## 2 Materials and Methods
### Methodology
#### 2.2.3 Figures-of-Merit Determination  
As previously commented, Mouormtseff number (\(Mo\)), introduced in 1942 by [PERSON] [5], is considered as a Figure-of-merit for discussing the heat transfer fluids thermal performance and can be estimated using the following expression:  
\[Mo=\frac{\rho^{a}\,k^{b}c_{p}\,^{c}}{\eta^{d}} \tag{2}\]  
in which constants \(a\), \(b\), \(c\), and \(d\) vary based on the mode of heat transfer (natural or forced convection), the flow regime (laminar or turbulent), and boundary conditions (constant heat flux or constant wall temperature). For all the heat transfer modes, the impact of thermal conductivity on Mo is more significant than that of the viscosity; therefore, \(b>d\)[10; 23].  
The \(Mo\) ratio for nanofluids and base fluid (\(Mo_{nf}/Mo_{bf}\)) is used to assess the overall performance of the proposed nanodispersion against its base fluid in terms of convective heat transfer and is equivalent to the ratio of nanofluid coefficients of convective heat transfer to that of the base fluid (\(h_{nf}/h_{bf}\)) at constant velocity and heat flux [4]. For hydrodynamically and thermally fully developed laminar flow, [PERSON] [24] stated that the coefficient of heat transfer is only affected by thermal conductivity. Therefore, in such conditions, the Mo ratio can be considered as the nanofluid-base fluid thermal conductivity ratio (\(k_{nf}/k_{bf}\)). In the scenario of fully developed internal turbulent flow within a pipe, the values reported in the literature for the constants \(a\), \(b\), \(c\), and \(d\) in Equation (2) differ across various authors in the literature. Applying the exponents procured from the Dittus-Boelter equation [3] for heating and cooling under turbulent flow conditions, the \(Mo\) ratio is defined as follows.  
\[\begin{split}\left(\frac{Mo_{nf}}{Mo_{bf}}\right)_{[PERSON]}& =\frac{\frac{\rho_{nf}^{0.8}\frac{Ab_{nf}^{0.6}\frac{Ab_{nf}^{0.4}}{c_{p}\, nf}}}{\frac{\rho_{nf}^{0.8}\frac{Ab_{nf}^{0.4}}{c_{p}\,nf}}{\rho_{nf}^{0.8}\frac{Ab_{nf}^{0.4}}{c_{p}\, nf}}}}{\frac{\rho_{nf}^{0.8}\frac{Ab_{nf}^{0.6}}{c_{p}\,nf}}{\rho_{nf}^{0.8}\frac{Ab_{nf}^{0.4}}{c_{ p}\,nf}}}\\ \left(\frac{Mo_{nf}}{Mo_{bf}}\right)_{[PERSON]}& =\frac{\frac{\rho_{nf}^{0.8}\frac{Ab_{nf}^{0.7}}{c_{p}\,nf}}{\rho_{nf}^{0.5}}}{ \frac{\rho_{nf}^{0.8}\frac{Ab_{nf}^{0.5}}{c_{p}\,nf}}{\rho_{nf}^{0.8}}}\\ \end{split} \tag{3}\]  
[PERSON] [24] also used the concept of the Mouormtseff number to show the effectiveness of various refrigerants, and the resultant Mo ratio can be obtained through the following expression.  
\[\left(\frac{Mo_{nf}}{Mo_{bf}}\right)_{[PERSON]}=\frac{\frac{\rho_{nf}^{0.8}\frac{Ab _{nf}^{0.67}\frac{Ab_{nf}^{0.33}}{c_{p}\,nf}}}{\frac{\rho_{nf}^{0.8}\frac{Ab_{nf }^{0.5}}{c_{p}\,nf}}}}{\frac{\rho_{nf}^{0.8}\frac{Ab_{nf}^{0.4}}{c_{p}\,nf}}{ \rho_{nf}^{0.8}\frac{Ab_{nf}^{0.5}}{c_{p}\,nf}}} \tag{5}\]Equations (3)-(5) are utilised to compare the proposed nanofluids with the base fluid at the temperatures defined in the previous section. The experimentally measured thermophysical properties of both the base fluid and the nanofluids are employed to calculate the different _Mo_ ratios.