## 4 Conclusions  
Aqueous GO-Al\({}_{2}\)O\({}_{3}\) hybrid nanofluids used in thermal ice storage were prepared and characterized. The influences of pH, dispersant, ultrasonic power and ultrasonic time on the stability of hybrid nanofluids were quantitatively analyzed. The thermal conductivities of the hybrid nanofluids were measured and correlated with temperature and concentration. Thermal conductivity of ice containing the hybrid nanoparticles was tested. A new model for the effective thermal conductivity of the hybrid nanofluids considering the structure and Brownian motion was proposed. The key results of this study were as follows:  
(1) The optimal conditions for stability of the aqueous GO-Al\({}_{2}\)O\({}_{3}\) hybrid nanofluids (mass fraction of GO: Al\({}_{2}\)O\({}_{3}\) = 1:1) were: pH = 11, 1% SDS, ultrasonic power of 375 W and ultrasonication time of 120 min.  
(2) With the increase in temperature and the mass fraction of the nanoparticles, thermal conductivity of the hybrid nanofluid increased. The influence of mass fraction on the thermal conductivity enhancement at a lower temperature was greater than that at a high temperature. At 0 \({}^{\circ}\)C, the thermal conductivity of 0.2 wt % hybrid nanofluids increased by 7.1% as compared to that of the base fluid, which means that this hybrid nanofluid had a potential advantage to enhance heat transfer performance.  
(3) The nanoparticle mass fraction had a significant influence on the thermal conductivity of the hybrid nanofluid. The influence of temperature on thermal conductivity enhancement at a lower concentration was larger, even though at a higher concentration there was greater thermal conductivity enhancement.  
Figure 20: Influence of temperature and mass fraction of hybrid nanoparticles on the thermal conductivity enhancement of ice mixing with the hybrid nanoparticles.  
(4) Comparison of thermal conductivity of the GO nanofluid with the hybrid nanofluid displays similar thermal conductivity. Using less GO in the hybrid nanofluid could reduce the cost of the hybrid nanofluid. Moreover, a low mass fraction of hybrid nanoparticles could enhance the thermal conductivity of ice.  
(5) The correlation generated for thermal conductivity of the hybrid nanofluid provided an accurate prediction of the thermal conductivity of water-based GO-Al\({}_{2}\)O\({}_{3}\) hybrid nanofluids. The new model for thermal conductivity of hybrid nanofluid shows the influence of thickness, length, flat rate and the interface thermal resistance of the graphene oxide, particle radius of Al\({}_{2}\)O\({}_{3}\), fluid viscosity, temperature and Brownian motion. Results presented in this study gave a better understanding of the influence of various important factors on the enhancement of thermal conductivity of hybrid nanofluids.  
[PERSON], [PERSON] and [PERSON] conceived and designed the experiments; [PERSON], [PERSON] and [PERSON] performed the experiments; [PERSON], [PERSON], [PERSON] and [PERSON] analyzed the data; [PERSON], [PERSON], [PERSON], [PERSON] and [PERSON] wrote and revised the paper. All authors have read and agreed to the published version of the manuscript.  
This study was supported by National Natural Science Foundation of China (51306060); Key Research and Development and Promotion Project in Henan province -Science and Technology (International Cooperation) (182102410087); Innovative Research Team (in Science and Technology) in University of Henan Province (19 IRTSTHN011); Special Support Plan for High-level Talents of Henan Province-\"ZHONGYUAN Thousand Talent Program\" (ZYQR201810075).  
[PERSON] acknowledges Mine Multiphysics research group at the Department of Mining and Materials Engineering, McGill University, Montreal, Quebec Canada.  
The authors declare no conflict of interest.