## 4 Conclusions  
In the present study, 3D numerical simulations have been carried out to examine the effects of two geometrical parameters, including the tube type and position of the shell, on the solidification process in an ice storage system. Three types of tubes, including a U-shaped tube, a coil tube with an inner return line, and a coil tube with an outer return line as well as two positions of the ice storage tank (horizontal and vertical positions) have been considered. The main result can be summarized as follows:  
* In both horizontal and vertical positions of the ice storage tank, the coil tube fastens the ice formation, as compared with the simple U-shaped tube. For the cases with the coil tube, the covered area of the domain is higher in comparison with the U-shaped tube, which leads to an increase of the solidification rate. * Between the different coil tubes, the coil tube with an outer return line exhibits a better performance (more produced ice) compared to the coil tube with an inner return line. In other words, the space through the coil tube solidifies more, even without the return line. The presence of the return line through the coil tube (inner return line) has no significant effect on the solidification rate. However, in the case with the outer return line, the covering area by the HTF tube increases, which leads to a higher solidification rate. * In the simple U-shaped tube configuration, the horizontal position enhances the ice formation, as compared with the vertical position. For the case with a coil tube and an inner return line, the differences between the two positions for this particular case remain insignificant. The effect of the position on the ice formation for the coil tube with an outer return line is significantly more pronounced than the case with the coil tube and an inner return line. In this case, the vertical position shows higher produced ice than the horizontal position. * After 8 h of solidification, the coil tube with the outer return line has about 6% and 8% lower liquid fraction in comparison with the coil tube with the inner return line and U-shaped tube, respectively. After 16 h of solidification, the coil tube with the outer return line has about 1.057% and 1.32% lower liquid fraction in comparison with the coil tube with the inner return line and U-shaped tube, respectively for both positions (vertical and horizontal). It is worth mentioning that, in addition to the present study, a comprehensive study is necessary as future work to study the effect of the coil geometrical parameters on the solidification process in an ice-on-coil ice storage system. Figure 16: Three-dimensional streamlines with contours of the velocity magnitude for the three different cases in the vertical position. **Author Contributions:** [PERSON] performed all the calculations, analyzed the results, and prepared the original draft. [PERSON] reviewed and edited the paper. [PERSON] and [PERSON] are the supervisors of [PERSON]. All authors have read and agreed to the published version of the manuscript. **Funding:** This research received no external funding. **Acknowledgments:** S.P. acknowledges the NSERC chair on industrial energy efficiency established at Universite de Sherbrooke in 2019 with the support of Hydro-Quebec, Natural Resources Canada and Emerson Canada. **Conflicts of Interest:** The authors declare no conflict of interest. **Nomenclature**