## 5 Conclusions  
In the present paper, internal discharge process (melting) in a horizontal shell and coil tube ice-on-coil type ice storage system was investigated numerically. Six models were considered by numerical simulations to study the influences of three different geometrical parameters regarding the coil including the coil pitch, its diameter, and height on the melting process. Also, the operational parameters of the HTF flow (inlet temperature and mass flowrate) were analyzed. The flow solver based on the enthalpy-porosity method has been first carefully validated against two sets of experimental data including the heat transfer process in a shell and coil tube heat exchanger, and the ice melting process in a double tube heat exchanger.  
Overall results indicate that increasing the HTF inlet temperature leads to a reduction of the melting time in the range of 23-33%; while, by increasing the mass flowrate, the melting time decreases very slightly by about 2%. This can be generalized to any combinations of the operational and geometrical parameters considered here. Regarding the influence of the geometrical parameters, after 280 min, by increasing the coil pitch from 0.04 to 0.12 m (by 200%), the melting rate decreases by 4.7%. In the same way, keeping all the other parameters constant, by increasing the coil diameter from 0.016 to 0.022 m (37.5%), the melting rate decreases by 31.0% after 266.7 min. The coil height has an opposite effect on the melting rate so that by increasing it from 0.24 to 0.42 m (75%), at \(t=160\) min, the melting rate is increased only by 1.32%. Generally, the coil diameter exhibits the most significant effect on the melting rate among the other parameters.  
It is worth mentioning that more numerical studies are necessary to extend the flow solver to model the condensation and the frost formation in air/air counter flow plate heat exchangers. In Nordic climates, the ice formation at the exhaust of such heat exchangers may drastically reduce the air flow and some strategies to reduce it need to be indeed developed.  
[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].  
This research received no external funding.  
[PERSON] would like to thank the support of the NSERC chair on industrial energy efficiency established in 2014 at Universite de Sherbrooke and founded by NSERC, Hydro-Quebec, Natural Resources Canada (CammetEnergy) and Rio Tinto Alcan. The authors also would like to appreciate the faculty members of Mechanical Engineering Department of Babol Noshirvani University of Technology in Iran for their helpful assistances.  
The authors declare no conflict of interest.  
\begin{tabular}{l l}
**A** & mushy zone constant (kg x m\({}^{3}\) x s) \\
**C\({}_{\text{P}}\)** & specific heat (\(\text{J}\) x kg\({}^{-1}\) x K\({}^{-1}\)) \\
**g** & gravitational acceleration (m x s\({}^{-2}\)) \\
**H** & enthalpy (\(\text{J}\) x kg\({}^{-1}\)) \\
**k** & thermal conductivity (W x m\({}^{-1}\) x K\({}^{-1}\)) \\
**L** & latent heat fusion (\(\text{J}\) x kg\({}^{-1}\)) \\
**T** & temperature (K) \\
**u** & velocity (m x s\({}^{-1}\)) \\
**Nu** & Nusselt number, Nu = hd/K \\
**De** & Dean number, De = Re \(\sqrt{\text{d}/\text{D}_{\text{c}}}\) \\
**Re** & Reynolds number, Re = 4\(\text{\text{m}}/\text{\text{\tau}}\)d \\
**Greek symbols** \\ \(\mu\) & dynamic viscosity of the fluid (kg x m\({}^{-1}\) x s\({}^{-1}\)) \\ \(\rho\) & density (kg x m\({}^{-3}\)) \\
**v** & kinematic viscosity (m\({}^{2}\) x s\({}^{-1}\)) \\ \(\lambda\) & liquid fraction (-) \\ \end{tabular}