalent experimental \(h_{nf}/h_{bf}\) should be done. Since the _Mo_ ratio of the studied nanofluids corresponds to the ratio of their convective heat transfer coefficients for fully developed internal turbulent flow over a pipe at constant velocity and heat flux [4], the experimental \(h_{nf}/h_{bf}\) ratio was estimated and compared to the \(Mo_{nf}/Mo_{bf}\) ratio, applying the criteria that \(Mo_{nf}/Mo_{bf}>1\) and \(h_{nf}/h_{bf}>1\) indicate a better performance for the nanofluids than for the base fluid. Results of the experimental \(h_{nf}/h_{bf}\) ratio and the \(Mo_{nf}/Mo_{bf}\) ratio obtained by using the Dittus-Boelter or Simons expressions--Equations (3)-(5)--are presented in Table 1. The \(Mo_{nf}/Mo_{bf}\) ratios correctly expect the decrease in the nanofluid coefficients of convective heat transfer with regard to those of the base fluid, with average discrepancies of 4-15% with regard to the experimental \(h_{nf}/h_{bf}\) ratio. Both \(Mo_{nf}/Mo_{bf}\) and \(h_{nf}/h_{bf}\) ratios are lower than 1, indicating that the dispersion of A-TiO\({}_{2}\) nanoparticles worsens the heat transfer performance of the base fluid in this case. The \(Mo_{nf}/Mo_{bf}\) ratios obtained through the Dittus-Boelter and Simons expressions report a decrease of up to 7% for the 2.0 wt% A-TiO\({}_{2}\)/PG:W 30:70 + PSS 1:4 nanofluid, while the experimental \(h_{nf}/h_{bf}\) ratio presented a maximum decrease of 24% for the same nanofluid.