**6. Conclusions**

In this study, numerical simulations and experimental measurements on the flow and heat transfer performance of Al2O<sup>3</sup> and TiO<sup>2</sup> NFs in a compact PHE are carried out. The PHE system was established and verified for the operation of the flows of two fluids (cold and hot) in separated loops. The Al2O<sup>3</sup> and TiO<sup>2</sup> NFs are prepared and their thermophysical properties such as thermal conductivity and viscosity are measured. The improvements in thermal conductivity caused by adding different concentrations of nanoparticles are presented, and maximum enhancements of about 7.30% for Al2O<sup>3</sup> NF and 4.20% for TiO<sup>2</sup> NF at 0.2 vol.% concentration were found. Additionally, the viscosity was found to increase by increasing concentration of nanoparticles for both NFs, and there was a decrease with increasing the temperature. The numerical methodology is developed using the CFD tools of the ANSYS-FLUENT software for the similar physical conditions of the experimental method.

The heat transfer investigations on the Al2O<sup>3</sup> and TiO<sup>2</sup> NFs through the hot loop of the compact plate heat exchanger were conducted for several flow rates at an inlet temperature of 40 ◦C, and the heat transfer characteristics were empirically determined. The experimental and numerical data obtained for both NFs regarding CHTC enhancements were compared for several flows. Good enhancements of the heat transfer were found for both NFs and it was found to increase with the concentration of particles for all the flow rates. However, Al2O<sup>3</sup> NFs showed better enhancement compared to TiO<sup>2</sup> NFs. The maximum enhancement of heat transfer (24.6%) was observed for the Al2O<sup>3</sup> NF at the highest particle concentration (0.2 vol.%) through the experimental measurements.

Moreover, the numerical results show lower heat transfer enhancements in comparison with the experimental measurements with a deviation between 1.0% and 3.3% for TiO<sup>2</sup> NFs and a deviation between 1.6% and 7.2% for Al2O<sup>3</sup> NFs. The deviation was changed based on the particles' concentration and the flow rate. The latter is presumed due to the nanoparticles' movements in the flow which is not considered in the numerical investigation and led to extra heat transfer enhancement.

Finally, the experimental and numerical findings of flows of Al2O<sup>3</sup> and TiO<sup>2</sup> NFs showed good heat transfer enhancements in the compact PHE. This study helps for a better understanding of the heat transfer performance and mechanisms of the NFs' behavior through such PHE as well as highlights the benefits of using CFD tools for modelling NFs with clarification of their thermal characteristics.

**Author Contributions:** Conceptualization, W.A. and S.M.S.M.; formal analysis, W.A. and S.M.S.M.; investigation, W.A.; writing—original draft preparation, W.A.; funding acquisition, S.M.S.M.; supervision, S.M.S.M.; writing—review and editing, S.M.S.M. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by Fundação para a Ciência e a Tecnologia (FCT) through project PTDC/NAN- MAT/29989/2017.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Acknowledgments:** This work has also been supported by Fundação para a Ciência e a Tecnologia (FCT) through IDMEC under LAETA, project UIDB/50022/2020.

**Conflicts of Interest:** The authors declare no conflict of interest.
