# The Influence of Water on the Heat Loss of Hot Mix Asphalt
## 4 Laboratory Verification of the Value of \(A\) Constant  
Due to the complicated nature of the processes on the surface of the HMA layer cooled down with small amounts of water, the authors assumed that the heat transfer coefficient \(\alpha\) derived from the (6) and (7) formulae needs to incorporate the main types of heat transfer. The authors chose convectional heat transfer with air and water and radiation heat transfer. The assumption required the revision of the \(A\) parameter (Table 1) which was determined in the study for constant thickness of the water layer with determined (constant) temperature. Therefore, the value of the \(\alpha\) will be the sum of heat transfer coefficient to (\(\alpha_{free},\alpha_{rad}\)) air and (\(\alpha_{free}\)) water. To determine the values of the A parameter (including mentioned forms of heat transfer) the following steps were taken:  
1. Preparation of seven HMA samples, varying with mix type, application and properties;
2. Determination of basic physical and thermal properties (density, bulk density, voids, thermal conductivity coefficient \(\lambda\), specific heat \(c\)) of the HMA samples;
3. The tests were conducted to determine the temperature changes after 1 h in a cross-section of 3 chosen HMA samples (initial assumption: Temperature of water and air 0, 5, 15 and 25 \({}^{\circ}\)C, amount of water 3 L/m\({}^{2}\)/h);
4. Calculation of the theoretical temperature in the HMA samples from the formula (1) for assumed conditions (the value of the heat transfer coefficient \(\alpha\) was calculated from (6) and (7) for the \(A\) parameter corresponding to the average temperature \(T_{m}\));
5. Determination of average deviations between the measured and theoretical temperatures for the assumed values of \(A\) parameters;
6. Correction of the \(A\) parameter values by means of iteration, based on the smallest average deviations between the measured and theoretical temperature for three time periods (0-5 min; 5-60 min; 0-60 min);
7. Verification of assumed values of the \(A\) parameter (for whole time range of 0-60 min) based on the measurements of temperature changes of the other four HMA samples;
8. Repeating the tests for determination of the temperature changes and determination of the \(A\) parameter for HMA samples cooled down with 6 L/m\({}^{2}\)/h of water;
9. Determination of the heat transfer coefficient \(\alpha\) in regards to the average water temperature (\(T_{m}\)) and layer width (\(d\)) for 3 L/m\({}^{2}\)/h and 6 L/m\({}^{2}\)/h water amount. Seven specimens were used, made of different HMA mixes. Three specimens were used for determining the value of \(A\) (based on the smallest average deviations). Two of them were made of asphalt concrete mixes: AC 16 W (W--for binder course) and AC 8 S (S--for wearing course) and one of stone mastic asphalt SMA 11. The remaining four specimens were used for verification of the adopted \(A\) values. Three of them were made of asphalt concrete mixes: AC 22 P (P--for base course), AC 11 W, AC 11 S and one of stone mastic asphalt SMA 8. The thermophysical parameters of HMA samples are shown in Table 2. The specific heat \(c\) was determined using the calorimeter, while the thermal conductivity coefficient \(\lambda\) was determined using the heat flow meter apparatus at 20 \({}^{\circ}\)C [12; 17]. The \(A\) values were calculated with the iterative method using the smallest mean deviations (\(\Psi\)) between the actual temperature (determined in laboratory) and the theoretical temperature (\(\Psi(A)\rightarrow\min\)). The deviations were calculated as follows (11):  
\[\Psi=\frac{\sum\sqrt{(T_{theor}-T_{lab})^{2}}}{n} \tag{11}\]  
where: \(T_{theor}\)--theoretical temperature obtained from the model (1) [\({}^{\circ}\)C], \(T_{lab}\)--actual temperature measured in the laboratory [\({}^{\circ}\)C], \(n\)--number of readings taken. \(A\) was the variable in these calculations. The temperature of water was taken as the average of the initial temperature of water and the temperature of the HMA surface.