## 4 Conclusions  
In this research, the thermal conductivity of aqueous theta-phase aluminum oxide nanofluids was measured for temperatures between 22.1 and 59.3 \({}^{\circ}\)C, mass fractions of nanoparticles from 1 to 10%, and using sonication times of 1.5, 4 and 16.5 h. The following conclusions have been derived from this research:  
* Thermal conductivity is improved by the temperature increase (0.001 W/m\(\cdot\)K per \({}^{\circ}\)C increase) and nanoparticle concentration increment (0.0027 W/m\(\cdot\)K per unit of wt% increase).
* A high sonication time (16.5 h), not used before in the open literature, was tested. The increase in the sonication time in the range investigated (from 1.5 to 16.5 h) has a negligible effect on the enhancement of thermal conductivity.  
Figure 8: Predicted vs. experimental thermal conductivity of the aluminum oxide-water nanofluid [14; 21; 32].  
Figure 7: Predicted vs. experimental thermal conductivity ratio of the aqueous theta-phase aluminum oxide nanofluid.  
* Comparing current experimental data with values taken from the literature, it can be concluded that a high dispersion of thermal conductivity data exists, evenly using the same nanoparticle volume fraction, close temperatures, and nanoparticle sizes. The volume fraction dependence of the thermal conductivity obtained in this work seems to be approximately similar to the one obtained in some of the previous reported data (three works). In the rest of cases (five works), a much higher increase in thermal conductivity with the nanoparticle volume fraction was obtained. Two of these last studies used gamma-phase nanoparticles, while, in the rest of investigations, the phase was not specified.
* A new correlation has been derived for the thermal conductivity that provides an excellent agreement with respect to experimental data. This correlation can be used to accurately predict the thermal conductivity of the aqueous theta-phase aluminum oxide nanofluid. The correlation significantly improves predictions with respect to the empirical correlations available in the open literature.
* Experimental data obtained and the correlation derived can be used to predict the performance of energy systems using theta-phase alumina-water nanofluids as working fluid.  
Conceptualization, M.V. and M.J.V.; methodology, M.V., M.d.V. and N.G.-H.; software, A.Z. and M.V.; validation, A.Z. and M.V.; formal analysis, A.Z., M.V., M.d.V. and N.G.-H.; investigation, A.Z., M.V., M.d.V. and N.G.-H.; resources, M.V., M.d.V. and N.G.-H.; data curation, A.Z. and M.V.; writing--original draft preparation, A.Z.; writing--review and editing, A.Z., M.V., M.d.V. and N.G.-H.; visualization, A.Z., M.d.V., N.G.-H. and M.V.; supervision, M.V. and M.d.V.; project administration, M.d.V. and M.V.; funding acquisition, M.V. and M.d.V. All authors have read and agreed to the published version of the manuscript.  
This research was funded by FEDER/Ministerio de Ciencia, Innovacion y Universidades-Agencia Estatal de Investigacion/_Proyecto (DPI2017-83123-R). [PERSON] acknowledges the research grant SIP20240435, by Instituto Politecnico Nacional of Mexico, and the scholarship 740638 granted by CONACYT.  
Not applicable.  
The data presented in this study are available on request from the corresponding author.  
The authors declare no conflicts of interest.