## 4 Results and Discussion
### Validation Study
#### 4.1.1 Validation of the Heat Transfer Process in a Shell and Coil Tube Heat Exchanger  
In order to model the melting process in the shell and coil tube PCM storage, the heat transfer process in a shell and coil tube heat exchanger should be modeled and validated first. The experimental results of [PERSON] et al. [27] are then used for comparison purpose with the predictions of the present flow solver. The computational domain and geometrical parameters are illustrated in Figure 2a. The hot and cold fluids flow in the tube and shell, respectively. The working fluid for both channels is water. Both flows are considered as steady-state and both fluids are assumed to be incompressible and in a single-phase. A tetrahedral unstructured mesh grid is applied for the simulation. To account for the larger temperature gradients, close to the coil wall, 10 prismatic layers are used near the coil for both sides (tube and shell) as shown in Figure 2b. The operational and geometrical parameters are listed in Table 1. The inlet temperatures of the hot and cold fluids are 50 and 20 \({}^{\circ}\)C, respectively. The coil tube is inserted at the center of the shell. For the boundary conditions, a mass flowrate is imposed at both inlets (coil tube and shell), whereas a pressure outlet condition is imposed at both outlets. The outer wall of the shell is adiabatic. The governing equations are computed initially from the coil tube inlet. Figure 3 displays the variations of the averaged Nusselt number within the inner side coil tube (hot side) with the Dean number based on the inner coil tube characteristics. Four different Dean numbers including 700, 1400, 2100, and 2800 are considered. As it can be clearly seen, the present results compare fairly well with the measurements of [PERSON] et al. [27] with a maximum difference of 4.8% at Dei = 700 and an averaged error of 2.5% over the whole range of Dean number considered here. \begin{table}
\begin{tabular}{c c c} \hline
**Parameter** & **Notation** & **Value** \\ \hline Helix Diameter & D\({}_{\text{C}}\) & 81.3 mm \\ Coil Diameter & d\({}_{\text{C}}\) & 9 mm \\ Coil Pitch & P\({}_{\text{C}}\) & 15 mm \\ Shell Length & L\({}_{\text{SH}}\) & 250 mm \\ Shell Diameter & D\({}_{\text{SH}}\) & 140 mm \\ Hot Flow Inlet Temperature & T\({}_{\text{Hot-Inlet}}\) & 50 \({}^{\circ}\)C \\ Cold Flow Inlet Temperature & T\({}_{\text{Cold-Inlet}}\) & 20 \({}^{\circ}\)C \\ Cold Flow Inlet Velocity (Shell) & V\({}_{\text{Cold-Inlet}}\) & 0.008 m/s \\ Hot Flow Inlet Velocity (Tube) & V\({}_{\text{Hot-Inlet}}\) & 0.08, 0.165, 0.248 and 0.331 m/s \\ \hline \end{tabular}
\end{table} 
Table 1: Operational and geometrical parameters for the validation case of [PERSON] et al. [27]. 1.2 Validation and Mesh Independent Study of the Ice Melting Process in a Double Tube Heat Exchanger  
The experimental study of [PERSON] et al. [7] is used for this second validation of the flow solver. Ethylene glycol flows within the inner tube while the shell is full of ice. The length of the tank,  
Figure 3: Comparison in terms of the averaged Nusselt number versus the Dean number between the present study and the experimental data of [PERSON] et al. [27]. Figure 2: (**a**) Computational domain with inlet and outlet positions of the hot and cold flows; (**b**) Computational domain with the relevant geometrical parameters of the shell and coil tube heat exchanger; (**c**) corresponding mesh grid. tube diameter, and shell diameter are 400, 15, and 180 mm, respectively (Figure 4). Because of the temperature difference between the tube and the tank at the initial conditions, heat transfers from the HTF wall (tube wall) to ice by both convection and conduction. Radiation heat transfer is neglected. The outer walls of all investigated models are well insulated. The inlet mass flowrate and temperature of ethylene glycol are fixed to 2 L/min and 5 \({}^{\circ}\)C, respectively. A quadrilateral structured mesh grid with 52,800 cells and a minimum orthogonal quality equal to 0.94 is applied for the simulation.