# Liquid Nanofilms' Condensation Inside a Heat Exchanger by Mixed Convection
## 4 Results and Discussion  
### Effect of the Inlet Volume Fraction of Nanoparticles  
In this work, we studied the impact of the inlet volume fraction of nanoparticles \(\varphi_{0}\) on the mass and heat transfer during liquid film condensation flowing down on a cooled vertical plate. Figure 3 illustrates the impact of the nanoparticles' concentration \(\Phi_{0}\) on the interfacial liquid-vapor temperature and vapour concentration. Figure 3a shows that the liquid-vapor interface temperature decreased with an augmentation of the inlet volume fraction of aluminium nanoparticles \(\Phi_{0}\). This result may be due to the high thermal conductivity and the lower heat capacity of the nanoparticles compared to the pure water (see Table 2). Figure 3b shows that the liquid-vapor interface concentration increased with an increase in the inlet volume fraction of aluminium nanoparticles \(\Phi_{0}\). This result was justified by the fact that a decrease in the temperature at the liquid-gas interface caused a decrease in the vapour concentration at the liquid-gas interface. Figure 4 shows a rise in the water film condensation for a higher value of \(\Phi_{0}\). We can justify these results by the fact that the increase in \(\Phi_{0}\) accelerated the cooling (Figure 3a) causing an elevation in the water vapour film condensation (Figure 4). This result is very important because the enhancement of water film condensation occurs only by the dispersion of copper nanoparticles in the liquid film and without an increase in energy consumption. Figure 5 shows the axial evolution of the relative heat fluxes for various values of \(\Phi_{0}\), which can be used to analyse the relative contributions of the heat exchange through sensible and \begin{table}
\begin{tabular}{c c c c c c} \hline
**I \(\times\) (J + K)** & **101 \(\times\) (101 + 41)** & **101 \(\times\) (71 + 41)** & **71 \(\times\) (51 + 41)** & **51 \(\times\) (51 + 21)** & **51 \(\times\) (21 + 31)** \\ \hline \(\xi\) = 0.25 & 3.960 & 3.900 & 3.973 & 3.959 & 3.936 \\ \(\xi\) = 0.50 & 6.651 & 6.530 & 6.572 & 6.593 & 6.567 \\ \(\xi\) = 0.75 & 9.140 & 9.200 & 8.984 & 8.986 & 8.959 \\ \(\xi\) = 1.00 & 11.473 & 11.400 & 11.442 & 11.425 & 11.495 \\ \hline \end{tabular}
\end{table} 
Table 1: Stability of the calculation from the mesh variations’ evaporating rate \(\overset{\bullet}{m}(\xi)\) (kg.s\({}^{-1}\).m\({}^{-2}\)) of the water film. Figure 2: Comparison of the temperature at the interface with that of [PERSON] et al. [14]. latent heat. Figure 5a shows that the relative latent heat transfer was improved with the nanoparticles' dispersion in the water, while the relative sensible heat transfer (Figure 5b) was reduced for a higher value of \(\Phi_{0}\). We can explain these results by the fact that the dispersion of aluminium nanoparticles in the water improved the liquid cooling and consequently enhanced the vapour film condensation inducing an augmentation of the relative latent heat and a reduction in the relative sensible heat. Figure 6 illustrates the liquid velocity at the channel exit for various values of \(\Phi_{0}\). An augmentation of \(\Phi_{0}\) reduced the velocity of the liquid at the channel exit. These results can be explained by the fact that an augmentation of \(\Phi_{0}\) induced an increase in the nanofluid viscosity compared to the basic fluid (water) causing a deceleration of the liquid film flow. Figure 3: Effect of inlet nanoparticles volume fraction on the temperature (**a**) and the vapor concentration (**b**) at the interface liquid-gas: T\({}_{0}\) = 293.15 K, T\({}_{0L}\) = 293.15 K, q\({}_{1}\) = \(-\)1000 W/m\({}^{2}\), T\({}_{\rm w}\) = 293.15 K, c\({}_{0}\) = 0.3, u\({}_{0}\) = 1 m/s, m\({}_{0L}\) = 0.015 kg/m.s, H = 1 m, d = 0.015 m, p\({}_{0}\) = 1 atm.