## 2 Experimental
### Experimental Setup
#### 2.2.2 Data Reduction and Uncertainty Analysis  
To measure the mass concentration of the nanofluid, Equation (1) was employed:  
\[wt.\%\ =\ \frac{w_{np}}{w_{bf}} \tag{1}\]  
Figure 10: Schematic diagram of the test facility used in the present study, **(a)** the structure of the evacuated tube utilized in the solar collector, **(b)** the test rig [40]. Figure is reprinted with permission from publisher.  
Here, \(w_{np}\) and \(w_{bf}\) stand for the weight of carbon particles and pure acetone, respectively. In addition, the filling ratio is the volumetric ratio of a nanofluid to the total volume of the HP as follows:  
\[\textit{iilling ratio}(\%)\ =\ \frac{\textit{vol. of NF}}{\textit{vol. of HP}} \tag{2}\]  
To measure the cumulative thermal energy absorbed by the collector, at each hour the thermal energy absorbed by the collector was measured and the following correlation was used to obtain the daily cumulative thermal energy absorbed by the collector:  
\[Q_{cum.}\ =\ \int_{t\ =\ 1\ \textit{hr}}^{t\ =\ 24\ \textit{hr}}Q_{col.}dt \tag{3}\]  
and  
\[Q_{col.}\ =\ \dot{m}\times C_{p}\times(T_{ET,out}-T_{ET,in}) \tag{4}\]  
Here, \(C_{p}\) is the fluid's heat capacity, \(ET\), \(in\) and \(ET\), \(out\), stand for the inlet and outlet temperatures of the collector. In addition, \(\dot{m}\) is the mass flow rate of the fluid introducing to the collector which can be calculated with Equation (5):  
\[\dot{m}\ =\ \rho\times\dot{Q} \tag{5}\]  
Here, \(\rho\) is the density and \(\dot{Q}\) is the volumetric flow rate of fluid, which can be acquired from the ultrasonic flow meter. Thus, the thermal efficiency of the collector can be obtained with the following equation:  
\[\eta\ =\ \frac{\dot{m}\times C_{p}\times(T_{ET,out}-T_{ET,in})}{G\times A_{c}} \tag{6}\]  
Here, G stands for the solar irradiance and \(A_{c}\) is the area of the collector. To compute the overall value of the uncertainty of the experiments, the Moffat method was employed [41] using the values given in Table 1. According to the uncertainty values of the instruments utilized in the research, the uncertainty for the efficiency measurements is deviation within \(\pm 3.5\%\) of the results. Table 2 also shows the geometrical specification of the evacuated tube solar collector.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Instrument** & **Uncertainty** \\ \hline \(G\) & Pyranometer, EKO & \(\pm 1\%\) of reading value (W/m\({}^{2}\)) \\ Temperature & Omega k type thermocouple & \(\pm 1\) (\({}^{\circ}\)C) \\ Ambient temperature & RTD, PT-100 Omega & \(\pm 0.5\) (\({}^{\circ}\)C) \\ Flow rate & FLownetiv ultrasonic sensor & 1\% of reading value (L/min) \\ Tilt angle & EuropacTM Inclinometer & \(\pm 0.1\) (degree) \\ Weight & A\&D balancer & \(\pm 1\%\) of reading value (g) \\ \hline \hline \end{tabular} The accuracy and uncertainty value for the apparatuses used in this work.  
\end{table}
Table 1: The accuracy and uncertainty value for the apparatuses used in this work.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Tube’s gross area & 1.75 m\({}^{2}\) \\ Tube’s aperture area & 0.77 m\({}^{2}\) \\ Total liquid capacity of the tube & 0.4 lit \\ Absorbance & 0.91 \\ Emission parameter & 0.04 \\ Collector’s dimension (L \(\times\) H \(\times\) W) & \(2\times 0.15\times 0.9\) m \\ \hline \hline \end{tabular}
\end{table}
Table 2: Geometrical details of the evacuated tube and the collector used in the present research.