## 2 Materials, Methods and Boundary Conditions  
Parabolic trough collector systems, as demonstrated in Figure 1a, in the studied geometry, a parabolic concentrator is used, which is due to the reduction of heat loss and increase of the produced temperature. Figure 1 shows the schematic of the checked geometry, and also Table 2 displays the geometrical constants and parameters. According to the check accomplished, for turbulent flow the entry region length is five times more than the diameter of the inner tube [35]; however, some researchers are of the opinion that it has a slight impact [45; 46]. The three-dimensional numerical simulations have been done by finite volume method using commercial CFD code, ANSYS FLUENT 18.2. The geometrical parameters of the considered heat exchanger are illustrated in Figure 1c. The 30 \({}^{\circ}\)C inflow enters the tube at different velocities, namely 0.2, 0.24, 0.28 and 0.32 m\(\cdot\)s\({}^{-1}\). Velocity-inlet and pressure-outlet boundary conditions were considered at the inlet and outlet ports, respectively. A heat flux of 60,000 W\(\cdot\)m\({}^{-2}\) (is calculated by dividing the power consumption (6000 W) to the side surface area (0.10 m\({}^{2}\)) is transferred and applied to the outer part of the geometry made of an internally threaded steel layer. Moreover, the thermos-physical properties of tube material and fluid are noted in Table 3. The following situations are assumed in simulations:  
* The inlet fluid at all velocities is 30 \({}^{\circ}\)C.
* The flow is turbulent and in a steady mood.
* The heat flux applied to the surface of the outer tube is 60,000 W\(\cdot\)m\(-\)2.  
The present work includes two sections. In the first part, three geometries with various schematics of the inner helical axial fins are considered and investigated, and the obtained results are compared with the simple collector without any insert (fins). The schematics of the evaluated geometries in the first section of present work are illustrated in Figure 2. In the second section, the selected model according to the first section obtained results is considered with various pitch of the inner helical axial fins (P) including 250, 500, 750 and 1000 mm which the evaluated cases are depicted in Figure 3.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{1}{c}{**Parameters**} & \multicolumn{1}{c}{**Value**} \\ \hline Diameter of inner the tube & D\({}_{1}\) & 30 mm \\ Diameter of outer the tube & D\({}_{2}\) & 60 mm \\ Length of the tube & L & 2000 mm \\ Height of the fins & H & 10 mm \\ Thickness of the fins & th & 5 mm \\ Helix pitch of the fins & P & 500 mm \\ Helical angle of the fins & \(\alpha\) & 180 \({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Physical parameters of the analyzed collector.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{1}{c}{**Fluid (Water)**} & \multicolumn{1}{c}{**Pipe (Steel)**} & \multicolumn{1}{c}{**Property**} \\ \hline
4182 & 502 & Specific Heat [J/(kg\(\cdot\)K)] \\
0.6 & 16 & Thermal Conductivity [W/(m\(\cdot\)K)] \\
998.2 & 7881.8 & Density [kg/m\({}^{3}\)] \\
0.001003 & – & Viscosity [kg/m\(\cdot\)s] \\ \hline \hline \end{tabular}
\end{table}
Table 3: The thermos–physical properties of materials [46].  
Figure 1: (**a**) A schematic of the PTC structure, (**b**) the schematic of the considered pipe and the inner helical axial fins, and (**c**) the geometrical parameters.  
Figure 2: The schematics of the evaluated geometries in the first section of present work.