## 3 Data Processing and Uncertainty Analysis
### Uncertainty Analysis  
In order to describe and quantify uncertainties in the experimental data obtained across multiple tests, uncertainty analysis is conducted. Measurement uncertainties can arise from a range of factors, including experimental conditions, measurement procedures, instrument types, data reading, and connection points of the gauge probes. Typically, the result \(R\) is expressed as a function of independent variables \(x_{1}\), \(x_{2}\),.., \(x_{n}\). The uncertainty in the outcome, \(W_{R}\), is a combination of the uncertainties in each independent variable, denoted by \(w_{1}\),\(w_{2}\),..,\(w_{n}\).  
The total uncertainty in the calculated quantity can therefore be estimated using the general partial derivative method expressed as follows [55]:  
\[\begin{split} W_{R}=\left[\left(\ \frac{\partial R}{\partial x_{1}}w_{1} \right)^{2}+\ \left(\frac{\partial R}{\partial x_{2}}w_{2}\ \right)^{2}+\ldots+\ \left(\frac{\partial R}{\partial x_{n}}w_{n}\right)^{2} \right]^{1/2}\end{split} \tag{24}\]  
In the present study, all fluid temperatures in the experimental setup were measured using K-type thermocouples with an accuracy of \(\pm 0.5\)\({}^{\circ}\)C. Data were collected via a datalogger with a reading accuracy of \(\pm 0.20\)\({}^{\circ}\)C. To ensure steady-state conditions, all temperature measurements were repeated three times, and the average values were recorded to minimize random errors and enhance the reliability of the data. The standard deviations were calculated using the sample-based formula, which estimates variability by computing the square root of the variance divided by n \(-\) 1, where n is the number of replicate measurements. The total uncertainty in the temperature measurement \(W_{T}\) may stem from various sources of error, including the accuracy of the thermocouples (\(w_{thermocouple\ accuracy}\)), the connections of each thermocouple (\(w_{thermocouple\ attachment}\)), and the data reading from the measurement equipment (\(w_{reading}\)). The combined uncertainty in temperature measurements \(W_{T}\) is calculated as \(\pm 1.27\)\({}^{\circ}\)C. The air flow rates were calculated using the air velocity, air density, and duct cross-sectional area. The air velocity was measured using an anemometer with a sensitivity of \(\pm 0.01\) m\(\cdot\)s\({}^{-1}\), while the duct dimensions were measured with a tape measure with \(\pm 0.001\) m precision. Additionally, the location of the anemometer within the duct introduced further uncertainty due to spatial variability in velocity distribution, estimated at \(\pm 0.5\%\). As a result, the combined uncertainty in mass flow rate measurement was computed as \(\pm 0.5\%\).  
While the system was insulated to minimize thermal losses using vacuum layers and operated under steady-state conditions, slight efficiency deviations may still occur due to unavoidable heat dissipation. These were not directly quantified; however, the uniformity of test conditions across all experiments ensures that the comparative analysis between different fluids remains valid. The calculated values confirm that the uncertainties in both the temperature and mass flow rate measurements remain within acceptable limits, ensuring the reliability and accuracy of the experimental results presented in this study.