# A High Thermal Conductivity of MgO-H\({}_{2}\)O Nanofluid Prepared by Two-Step Technique
## 3 Results and Discussion
### Thermophysical Properties Measurements
#### 3.3.2 Dynamic Viscosity  
The concentration ratio of nanoparticles and ultrasonication time are major factors that influence the viscosity of nanofluids. Figure 6a,b shows the changes in viscosity and relative viscosity with volume concentration ratios of MgO-DW nanofluid, at room temperature.  
Figure 6a shows that the viscosity of MgO-DW nanofluid is directly proportional to the MgO nanoparticles loading. The viscosity of nanofluid samples was gradually increased  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Concentration Ratios** & **Improvement of Thermal Conductivity** \\ \(\Phi\) **(vol.\%)** & **(K\({}_{\text{eff}}\)\%)** \\ \hline
45 & 13.71 \\
90 & 25.08 \\
135 & 31.10 \\
180 & 32.61 \\ \hline \hline \end{tabular}
\end{table}
Table 7: The improvement ratios of the thermal conductivity with ultrasonication time of MgO-DW nanofluid at room temperature.  
Figure 6: (**a**) The viscosity; (**b**) the relative viscosity (\(\mu_{\text{eff}}/\mu_{\text{bf}}\)), as a function of solid volume concentration of MgO-DW nanofluid at room temperature.  
with increasing concentrations of MgO nanopowder. The intersection on the viscosity axis corresponded to the viscosity value of base fluid as 0.001 (Pa-sec). The increase in nanofluid viscosity is narrow over the range of nanoparticle concentration of \(\leq\)0.05 vol.%, while the increasing is fast over a range of more than 0.05 to 0.25 vol.% of the MgO nanoparticle concentration. Furthermore, the resistance to flow increased to 0.0052 (Pa-Sec) at a higher solid content of 0.25 vol.% MgO-DW nanofluid. The dynamic viscosity behavior of MgO-DW nanofluid is harmonious with the predictions in [87, 88]. The viscosity of nanofluids is compared to that of base fluid producing relative viscosity, as seen in Figure 6b. It shows how much the nanofluid viscosity differs from the viscosity of the base fluid. From Figure 6, it can be observed that the relative viscosity increases with increasing volume concentrations of MgO-DW nanofluid.  
The lowest value of relative viscosity, i.e., 1.2, was obtained by 0.05 vol.% MgO-DW nanofluid, with respect to a base fluid viscosity, while the higher value was obtained by nano solid content of 0.25 vol.%. When the MgO nanoparticle content increases within the base fluid, the Brownian motion is restricted as a result of intense collisions between nanoparticles. Subsequently, the relative viscosity of MgO-DW nanofluid increases with nanopowder volume concentration.  
The effects of ultrasonication time on the viscosity of the MgO-DW nanofluid were investigated, as shown in Figure 7. The results show that the viscosity experiences a sharp decrease by increasing the ultrasonication treatment time.  
On the one hand, the minimal value of dynamic viscosity was measured at 180 min of ultrasonication treatment, indicating a decreasing tendency. On the other hand, the maximum value of viscosity was obtained by the nanofluid sample which was synthesized by stirring only without ultrasonication treatment of 0.0122 Pa-sec. This trend is identical to the results reported by [PERSON] et al. [89] and [PERSON] et al. [90]. Because the nanoparticles are uniformly dispersed in the base fluid, there are few or no clusters. As a result, the majority of nanoparticles, if not all, are involved in the flow, lowering the resistance to the viscometer's spindle. Additionally, the motion of the various layers of the nanofluid is made easier, hence, the dynamic viscosity decreases.  
It is worth noting that increasing the ultrasonication time improves the dispersion stability and the thermal conductivity, while decreasing the dynamic viscosity of the prepared nanofluid. Ultrasonication time and dynamic viscosity are highly important in engineering applications where both of them have direct influences on the heat transfer performance, pumping power, and pressure drop.  
Figure 7: The viscosity as a function of ultrasonication time of 0.25 vol.% MgO-DW nanofluid at room temperature.