# Dynamic and Static Investigation of Ground Heat Exchangers Equipped with Internal and External Fins
## 5 Results and Discussions
### Fluid Velocity Effects with Sinusoidal Inlet Temperature  
A comparison of the fluid outlet temperature at different velocities with the Reynolds of 1200, 1800, 2300 for simple and finned U-tubes is illustrated in Figure 8 and the outlet values are listed in Table 8. For all cases, the laminar flow condition is considered. The inlet temperature is considered the same as the previous section with a period of 80 min.  
In Table 8, as the inlet velocity increases, the mean and amplitude values of the fluid outlet temperature increase for the cooling purpose; increasing the velocity reduces the difference between the inlet and outlet temperatures of the fluid (\(dT\)). By increasing the velocity, the heat transfer rate between the pipe and the surrounding soil increases, but the fluid temperature change decreases. At low velocities, the fluid remains longer in the pipe, which increases the temperature change of the fluid [34].  
Figure 8: \(Cont\).  
Figure 8: _Cont._  
According to Figure 8, as the velocity of flow decreases, the phase shift of the fluid outlet temperature increases which means a delay in the thermal response of the BHE. Output temperature time shift for the simple U-tube for the first velocity (v = 0.07 m/s) is 960 s, for the second velocity (v = 0.053 m/s) is 1200 s and for the third velocity (v = 0.035 m/s) is 1680 s. These values for the externally finned pipe are 1020 s, 1200 s and 1680 s and for the internally finned pipe are 1080 s, 1320 s and 1740 s, respectively.  
Figure 9 shows a comparison of borehole wall temperature for the simple and finned pipes at different velocities. According to the results obtained in the previous section, as the velocity of the fluid decreases, the difference between the inlet and outlet temperatures of the fluid increases and the average temperature of the fluid decreases in the cooling mode. As a result, by reducing the temperature difference between the fluid and the soil around the GHE, the heat transfer rate will be reduced.  
Figure 8: Fluid temperature trends under different velocities: (**a**) simple U-tube; (**b**) U-tube with outer fins; (**c**) U-tube with inner fins; (**d**) comparison of simple and finned pipes.  
\begin{table}
\begin{tabular}{c c c c c} \hline  & **Velocity** & **Amplitude of Wave** & **Mean of Wave** & _dT_ \\  & **(m/s)** & **(\({}^{\circ}\)C)** & **(\({}^{\circ}\)C)** & _dT_ \\ \hline  & 0.035 & 1.59 & 22.10 & 26.7\% \\ Simple U-tube & 0.053 & 2.62 & 23.54 & 19\% \\  & 0.070 & 3.24 & 24.26 & 15.4\% \\ \hline  & 0.035 & 1.40 & 21.98 & 27.4\% \\ U-tube with outer fins & 0.053 & 2.40 & 23.41 & 19.6\% \\  & 0.070 & 3.00 & 24.14 & 16\% \\ \hline  & 0.035 & 1.12 & 21.57 & 29.8\% \\ U-tube with inner fins & 0.053 & 2.06 & 23.03 & 21.5\% \\  & 0.070 & 2.68 & 23.81 & 17.6\% \\ \hline \end{tabular}
\end{table}
Table 8: Output wave parameters with a frequency of 1/4800 Hz at different velocities.  
Table 9 shows borehole temperature trends under different velocities. The fourth column shows the borehole wall temperature changes in three modes of pipes (\(dT_{Bore}\)). The problem that should be considered in the comparison between simple and internally finned pipes, with the same fluid velocities, is the reduction in mass flow rate in the finned pipe due to the reduction in the cross-section. By comparing three numerical models, the increase in borehole wall temperature for the pipe with outer fins is more than two other pipes in applied velocities. This temperature change for the simple U-tube for the velocity of 0.035 m/s is more than that of the internally finned U-tube, but by increasing the fluid velocity, the bore wall temperature change for the finned pipe is more than the smooth one with the velocity of 0.07 m/s.  
Figure 9: \(Cont.\)