## 2 Materials and Methods
### Numerical Model and Procedure  
The horizontal mantle hot water tank, which is detailed in Figure 1 and Table 1, is modeled numerically. The numerical model was designed in accordance with the experimental system. The model and grid structure of the horizontal hot water tank are shown in Figure 2. During numerical modeling, the solid parts of the tank (tank walls, barriers) were not modeled. In order to achieve more accurate modeling of the flow and heat transfer between the inner tank and the contact surface, the analysis was conducted without incorporating the solid surfaces into the model. Only the volume of the mantle and the volume of the inner tank are modeled. ANSYS Workbench 18 software and submodules were used in numerical modeling. Grid independence was applied to make the numerical solution independent from the number of elements. In this context, 30, 20, 15, and 10 mm element dimensions were tried. On account of modeling the heat transfer and flow in the contact surface between the inner tank and the mantle more precisely, 50% lower than the normal element number was used. After the grid independence process, the size of the element was determined as 15 mm. There are approximately 3.8 million elements in the numerical models.  
\begin{table}
\begin{tabular}{l l} \hline Diameter of inner tank (D) & 400 mm \\ Tank Length (L) & 1000 mm \\ Mantle Cavity (t) & 20 mm \\ Position of input and output ports (X\({}_{1}\), X\({}_{2}\), Y\({}_{1}\), Y\({}_{2}\)) & 50 mm \\ Distance from obstacle tank edge (m) & 50, 100, 150 mm \\ Angle of obstruction with horizontal axis (a) & 60\({}^{\circ}\) \\ Distance between two obstacles (l) & 100, 200 mm \\ \hline \end{tabular}
\end{table}
Table 1: The structural parameters of the horizontal hot water tank.  
Figure 1: Schematic of the horizontal mantled hot water tank.  
FLUENT 18 software was used for numerical analysis. The analyzes were performed in a three-dimensional and time-dependent manner for a period of 120 min. The impact on the results of the time step is very important in time-dependent analysis. Thus, 0.25, 0.5, 1, 1.5 s time steps were tried, and the results were independent of time step. In view of the fact that the time steps that are less than 0.5 s do not change the results much, the time step is assumed to be 0.5 s. The mantle and mains inputs are \"velocity inlet\" and the outputs are set to \"pressure outlet\". The outer surfaces of the tank are considered adiabatic. Different turbulence models have been tried to solve turbulence effects. The best solution among these models is the standard k-w turbulence model. SIMPLE algorithm was used during the analysis. Figure 2 shows the numerical model and grid structure for the horizontal tank. Water was used for working fluid. The velocity inlet boundary conditions were applied to the mantle entrance and the main entrance. The mantle outlet and main outlet ports were defined as pressure outlets. Studied inlet and boundary conditions are given in Table 2.  
\begin{table}
\begin{tabular}{c c c c c c} \hline  & \(\mathbf{V_{mantle}}\) m/s & \(\mathbf{T_{mantle}}\) (K) & \(\mathbf{V_{main}}\) m/s & \(\mathbf{T_{main}}\) (K) & **Model** \\ \hline Case 1 & 0.147 & 353 & 0.036 & 290 & a.60- \\ \hline Case 2 & 0.147 & 353 & 0.073 & 290 & m.50- \\ \hline Case 3 & 0.147 & 353 & 0.11 & 290 & 1.100 P \\ \hline Case 4 & 0.147 & 353 & 0.147 & 290 & \\ \hline Case 5 & 0.147 & 353 & 0.036 & 290 & \\ \hline Case 6 & 0.147 & 353 & 0.073 & 290 & m.50- \\ \hline Case 7 & 0.147 & 353 & 0.11 & 290 & 1.200 P \\ \hline Case 8 & 0.147 & 353 & 0.147 & 290 & \\ \hline Case 9 & 0.147 & 353 & 0.036 & 290 & \\ \hline Case 10 & 0.147 & 353 & 0.073 & 290 & m.100- \\ \hline Case 11 & 0.147 & 353 & 0.11 & 290 & 1.100 P \\ \hline Case 12 & 0.147 & 353 & 0.147 & 290 & \\ \hline \end{tabular}
\end{table}
Table 2: Boundary conditions of numerical model of horizontal hot water tank.  
Figure 2: (**a**) The model of a horizontal hot water tank for a = 60\({}^{\circ}\) and m = 50 mm, 1 = 200 mm, (b) Grid structure of a horizontal hot water tank.