## 2 Materials and Methods
### Uncertainty Propagation Analysis  
Uncertainty analysis is necessary to prove the accuracy of the experiments. In the present work, the errors and uncertainties arose from the instrument selection, instrument condition, instrument calibration, ambient conditions, observation and reading, and test planning. The uncertainly analysis method described by [PERSON] (1975) was adopted to calculate the uncertainties of the measured parameters (\(T_{0}\), \(RH_{0}\), \(T_{fg,in}\), \(T_{fg,out}\), \(T_{tube}\), \(v_{fg}\), \(v_{air}\)) and \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Day**} & \multicolumn{4}{c}{**Experimental Data**} & \multicolumn{4}{c}{**Key Parameters**} \\ \cline{2-13}  & \(\mathbf{t}\) & \(\mathbf{T_{0}}\) & \(RH_{0}\) & \(T_{fg,in}\) & \(T_{fg,out}\) & \(T_{tube}\) & \(v_{fg}\) & \(v_{air}\) & \multicolumn{2}{c}{**Pr**} & \multicolumn{2}{c}{\(\mathbf{u\times 10^{-5}}\) (kg\(\cdot\)m\({}^{-1}\cdot\)s\({}^{-1}\))**} \\ \cline{2-13}  & **(min)** & **(\({}^{\circ}\)C)** & **(\({}^{\circ}\)C)** & **(\({}^{\circ}\)C)** & **(\({}^{\circ}\)C)** & **(\({}^{\circ}\)C)** & **(\({}^{\circ}\)C)** & **(m\(\cdot\)s\({}^{-1}\))** & **(m\(\cdot\)s\({}^{-1}\))** & **Pr\({}_{fg}\)** & \(\mathbf{Pr}_{air}\)** & \(\mathbf{u_{fg}}\) & \(\mathbf{u_{air}}\) \\ \hline \multirow{4}{*}{19 th October} & 10 & 7.84 & 78.9 & 859.9 & 108.2 & 125.6 & 3.12 & 4.98 & 0.631 & 0.706 & 3.431 & 0.558 \\  & 35 & 7.92 & 79.2 & 901.2 & 109.4 & 122.3 & 3.06 & 5.12 & 0.629 & 0.713 & 3.496 & 0.416 \\  & 75 & 8.12 & 80.8 & 883.5 & 108.7 & 121.6 & 3.22 & 4.88 & 0.631 & 0.724 & 3.468 & 0.532 \\  & 130 & 8.18 & 81.4 & 921.1 & 111.5 & 119.6 & 3.13 & 5.05 & 0.628 & 0.728 & 3.531 & 0.582 \\  & Average & **8.06** & **80.2** & **905.6** & **104.3** & **123.2** & **3.05** & **5.11** & **0.629** & **0.722** & **3.495** & **0.414** \\ \hline \multirow{4}{*}{21 th October} & 5 & 7.62 & 82.6 & 941.1 & 102.5 & 125.6 & 3.21 & 4.88 & 0.627 & 0.747 & 3.548 & 0.312 \\  & 35 & 7.82 & 86.5 & 902.5 & 104.3 & 127.6 & 3.12 & 4.96 & 0.629 & 0.781 & 3.491 & 0.318 \\  & 90 & 7.94 & 84.6 & 870.3 & 101.4 & 119.6 & 3.06 & 5.12 & 0.631 & 0.763 & 3.436 & 0.362 \\  & 145 & 8.26 & 87.2 & 847.1 & 107.4 & 127.2 & 3.02 & 5.03 & 0.632 & 0.786 & 3.409 & 0.408 \\  & Average & **8.02** & **85.3** & **898.6** & **101.2** & **126.3** & **3.08** & **5.02** & **0.630** & **0.768** & **3.480** & **0.419** \\ \hline \multirow{4}{*}{23 th October} & 15 & 7.82 & 88.6 & 893.6 & 100.6 & 128.6 & 2.96 & 5.11 & 0.630 & 0.794 & 3.471 & 0.535 \\  & 85 & 7.93 & 89.3 & 866.3 & 98.6 & 122.6 & 3.93 & 5.03 & 0.631 & 0.799 & 3.426 & 0.573 \\ \cline{1-1}  & 105 & 8.03 & 90.6 & 922.8 & 101.2 & 124.1 & 3.06 & 4.98 & 0.628 & 0.811 & 3.517 & 0.555 \\ \cline{1-1}  & 150 & 8.22 & 92.1 & 913.5 & 98.6 & 123.5 & 3.08 & 5.03 & 0.629 & 0.831 & 3.499 & 0.354 \\ \cline{1-1}  & Average & **8.05** & **89.6** & **900.8** & **98.6** & **125.3** & **3.12** & **5.06** & **0.630** & **0.810** & **3.479** & **0.305** \\ \hline \multirow{4}{*}{24 th October} & 0–50 & 7.82 & 89.2 & 907 & 101.9 & 125.3 & **3.06** & 5.21 & 0.629 & 0.804 & 3.494 & 0.362 \\  & 50–100 & 8.03 & 89.8 & 905.5 & 100.8 & 118.6 & **5.12** & 5.11 & 0.629 & 0.808 & 3.490 & 0.414 \\ \cline{1-1}  & 100–150 & 8.10 & 91.2 & 882.8 & 109.3 & 116.5 & **6.95** & 5.16 & 0.630 & 0.819 & 3.468 & 0.485 \\ \cline{1-1}  & Average & **8.08** & **90.5** & **908.3** & **100.9** & **118.3** & - & **5.16** & **0.629** & **0.812** & **3.494** & **0.501** \\ \hline \hline \end{tabular} Note: The bold numbers are the average values which were used for the calculation.  
\end{table} 
Table 2: Experimental design.