## 5 Simulation Results  
The impacts of the distances between the obstacles and the distance of the first barrier from the network inlet were examined numerically in this research, which involved placing obstacles inside a horizontal jacketed hot water storage tank. The findings obtained from numerical analyses were evaluated based on the temperature distribution within the tank, mantle outlet temperature, main outlet temperature, and the ambient temperature of the water stored within the tank. The temperature of the stored water as well as the temperatures of the mantle and main outlets were estimated using a feed-forward artificial neural network (ANN) model. In Figures 15-20, the predicted values of the main and mantle storage temperatures for different obstacle distances are shown.  
Figure 16: Prediction results for a = 60\({}^{\circ}\), m = 100 mm, 1 = 100 mm (**a**) T\({}_{\rm main}\), (**b**) T\({}_{\rm mantle}\), (**c**) T\({}_{\rm storage}\).  
Figure 19: Prediction results for a = 60\({}^{\circ}\), m = 100 mm, l = 200 mm (**a**) T\({}_{\rm main}\), (**b**) T\({}_{\rm mantle}\), (**c**) T\({}_{\rm storage}\).  
Actual temperature and model a = 60\({}^{\circ}\), m = 50, l = 100 estimation results are displayed in Figure 15. The MNN technique produced the greatest results for both temperatures. As seen in Figure 16, which displays the model a = 60\({}^{\circ}\), m = 100, l = 100 output temperature estimation results. The best estimate was produced by a structure. The ANN output values for model a = 60\({}^{\circ}\), m = 150, l = 100 were shown to be consistent with the real values in Figure 17. The patterns between the actual and anticipated values for model a = 60\({}^{\circ}\), m = 50, l = 200 are shown in Figure 18. The curves produced by the real data and the MNN structure of ANN share the same form. The ANN output for model a = 60\({}^{\circ}\), m = 200, l = 200 was found to be compatible with the actual temperature measurements, as shown in Figure 19. The ANN output for model a = 60\({}^{\circ}\), m = 100, l = 200 was found to be compatible with the actual temperature measurements, as shown in Figure 19. Analyzing model a = 60\({}^{\circ}\), m = 150, l = 200, the temperature estimation findings in Figure 20 revealed that the ANN structure produced accurate estimates. Table 3 provides the ANN model's performance values. The error rate is found to be multi-level when the performance criterion values are analyzed. When it comes to temperature prediction, the quick and flexible structure of ANN has demonstrated exceptional performance.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{\(\mathbf{T_{main}}\)} & \multicolumn{2}{c}{\(\mathbf{T_{mantle}}\)} & \multicolumn{2}{c}{\(\mathbf{T_{storage}}\)} \\ \hline  & \(\mathbf{R^{2}}\) & **MSE** & \(\mathbf{R^{2}}\) & **MSE** & \(\mathbf{R^{2}}\) & **MSE** \\ \hline a = 60\({}^{\circ}\), m = 50 mm, l = 100 mm & 0.99841 & 0.0132 & 0.99869 & 0.0104 & 0.99891 & 0.0100 \\ \hline a = 60\({}^{\circ}\), m = 100 mm, l = 100 mm & 0.99856 & 0.0121 & 0.99873 & 0.0142 & 0.99844 & 0.0126 \\ \hline a = 60\({}^{\circ}\), m = 150 mm, l = 100 mm & 0.99799 & 0.0201 & 0.99766 & 0.0217 & 0.99785 & 0.0204 \\ \hline a = 60\({}^{\circ}\), m = 50 mm, l = 200 mm & 0.99886 & 0.0116 & 0.99859 & 0.0115 & 0.99896 & 0.0153 \\ \hline a = 60\({}^{\circ}\), m = 100 mm, l = 200 mm & 0.99967 & 0.0101 & 0.99977 & 0.0110 & 0.99943 & 0.0108 \\ \hline a = 60\({}^{\circ}\), m = 150 mm, l = 200 mm & 0.99563 & 0.0325 & 0.99545 & 0.0368 & 0.99541 & 0.0389 \\ \hline \hline \end{tabular}
\end{table}
Table 3: ANN model performance (R square and MSE).