# The Influence of Water on the Heat Loss of Hot Mix Asphalt
## 3 Heat Transfer to the Environment by Combined Convection and Conduction
### Heat Transfer to Water
The flow type is determined by the value of the product of the Grashof number (Gr) and Prandtl number (Pr) [12; 15; 16; 24]:  
\[\Pr=\frac{c_{p}\eta_{p}}{\lambda_{p}} \tag{8}\]  
\[\Gr=\frac{g\beta\Delta Td^{3}\gamma_{p}^{2}}{\eta_{p}^{2}} \tag{9}\]  
where: \(c_{p}\)--specific heat of fluid (water) at a constant pressure [J/(kg\(\cdot\)K), \(\eta_{p}\)--dynamic viscosity coefficient of water at a constant pressure [N\(\cdot\)s/m\({}^{2}\)], \(\lambda_{p}\)--thermal conductivity of water at a constant pressure \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multicolumn{4}{c}{**Laminar Flow**} & \multicolumn{4}{c}{**Turbulent Flow**} \\  & \multicolumn{4}{c}{**(Gr\(\cdot\)Pr = 5\(\cdot\)10\({}^{2}\) \(\div\) 2\(\cdot\)10\({}^{7}\))**} & \multicolumn{4}{c}{**(Gr\(\cdot\)Pr > 2\(\cdot\)10\({}^{7}\))**} \\ \hline Temperature, \({}^{\circ}\)C & 40 & 60 & 80 & 100 & 40 & 60 & 80 & 100 \\ Values of A & 128 & 153 & 176 & 195 & 250 & 312 & 366 & 414 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Values of A constant for water excluding the effect of radiation [12; 19]. Figure 7: Amount of heat needed to vaporize water having initial temperatures of 5, 15 and 25 \({}^{\circ}\)C and to heat up water vapor to 120 \({}^{\circ}\)C. Legend: Q1—amount of heat used to heat up water from its initial temperature to 100 \({}^{\circ}\)C, Q2—amount of heat used in the vaporization process, Q3—amount of heat used to rise the water steam temperature to 120 \({}^{\circ}\)C.  
[W/(m\(\cdot\)K)], \(g\)--acceleration of terrestrial gravity force [9.81 m/s\({}^{2}\)], \(\beta\)--volumetric coefficient of thermal expansion of fluid (water), calculated as 1/\(T_{m}\) [1/K], \(\Delta T\)--HMA surface (\(T_{m}\))/ water temperature difference [K], \(d\)--characteristic dimension of cooled HMA layer (width) [m], \(\gamma_{p}\)--water density [kg/m\({}^{3}\)],  
The properties of water are determined for the average temperature \(T_{m}\) are derived from (10):  
\[T_{m}=\frac{T_{in}+T_{med}}{2} \tag{10}\]  
where: \(T_{m}\)--the average of the initial HMA surface temperature and the initial water temperature [K]. Equations (6) and (7) were derived on the basis of experimental results with the value of \(A\) constant determined for a water film with a constant thickness and temperature. Actually, during placement of HMA both the thickness and temperature of the water film vary both for water present in the damp substrate (the bottom surface of HMA layer) and for water used for wetting steel wheels of compacting rollers (the top surface of HMA layer). Other factors affecting the value of \(A\) are the physical transformations of water during the placement of HMA (boiling and evaporation) and heat release by radiation. These processes significantly affect the heat removal from the hot surface of HMA. In response to these differences it was necessary to adjust the values of \(A\), and, as a consequence, also the value of the heat transfer coefficient \(\propto_{free}\).