# Enhancement of Convection Heat Transfer in Air Using Ultrasound
## 4 Results and Discussion  
Exemplary results of the temperature evolution of the cubic sample are presented in Figure 3 (applied US power: 0, 50, 100, 200 W). The results confirmed both the acceleration of heat transfer and US energy absorption. The enhancement of heat transfer results in an increase of the curve's slope and the energy absorption causes an increase in final sample temperature. On the base of temperature evolution curves, the final temperature \(T_{f}\) was established and then the time evolution of the logarithm of dimensionless temperature \(\vartheta\) was calculated (exemplary results are shown in Figure 4). Figure 4: The logarithm of dimensionless temperature \(\vartheta\) versus time—exemplary results for cylindrical sample, air temperature 40 \({}^{\circ}\)C, US power: (**a**) 0 W (**b**) 200 W.  
Figure 3: Temperature evolution of cubic sample. Applied US power: 0, 50, 100, 200 W. Air temperature: (**a**) 40 \({}^{\circ}\)C; (**b**) 60 \({}^{\circ}\)C.  
Next, the slopes \(a\) of all lines were established and both the heat transfer coefficient \(h\) (Equation (8)) and the ultrasound absorption \(\dot{Q}_{abs}\) (Equation (9)) were calculated. The results are presented in Tables 3 and 4. Dependencies of the heat transfer coefficient \(h\) on the applied ultrasound power are shown in Figure 5.  
The results show that, for all the samples, an enhancement of heat transfer due to ultrasound was obtained. This enhancement is a linear function of the applied ultrasound power. The heat transfer enhancement ratio \(\eta\) is defined as [30; 39]:  
\[\eta=\frac{h_{US}-h_{0}}{h_{0}}.100\% \tag{10}\]  
where \(h_{US}\) represents the heat transfer coefficient with ultrasound, while \(h_{0}\) represents the heat transfer coefficient without ultrasound. The obtained heat transfer enhancement ratios \(\eta\) are presented in Figure 6. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Applied US Power**} & \multicolumn{2}{c}{**0 W**} & \multicolumn{2}{c}{**50 W**} \\ \cline{2-5}  & \(h\) **(W/K-m2)** & \(\dot{Q}_{abs}\) **(W)** & \(h\) **(W/K-m2)** & \(\dot{Q}_{abs}\) **(W)** \\ \hline Small cylinder & 20.78 \(\pm\) 0.24 & - & 31.58 \(\pm\) 0.63 & 0.061 \(\pm\) 0.04 \\ \hline Cylinder & 17.73 \(\pm\) 0.05 & - & 22.87 \(\pm\) 0.72 & 0.039 \(\pm\) 0.011 \\ \hline Cube & 16.17 \(\pm\) 0.20 & - & 26.39 \(\pm\) 0.65 & 0.037 \(\pm\) 0.009 \\ \hline Cuboid & 10.68 \(\pm\) 0.27 & - & 11.27 \(\pm\) 0.58 & 0.16 \(\pm\) 0.03 \\ \hline \multirow{2}{*}{**Applied US Power**} & \multicolumn{2}{c}{**100 W**} & \multicolumn{2}{c}{**200 W**} \\ \cline{2-5}  & \(h\) **(W/K-m2)** & \(\dot{Q}_{abs}\) **(W)** & \(h\) **(W/K-m2)** & \(\dot{Q}_{abs}\) **(W)** \\ \hline Small cylinder & 34.34 \(\pm\) 0.53 & 0.11 \(\pm\) 0.05 & 54.44 \(\pm\) 0.93 & 0.33 \(\pm\) 0.09 \\ \hline Cylinder & 34.60 \(\pm\) 0.55 & 0.05 \(\pm\) 0.01 & 54.28 \(\pm\) 0.12 & 0.78 \(\pm\) 0.17 \\ \hline Cube & 34.96 \(\pm\) 0.75 & 0.08 \(\pm\) 0.01 & 56.32 \(\pm\) 0.63 & 1.12 \(\pm\) 0.25 \\ \hline Cuboid & 14.71 \(\pm\) 0.51 & 0.23 \(\pm\) 0.03 & 17.61 \(\pm\) 0.55 & 0.92 \(\pm\) 0.04 \\ \hline \hline \end{tabular}
\end{table}