# The Influence of Water on the Heat Loss of Hot Mix Asphalt
## 4 Laboratory Verification of the Value of \(A\) Constant
Figure 11: Drops of temperature in the AC 16 W specimen over time at ambient air temperature of 0 °C. Legend: 1, 2, 3, 4, 5—measurement points according to Figure 8, theor.—theoretical temperature obtained from the model, meas.—measured temperature. Figure 12: The mean absolute deviation \(\overline{\Psi}\) between the measured and theoretical temperatures for HMA specimens depending on the value of A and the ambient air temperature for 0–5 min. and 5–60 min. time spans. The greatest convergence was obtained for 11% of the nominal value of \(A\) in the first time span (0-5 min.) and for 7.5% of that value in the second time span (5-60 min.). Based on the analysis performed for the total test time the optimum value of \(A\) at the assumed amount of water should be ca. 8%. The average deviation between the measured and theoretical temperature for the assumed \(A\) parameter values in three studied samples cooled down with 3 L/m\({}^{2}\)/h of water are shown in Table 4.  
The assumptions concerning the value of \(A\) were verified by comparing the sum of differences between the theoretical and measured temperatures, based on the experimental results obtained from testing the remaining four specimens (AC 22 P, AC 11 W, AC 11 S, SMA 8). The values of \(\Psi\) (\(A\)) for the respective specimens were in the range of 6.3-7.7 \({}^{\circ}\)C, consistent with the range obtained in the quantification of this parameter for the first three specimens (Figures 12 and 13). Figure 14 presents the example experimental determinations of heat loss due to the action of water, through free convection and through radiation for the value of \(A\) of 8% (nominal values from Table 1), the average for the total test time, for a chosen specimen of asphalt concrete for wearing course designated AC 11 S.  
The extremely well correlation of the theoretical model and measured conditions is visible already at 1 cm from the HMA surface. Near (up to 5 mm) and at the surface of the layer the differences are noticeable. This is a result of the extensive outward heat transfer from the surface at the beginning of the cooling down due to boiling and evaporation processes. The reduction of the deviation between the theoretical and measured temperature was noticed with the increase of the initial temperatures of water and air. At 25 \({}^{\circ}\)C the deviations were 1.5 \({}^{\circ}\)C lower than at 0 \({}^{\circ}\)C. This results from the lower heat demand (necessary for heating water) transferred from the surface of the HMA, thus the lower temperature drops in the initial stage of cooling down. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Value of A Parameter**} & \multicolumn{3}{c}{**Value of Average Deviation \(\Psi\) between Measured and**} \\  & \multicolumn{3}{c}{**Theoretical Temperature for Specific Time Range [\({}^{\circ}\)C]**} \\ \cline{2-4}  & **0–5 [min]** & **5–60 [min]** & **0–60 [min]** \\ \hline
100 & 14.2 & 20.7 & 17.2 \\
11 & 6.0 & 8.6 & 7.6 \\
7.5 & 8.7 & 5.9 & 7.1 \\
8 & 7.7 & 6.2 & 6.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Value of average deviation \(\Psi\) between measured and theoretical temperature for the assumed A parameter and 3 L/m\({}^{2}\)/h of water. Figure 13: The mean absolute deviation \(\Psi\) between the measured and theoretical temperatures for HMA specimens depending on the value of \(A\) and ambient air temperature for the total test time. The heat loss testing was continued with increased amounts of water applied on selected specimens (400 mL water was sprayed i.e., twice as much as previously). Initially all the water sprayed on the surface evaporated without forming a fluid film. The process slowed down over time and finally ca. 1 mm thick film has formed on the specimen surface. This behavior is an evidence of the complexity of the cooling process reflecting the physical transformations of water. The first minutes show that the HMA heat is used to turn water to vapor (with participation of boiling).